View source for Roman numerals

{{Short description|Numbers in the Roman numeral system}}
{{For|the Latin names of numbers|Latin numerals}}
{{Pp-semi-indef}}
{{Contains special characters}}
{{Use dmy dates|date=October 2019}}
[[File:Year 1575 in Arabic and Roman numbers.jpg|thumb|Year 1575 in Arabic and Roman numbers]]
{{Numeral systems|expand=Sign-value notation}}

'''Roman numerals''' are a [[numeral system]] that originated in [[ancient Rome]] and remained the usual way of writing numbers throughout Europe well into the [[Late Middle Ages]]. Numbers are written with combinations of letters from the [[Latin alphabet]], each with a fixed integer value. The modern style uses only these seven:
{| class="wikitable nounderlines" style="margin-left: 3em; text-align: center"
|-
| {{rn|[[I]]}}
| {{rn|[[V]]}}
| {{rn|[[X]]}}
| {{rn|[[L]]}}
| {{rn|[[C]]}}
| {{rn|[[D]]}}
| {{rn|[[M]]}}
|-
| 1
| 5
| 10
| 50
| 100
| 500
| 1000
|}

The use of Roman numerals continued long after the [[Fall of the Western Roman Empire|decline of the Roman Empire]]. From the 14th century on, Roman numerals began to be replaced by [[Arabic numerals]]; however, this process was gradual, and the use of Roman numerals persisted in various places, including on [[clock face|clock faces]]. For instance, on the clock of [[Big Ben]] (designed in 1852), the hours from 1 to 12 are written as:

{{block indent|1={{rn|'''I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII'''}}}}

The notations {{rn|IV}} and {{rn|IX}} can be read as "one less than five" (4) and "one less than ten" (9), although there is a tradition favouring the representation of "4" as "{{rn|IIII}}" on Roman numeral clocks.<ref>{{Cite news |last=Judkins |first=Maura |date=4 November 2011 |title=Public clocks do a number on Roman numerals |newspaper=The Washington Post |url=https://www.washingtonpost.com/blogs/arts-post/post/public-clocks-do-a-number-on-roman-numerals/2011/11/04/gIQAenKllM_blog.html |url-status=dead |access-date=13 August 2019 |archive-url=https://web.archive.org/web/20201115002205/https://www.washingtonpost.com/blogs/arts-post/post/public-clocks-do-a-number-on-roman-numerals/2011/11/04/gIQAenKllM_blog.html |archive-date=15 November 2020 |quote=Most clocks using Roman numerals traditionally use IIII instead of IV... One of the rare prominent clocks that uses the IV instead of IIII is Big Ben in London.}}</ref>

Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of films and television programmes. {{rn|MCM}}, signifying "a thousand, and a hundred less than another thousand", means 1900, so 1912 is written {{rn|MCMXII}}. For the years of the current (21st) century, {{rn|MM}} indicates 2000; this year is {{rn|{{#time:xrY}}}} ({{CURRENTYEAR}}).

==Description==
[[File:CuttySarkRomNum.jpg|thumb|upright=1.2|Roman numerals on stern of the ship {{ship||Cutty Sark}} showing [[draft (hull)|draught]] in [[foot (unit)|feet]]. The numbers range from 13 to 22, from bottom to top.]]
Roman numerals use different symbols for each power of ten, and there is no zero symbol, in contrast with the [[place value notation]] of Arabic numerals (in which place-keeping zeros enable the same digit to represent different powers of ten).

This allows some flexibility in notation, and there has never been an official or universally accepted standard for Roman numerals. Usage varied greatly in ancient Rome and became thoroughly chaotic in medieval times. The more recent restoration of a largely "classical" notation has gained popularity among some, while variant forms are used by some modern writers as seeking more "flexibility".<ref name="adams">{{Cite web |last=Adams |first=Cecil |date=23 February 1990 |title=What is the proper way to style Roman numerals for the 1990s? |url=http://www.straightdope.com/columns/read/1371/what-is-the-proper-way-to-style-roman-numerals-for-the-1990s |website=[[The Straight Dope]]}}</ref> Roman numerals may be considered legally binding expressions of a number, as in U.S. copyright law before the [[Berne Convention Implementation Act of 1988]] (where an "incorrect" or ambiguous numeral in a [[copyright notice]] could invalidate a copyright claim or affect the termination date of the copyright period).<ref name="Hayes">{{Cite web |last=Hayes |first=David P. |title=Guide to Roman Numerals |url=https://chart.copyrightdata.com/ch02.html#Roman |website=Copyright Registration and Renewal Information Chart and Web Site}}</ref>

===Standard form===
The following table displays how Roman numerals are usually written in modern times:<ref>{{Cite book |last1=Reddy |first1=Indra K. |url=https://books.google.com/books?id=U3QY7gz0C2cC |title=Essential Math and Calculations for Pharmacy Technicians |last2=Khan |first2=Mansoor A. |date=2003 |publisher=CRC Press |isbn=978-0-203-49534-6 |page=3 |chapter=1 (Working with Arabic and Roman numerals) |quote="Table 1-1 Roman and Arabic numerals (table very similar to the table here, apart from inclusion of Vinculum notation."}}</ref><br>
{| class="wikitable"
|+ Individual decimal places
|-
!   !! Thousands  !! Hundreds    !! Tens        !! Units
|-
| 1 || {{rn|M}}   || {{rn|C}}    || {{rn|X}}    || {{rn|I}}
|-
| 2 || {{rn|MM}}  || {{rn|CC}}   || {{rn|XX}}   || {{rn|II}}
|-
| 3 || {{rn|MMM}} || {{rn|CCC}}  || {{rn|XXX}}  || {{rn|III}}
|-
| 4 ||            || {{rn|CD}}   || {{rn|XL}}   || {{rn|IV}}
|-
| 5 ||            || {{rn|D}}    || {{rn|L}}    || {{rn|V}}
|-
| 6 ||            || {{rn|DC}}   || {{rn|LX}}   || {{rn|VI}}
|-
| 7 ||            || {{rn|DCC}}  || {{rn|LXX}}  || {{rn|VII}}
|-
| 8 ||            || {{rn|DCCC}} || {{rn|LXXX}} || {{rn|VIII}}
|-
| 9 ||            || {{rn|CM}}   || {{rn|XC}}   || {{rn|IX}}
|}

{{anchor|Subtractive notation<!--[[Sign-value notation]] links to this anchor; please update that article if this anchor is changed or deleted.-->}} The numerals for 4 ({{rn|IV}}) and 9 ({{rn|IX}}) are written using [[subtractive notation]],<ref name="deha1997">{{Cite book |last=Dehaene |first=Stanislas |title=The Number Sense : How the Mind Creates Mathematics |date=1997 |publisher=Oxford University Press |isbn=9780199723096}} 288 pages.</ref> where the smaller symbol ({{rn|I}}) is ''subtracted'' from the larger one ({{rn|V}}, or {{rn|X}}), thus avoiding the clumsier {{rn|IIII}} and {{rn|VIIII}}.{{efn|Without theorising about causation, it may be noted that {{rn|IV}} and {{rn|IX}} not only have fewer characters than {{rn|IIII}} and {{rn|VIIII}}, but are less likely to be confused (especially at a quick glance) with {{rn|III}} and {{rn|VIII}}.}} Subtractive notation is also used for 40 ({{rn|XL}}), 90 ({{rn|XC}}), 400 ({{rn|CD}}) and 900 ({{rn|CM}}).<ref name="ema1990">{{Cite encyclopedia |title=Numbers, Representations of |encyclopedia=Encyclopaedia of Mathematics |publisher=Springer |url=https://books.google.com/books?id=kwMdtnhtUMMC&dq=%22Roman+numerals%22+additive&pg=PA502 |date=1990 |editor-last=Hazewinkel |editor-first=Michiel |volume=6 |page=502 |isbn=9781556080050}} 546 pages.</ref> These are the only subtractive forms in standard use.

A number containing two or more decimal digits is built by appending the Roman numeral equivalent for each, from highest to lowest, as in the following examples:
* &nbsp;&numsp;&numsp;39 = {{rn|XXX}} + {{rn|IX}} = '''{{rn|XXXIX}}'''.
* &nbsp;&numsp;246 = {{rn|CC}} + {{rn|XL}} + {{rn|VI}} = '''{{rn|CCXLVI}}'''.
* &nbsp;&numsp;789 = {{rn|DCC}} + {{rn|LXXX}} + {{rn|IX}} = '''{{rn|DCCLXXXIX}}'''.
* 2,421 = {{rn|MM}} + {{rn|CD}} + {{rn|XX}} + {{rn|I}} = '''{{rn|MMCDXXI}}'''.

Any missing place (represented by a zero in the place-value equivalent) is omitted, as in Latin (and English) speech:
* &nbsp;&numsp;160 = {{rn|C}} + {{rn|LX}} = '''{{rn|CLX}}'''
* &nbsp;&numsp;207 = {{rn|CC}} + {{rn|VII}} = '''{{rn|CCVII}}'''
* 1,009 = {{rn|M}} + {{rn|IX}} = '''{{rn|MIX}}'''
* 1,066 = {{rn|M}} + {{rn|LX}} + {{rn|VI}} = '''{{rn|MLXVI}}'''<ref>{{Cite book |last1=Dela Cruz |first1=M. L. P. |url=https://books.google.com/books?id=PVK6lt2xXz4C |title=Number Smart Quest for Mastery: Teacher's Edition |last2=Torres |first2=H. D. |date=2009 |publisher=Rex Bookstore, Inc. |isbn=9789712352164}}</ref><ref name="martelli">{{Cite book |last1=Martelli |first1=Alex |url=https://archive.org/details/pythoncookbook00mart |title=Python Cookbook |last2=Ascher |first2=David |date=2002 |publisher=O'Reilly Media Inc. |isbn=978-0-596-00167-4 |url-access=registration}}</ref>

The largest number that can be represented in this manner is 3,999 ('''{{rn|MMMCMXCIX}}'''), but this is sufficient for the values for which Roman numerals are commonly used today, such as year numbers:
* 1776 = {{rn|M}} + {{rn|DCC}} + {{rn|LXX}} + {{rn|VI}} = '''{{rn|MDCCLXXVI}}''' (the date written on the book held by the [[Statue of Liberty]]).
* 1918 = {{rn|M}} + {{rn|CM}} + {{rn|X}} + {{rn|VIII}} = '''{{rn|MCMXVIII}}''' (the first year of the [[Spanish flu]] pandemic)
* 1944 = {{rn|M}} + {{rn|CM}} + {{rn|XL}} + {{rn|IV}} = '''{{rn|MCMXLIV}}''' (erroneous copyright notice of the 1954 movie ''[[The Last Time I Saw Paris#Copyright|The Last Time I Saw Paris]]'')<ref name="Hayes" />
* {{#time:Y}} = '''{{rn|{{#time:xrY}}}}''' (this year){{efn|This is the Coordinated Universal Time (UTC) year in which Wikipedia's cache of this page was last updated, so may be a few hours out of date.}}

Prior to the introduction of Arabic numerals in the West, ancient and medieval users of Roman numerals used various means to write larger numbers {{xref|(see {{slink||Large numbers}} below)}}.

===Other forms===
Forms exist that vary in one way or another from the general standard represented above.

====Other additive forms====
[[File:BadSalzdetfurthBadenburgerStr060529.jpg|thumb|upright=0.9|A [[clock face]] with the Roman numerals typical for clocks, in [[Bad Salzdetfurth]], Germany]]

While subtractive notation for 4, 40, and 400 ({{rn|IV}}, {{rn|XL}}, and {{rn|CD}}) has been the usual form since Roman times {{Citation needed|reason=From what I've seen it seems that the additive notation was by far the normal until somewhere around the 18th century, at least for 4.|date=January 2024}}, [[additive notation]] to represent these numbers ({{rn|IIII}}, {{rn|XXXX}}, and {{rn|CCCC}})<ref name="caes0050">{{Cite Wikisource |author=Gaius Iulius Caesar |title=Commentarii de bello Gallico, Book II, Section 4 |wslink=Commentarii de bello Gallico/Liber II |anchor=4 |wslanguage=la}} <br />Book II, Section 4: "{{lang|la|... XV milia Atrebates, Ambianos X milia, Morinos XXV milia, Menapios VII milia, Caletos X milia, Veliocasses et Viromanduos totidem, Atuatucos XVIIII milia; ...}}" <br />Book II, Section 8: "{{lang|la|... ab utroque latere eius collis transversam fossam obduxit circiter passuum CCCC et ad extremas fossas castella constituit...}}" <br />Book IV, Section 15: "{{lang|la|Nostri ad unum omnes incolumes, perpaucis vulneratis, ex tanti belli timore, cum hostium numerus capitum CCCCXXX milium fuisset, se in castra receperunt.}}" <br />Book VII, Section 4: "{{lang|la|...in hiberna remissis ipse se recipit die XXXX Bibracte.}}"</ref> very frequently continued to be used, including in compound numbers like 24 ({{rn|XXIIII}}),<ref name="rocc1612">{{Cite book |last=Rocca |first=Angelo |title=De campanis commentarius |date=1612 |publisher=Guillelmo Faciotti |location=Rome}} [[:File:Campana a XXIIII hominibus pulsata.jpg|Title of a Plate]]: "Campana a XXIIII hominibus pulsata" ("Bell to be sounded by 24 men").</ref><!--Can't find a good internet source for this text from Cicero: <ref name="otle1834">William Young Ottley (1834): ''Aratus astronomical poem (with Ten lines not heretofore known,) with Cicero's latin translation''. Royal Society of Antiquaries, London. 191 pages. Page 158: "De Concordia Solaris Cursus et Lunaris://Novem horis in luna pro quinque diebus in sole computatis, idem luna novem horis tantum itineris peragitur quantum sol in quinque diebus, et ideo unius signi horis iuxta lunarem velocitatem enumeratis, inveniuntur LIIII, quod sunt sexies VIIII. duobus enim ... et sic demum possunt XIIII horae lunares cum quinque diebus solaribus concordare.//Item de eadem ratione://Luna lucere dodrantis semuncias dicitur. duodecim unciae libram faciunt, XXIIII horae diem integrum; totidem enim sunt semunciae in libra plena. quas si diviseris in IV, quarta pars quadrantis nomen sortita est, reliquae III dodrantis; et ideo dixi dodrantis semuncias horarum, id est IIII punctos; "</ref>--> 74 ({{rn|LXXIIII}}),<ref name="borc1673">Gerard Ter Borch (1673): ''[[:File:Cornelis de Graeff (1650-1678).png|Portrait of Cornelis de Graef]]''. Date on painting: "Out. XXIIII Jaer. // M. DC. LXXIIII".</ref> and 490 ({{rn|CCCCLXXXX}}).<ref name=plin2015>{{Cite Wikisource |author=Gaius Plinius Secundus |title=Naturalis Historia, Book III |wslink=Naturalis Historia/Liber III |anchor=IV |wslanguage=la}} Book III: "{{lang|la|Saturni vocatur, Caesaream Mauretaniae urbem {{overline|CCLXXXXVII}} p[assum]. traiectus. reliqua in ora flumen Tader ... ortus in Cantabris haut procul oppido Iuliobrica, per {{overline|CCCCL}} p. fluens ...}}" <br />Book IV: "{{lang|la|Epiri, Achaiae, Atticae, Thessalia in porrectum longitudo CCCCLXXXX traditur, latitudo CCLXXXXVII.}}" <br />Book VI: "{{lang|la|tam vicinum Arsaniae fluere eum in regione Arrhene Claudius Caesar auctor est, ut, cum intumuere, confluant nec tamen misceantur leviorque Arsanias innatet MMMM ferme spatio, mox divisus in Euphraten mergatur.}}"</ref> The additive forms for 9, 90, and 900 ({{rn|VIIII}},<ref name=caes0050/> {{rn|LXXXX}},<ref name="benn1731">{{Cite book |last=Bennet |first=Thomas |title=Grammatica Hebræa, cum uberrima praxi in usum tironum ... Editio tertia |date=1731 |publisher=T. Astley |page=24}} Copy in the British Library; 149 pages. <br />Page 24: "{{lang|la|PRÆFIXA duo sunt}} ''viz.'' ''He'' {{lang|la|emphaticum vel relativum (de quo Cap VI Reg. LXXXX.) &}} ''Shin'' {{lang|la|cum}} ''Segal'' {{lang|la|sequente}} ''Dagesh'', {{lang|la|quod denotat pronomen relativum...}}"</ref> and {{rn|DCCCC}}<ref name="mira1486">{{Cite book |last=Della Mirandola |first=Pico |url=http://www.esotericarchives.com/pico/conclus.htm |title=Conclusiones sive Theses DCCCC |date=1486 |language=la |trans-title=Conclusions, or 900 Theses}}</ref>) have also been used, although less often.

The two conventions could be mixed in the same document or inscription, even in the same numeral. For example, on the numbered gates to the [[Colosseum]], {{rn|IIII}} is systematically used instead of {{rn|IV}}, but subtractive notation is used for {{rn|XL}}; consequently, gate 44 is labelled {{rn|XLIIII}}.<ref>{{Cite web |date=2 January 2011 |title=360:12 tables, 24 chairs, and plenty of chalk |url=https://threesixty360.wordpress.com/2011/01/01/roman-numerals-not-quite-so-simple/ |website=Roman Numerals...not quite so simple}}</ref><ref>{{Cite web |date=13 November 2021 |title=Paul Lewis |url=http://www.web40571.clarahost.co.uk/roman/howtheywork.htm |website=Roman Numerals...How they work}}</ref>

Especially on tombstones and other funerary inscriptions, 5 and 50 have been occasionally written {{rn|IIIII}} and {{rn|XXXXX}} instead of {{rn|V}} and {{rn|L}}, and there are instances such as {{rn|IIIIII}} and {{rn|XXXXXX}} rather than {{rn|VI}} or {{rn|LX}}.<ref>{{Cite encyclopedia |title=numbers, Roman |encyclopedia=[[Oxford Classical Dictionary]] |publisher=Oxford University Press |url=https://archive.org/details/isbn_9780198661726 |date=1996 |editor-last=Hornblower |editor-first=Simon |edition=3rd |isbn=0-19-866172-X |last2=Spawforth |first2=Anthony J. S. |first1=Joyce Maire |last1=Reynolds |editor2-first=Anthony |editor2-last=Spawforth |url-access=registration}}</ref><ref>{{Cite book |last=Kennedy |first=Benjamin Hall |title=The Revised Latin Primer |date=1923 |publisher=Longmans, Green & Co. |location=London}}</ref>

Modern [[clock face]]s that use Roman numerals still very often use {{rn|IIII}} for four o'clock but {{rn|IX}} for nine o'clock, a practice that goes back to very early clocks such as the [[Wells Cathedral clock]] of the late 14th century.<ref>{{Cite book |last=Milham |first=W.I. |title=Time & Timekeepers |date=1947 |publisher=Macmillan |location=New York |page=196}}</ref><ref name="pickover">{{Cite book |last=Pickover |first=Clifford A. |url={{google books|id = 52N0JJBspM0C|page = 282|plainurl = yes }} |title=Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning |date=2003 |publisher=Oxford University Press |isbn=978-0-19-534800-2 |page=282 |author-link=Clifford A. Pickover}}</ref><ref>{{Cite book |last1=Adams |first1=Cecil |url=https://archive.org/details/moreofstraightdo00adam/page/154 |title=More of the straight dope |last2=Zotti |first2=Ed |date=1988 |publisher=Ballantine Books |isbn=978-0-345-35145-6 |page=[https://archive.org/details/moreofstraightdo00adam/page/154 154]}}</ref> However, this is far from universal: for example, the clock on the [[Palace of Westminster]] tower (commonly known as [[Big Ben]]) uses a subtractive {{rn|IV}} for 4 o'clock.<ref name="pickover" />{{efn|[[Isaac Asimov]] once mentioned an "interesting theory" that Romans avoided using {{rn|IV}} because it was the initial letters of {{lang|la|IVPITER}}, the Latin spelling of [[Jupiter (mythology)|Jupiter]], and might have seemed [[Piety|impious]].<ref name="asimov on numbers 12">{{Cite book |last=Asimov |first=Isaac |url=http://www.arvindguptatoys.com/arvindgupta/asimov-on-numbers.pdf |title=Asimov on Numbers |date=1966 |publisher=Pocket Books, a division of Simon & Schuster, Inc |page=12}}</ref> He did not say whose theory it was.}}

[[File:AdmiraltyArchLondonCloseup.jpg|thumb|upright=1|The year number on [[Admiralty Arch]], London. The year 1910 is rendered as {{rn|MDCCCCX}}, rather than the more usual {{rn|MCMX}}|alt=]]

Several monumental inscriptions created in the early 20th century use variant forms for "1900" (usually written {{rn|MCM}}). These vary from {{rn|MDCCCCX}} for 1910 as seen on [[Admiralty Arch]], London, to the more unusual, if not unique {{rn|MDCDIII}} for 1903, on the north entrance to the [[Saint Louis Art Museum]].<ref>{{Cite web |title=Gallery: Museum's North Entrance (1910) |url=http://www.slam.org/century_of_free/gallery.php |url-status=dead |archive-url=https://web.archive.org/web/20101204081437/http://slam.org:80/century_of_free/gallery.php |archive-date=4 December 2010 |access-date=10 January 2014 |publisher=Saint Louis Art Museum |quote=The inscription over the North Entrance to the Museum reads: "Dedicated to Art and Free to All MDCDIII." These roman numerals translate to 1903, indicating that the engraving was part of the original building designed for the 1904 World's Fair.}}</ref>

[[File:Epitaph des Marcus Caelius.JPG|thumb|upright=0.9|left|Epitaph of [[centurion]] Marcus Caelius, showing "{{rn|XIIX}}"]]

====Other subtractive forms====
There are numerous historical examples of {{rn|IIX}} being used for 8; for example, {{rn|XIIX}} was used by officers of the [[Legio XVIII|XVIII Roman Legion]] to write their number.<ref>{{Cite book |last1=Adkins |first1=Lesley |title=Handbook to life in ancient Rome |last2=Adkins |first2=Roy A |date=2004 |isbn=0-8160-5026-0 |edition=2 |page=270|publisher=Facts On File }}</ref><ref>{{Cite book |last=Boyne |first=William |title=A manual of Roman coins |date=1968 |page=13}}</ref> The notation appears prominently on the [[cenotaph]] of their senior [[centurion]] [[Marcus Caelius]] ({{circa|45 BC|lk=no}} – 9 AD). On the publicly displayed official Roman calendars known as [[Fasti]], {{rn|XIIX}} is used for the 18 days to the next [[Calends|Kalends]], and {{rn|XXIIX}} for the 28 days in February. The latter can be seen on the sole extant pre-Julian calendar, the [[Fasti Antiates Maiores]].<ref name="Degrassi">{{Cite book |title=Inscriptiones Italiae |date=1963 |publisher=Istituto Poligrafico dello Stato |editor-last=Degrassi |editor-first=Atilius |editor-link=Attilio Degrassi |volume=13: Fasti et Elogia |location=Rome |at=Fasciculus 2: Fasti anni Numani et Iuliani}}</ref>
There are historical examples of other subtractive forms: {{rn|IIIXX}} for 17,<ref name="lvnd1621">{{Cite book |last=Lundorphio |first=Michaele Gaspar |url=https://books.google.com/books?id=C41mAAAAcAAJ&pg=PA123 |title=Acta publica inter invictissimos gloriosissimosque&c. ... et Ferdinandum II. Romanorum Imperatores... |date=1621 |publisher=Ian-Friderici Weissii |page=123 |language=la}} <br />Page 123: "{{lang|la|Sub Dato Pragæ IIIXX Decemb. A. C. M. DC. IIXX}}". <br />Page 126, end of the same document: "{{lang|la|Dabantur Pragæ 17 Decemb. M. DC. IIXX}}".</ref> {{rn|IIXX}} for 18,<ref name="sulp1692">{{Cite book |last=Sulpicius à Munscrod |first=Raphael |url=https://archive.org/details/bub_gb_N43WFqB1wtoC/page/n69 |title=Vera Ac Germana Detecto Clandestinarvm Deliberationvm |date=1621 |page=16 |language=la}} <br />Page 16, line 1: "{{lang|la|repertum Originale Subdatum IIIXXX Aug. A. C. MDC.IIXX}}". <br />Page 41, upper right corner: "{{lang|la|Decemb. A. C. MDC.IIXX}}". Page 42, upper left corner: "{{lang|la|Febr. A. C. MDC.XIX}}". Page 70: "{{lang|la|IIXX. die Maij sequentia in consilio noua ex Bohemia allata....}}". <br />Page 71: "{{lang|la|XIX. Maij}}.</ref> {{rn|IIIC}} for 97,<ref name="tent1699">{{Cite book |last=Tentzel |first=Wilhelm Ernst |url=https://books.google.com/books?id=VN9lAAAAcAAJ&pg=PA39 |title=Als Ihre Königl. Majestät in Pohlen und ... |date=1699 |page=39 |language=de}} <br />Page 39: "{{lang|de|... und der Umschrifft: LITHUANIA ASSERTA M. DC. IIIC [1699].}}"</ref> {{rn|IIC}} for 98,<ref name="posn1698">{{Cite book |last=Posner |first=Johann Caspar |url=https://books.google.com/books?id=bmtOAAAAcAAJ&pg=PP9 |title=Mvndvs ante mvndvm sive De Chao Orbis Primordio |date=1698 |language=la}} <br />Title page: "{{lang|la|Ad diem jvlii A. O. R. M DC IIC}}".</ref><ref name="tent1700">{{Cite book |last=Tentzel |first=Wilhelm Ernst |url=https://books.google.com/books?id=qFVPAAAAcAAJ&pg=PA93 |title=Saxonia Nvmismatica: Das ist: Die Historie Des Durchlauchtigsten... |date=1700 |page=26 |language=de}} <br />Page 26: "{{lang|de|Die Revers hat eine feine Inscription}}: {{lang|la|SERENISSIMO DN.DN... SENATUS.QVERNF. A. M DC IIC D. 18 OCT [year 1698 day 18 oct].}}"</ref> and {{rn|IC}} for 99.<ref name="picc1699">{{Cite book |last=Piccolomini |first=Enea Silvio |url=https://books.google.com/books?id=0RNXAAAAcAAJ&pg=PA1 |title=Opera Geographica et Historica |date=1698 |publisher=J. M. Sustermann |edition=1st |location=Helmstadt |language=la |author-link=Pope Pius II}} Title page of first edition: "{{lang|la|Bibliopolæ ibid. M DC IC}}".</ref> A possible explanation is that the word for 18 in Latin is {{lang|la|duodeviginti}}{{px2}}{{mdash}}{{tsp}}literally "two from twenty"⁠{{mdash}}{{tsp}}while 98 is {{lang|la|duodecentum}} (two from hundred) and 99 is {{lang|la|undecentum}} (one from hundred).<ref name="kenn1879">{{Cite book |last=Kennedy |first=Benjamin H. |url=https://archive.org/details/publiclatin00kennrich |title=Latin grammar |date=1879 |publisher=Longmans, Green, and Co. |isbn=9781177808293 |location=London |page=[https://archive.org/details/publiclatin00kennrich/page/150 150]}}</ref> However, the explanation does not seem to apply to {{rn|IIIXX}} and {{rn|IIIC}}, since the Latin words for 17 and 97 were {{lang|la|septendecim}} (seven ten) and {{lang|la|nonaginta septem}} (ninety seven), respectively.

The {{code|ROMAN()}} function in [[Microsoft Excel]] supports multiple subtraction modes depending on the "{{tt|Form}}" setting. For example, the number "499" (usually {{rn|CDXCIX}}) can be rendered as {{rn|LDVLIV}}, {{rn|XDIX}}, {{rn|VDIV}} or {{rn|ID}}. The relevant Microsoft help page offers no explanation for this function other than to describe its output as "more concise".<ref>{{Cite web |title=ROMAN function |url=https://support.microsoft.com/en-us/office/roman-function-d6b0b99e-de46-4704-a518-b45a0f8b56f5 |website=Microsoft Support}}</ref>

====Non-standard variants====

[[File:Padlock,_Athlone.jpg|thumb|upright=1.1|Padlock used on the north [[City gate|gate]] of the Irish town of [[Athlone]]. "1613" in the date is rendered {{rn|XVIXIII}}, (literally "16, 13") instead of {{rn|MDCXIII}}.]]
[[File:Excerpt from BnF ms. 1433 fr., fol. 24r.png|thumb|upright=1.1|Excerpt from [[Bibliothèque nationale de France]].<ref>{{Cite book |url=https://gallica.bnf.fr/ark:/12148/btv1b105096493 |via=Gallica |title=L' Atre périlleux et Yvain, le chevalier au lion . |date=1301–1350 |language=EN}}</ref> The Roman numeral for 500 is rendered as {{Rn|{{Overset|C|V}}}}, instead of {{Rn|D}}.]]
There are also historical examples of other additive and multiplicative forms, and forms which seem to reflect spoken phrases. Some of these variants may have been regarded as errors even by contemporaries.

* {{rn|IIXX}} was how people associated with the [[Legio XXII Deiotariana|XXII Roman Legion]] used to write their number. The practice may have been due to a common way to say "twenty-second" in Latin, namely {{lang|la|duo et vice(n)sima}} (literally "two and twentieth") rather than the "regular" {{lang|la|vice(n)sima secunda}} (twenty second).<ref name="malo2005">{{Cite thesis |last=Malone |first=Stephen James |title=Legio XX Valeria Victrix: A Prosographical and Historical Study |date=Aug 2005 |publisher=University of Nottingham |url=http://eprints.nottingham.ac.uk/13316/2/423645_vol2.pdf |volume=2}} <br />On page 396 it discusses many coins with "Leg. IIXX" and notes that it must be Legion 22. <br />The footnote on that page says: "The form IIXX clearly reflecting the Latin {{lang|la|duo et vicensima}} 'twenty-second': cf. X5398, {{lang|la|legatus I[eg II] I et vicensim(ae) Pri[mi]g}}; VI 1551, {{lang|la|legatus leg] IIXX Prj}}; III 14207.7, {{lang|la|miles leg IIXX}}; and III 10471-3, a vexillation drawn from four German legions including 'XVIII PR' – surely here the stonecutter's hypercorrection for IIXX PR.</ref> Apparently, at least one ancient [[stonecutter]] mistakenly thought that the {{rn|IIXX}} of "22nd Legion" stood for 18, and "corrected" it to {{rn|XVIII}}.<ref name=malo2005/>

* Other numerals that do not fit the usual patterns – such as {{rn|VXL}} for 45, instead of the usual {{rn|XLV}} — may be due to scribal errors, or the writer's lack of familiarity with the system, rather than being genuine variant usage.

====Non-numeric combinations====
As Roman numerals are composed of ordinary alphabetic characters, there may sometimes be confusion with other uses of the same letters. For example, "[[XXX (disambiguation)|XXX]]" and "[[XL (disambiguation)|XL]]" have other connotations in addition to their values as Roman numerals, while "[[IXL (disambiguation)|IXL]]" more often than not is a [[gramogram]] of "I excel", and is in any case not an unambiguous Roman numeral.<ref name="ixl-story">{{Cite web |title=Our Brand Story |url=http://spcardmona.com.au/healthy-brands/ixl/our-brand-story |access-date=2014-03-11 |publisher=SPC Ardmona}}</ref>

===Zero===
As a non-[[positional notation|positional numeral system]], Roman numerals have no "place-keeping" zeros. Furthermore, the system as used by the Romans lacked a numeral for the number [[0 (number)|zero]] itself (that is, what remains after 1 is subtracted from 1). The word {{wikt-lang|la|nulla}} (the [[Latin]] word meaning "none") was used to represent 0, although the earliest attested instances are medieval. For instance [[Dionysius Exiguus]] used {{lang|la|nulla}} alongside Roman numerals in a manuscript from 525 AD.<ref>{{Cite book |title=Bede: The Reckoning of Time |date=2004 |publisher=Liverpool University Press |isbn=0-85323-693-3 |location=Liverpool |translator-last=Wallis |translator-first=Faith |orig-date=725}}</ref><ref>{{Cite book |title=Byrhtferth's Enchiridion |date=1995 |publisher=Early English Text Society |isbn=978-0-19-722416-8 |editor-last=Baker |editor-first=Peter S. |orig-date=1016 |editor-last2=Lapidge |editor-first2=Michael}}</ref> About 725, [[Bede]] or one of his colleagues used the letter {{rn|N}}, the initial of {{lang|la|nulla}} or of {{wikt-lang|la|nihil}} (the Latin word for "nothing") for 0, in a table of [[epacts]], all written in Roman numerals.<ref name="zero">{{Cite book |title=Opera Didascalica |editor-last=Jones |editor-first=C. W. |series=Corpus Christianorum, Series Latina |volume=123C}}</ref>

The use of {{rn|N}} to indicate "none" long survived in the historic [[apothecaries' system]] of measurement: used well into the 20th century to designate quantities in pharmaceutical prescriptions.<ref name="Bachenheimer">{{Cite book |last=Bachenheimer |first=Bonnie S. |title=Manual for Pharmacy Technicians |date=2010 |isbn=978-1-58528-307-1}}</ref>

In later times, the Arabic numeral "0" has been used as a zero to open enumerations with Roman numbers. Examples include the 24-hour [[Shepherd Gate Clock]] from 1852 and [[tarot]] packs such as the 15th-century [[Sola Busca tarot|Sola Busca]] and the 20th century [[Rider-Waite Tarot|Rider–Waite]] packs.

===Fractions===
[[File:Vecchi 003.jpg|thumb|left|upright=0.7|A {{lang|la|[[triens]]}} coin ({{frac|1|3}} or {{frac|4|12}} of an {{lang|la|as}}). Note the four dots ('''····''') indicating its value.]]
[[File:Semisse.jpg|thumb|right|upright=0.9|A {{lang|la|[[semis]]}} coin ({{frac|1|2}} or {{frac|6|12}} of an {{lang|la|as}}). Note the {{rn|S}} indicating its value.]]

The base "Roman fraction" is {{rn|S}}, indicating {{frac|1|2}}. The use of {{rn|S}} (as in {{rn|VIIS}} to indicate 7{{frac|1|2}}) is attested in some ancient inscriptions<ref>{{Cite web |title=RIB 2208. Distance Slab of the Sixth Legion |url=https://romaninscriptionsofbritain.org/inscriptions/2196 |access-date=11 November 2020 |website=Roman Inscriptions in Britain}}</ref> and in the now rare apothecaries' system (usually in the form {{rn|SS}}):<ref name="Bachenheimer" /> but while Roman numerals for [[Integers|whole numbers]] are essentially [[decimal]], {{rn|S}} does not correspond to {{frac|5|10}}, as one might expect, but {{frac|6|12}}.

The Romans used a [[duodecimal]] rather than a decimal system for [[rational number|fractions]], as the [[divisibility]] of twelve {{nowrap|1= (12 = 2<sup>2</sup> × 3)}} makes it easier to handle the common [[Fraction (mathematics)|fractions]] of {{frac|1|3}} and {{frac|1|4}} than does a system based on ten {{nowrap|1= (10 = 2 × 5)}}. Notation for fractions other than {{frac|1|2}} is mainly found on surviving [[Roman coin]]s, many of which had values that were duodecimal fractions of the unit {{lang|la|[[As (coin)|as]]}}. Fractions less than {{frac|1|2}} are indicated by a dot ('''·''') for each {{lang|la|uncia}} "twelfth", the source of the English words ''inch'' and ''ounce''; dots are repeated for fractions up to five twelfths. Six twelfths (one half), is {{rn|S}} for {{lang|la|semis}} "half". ''Uncia'' dots were added to {{rn|S}} for fractions from seven to eleven twelfths, just as tallies were added to {{rn|V}} for whole numbers from six to nine.<ref>{{Cite journal |last1=Maher |first1=David W. |last2=Makowski |first2=John F. |date=2011 |title=Literary Evidence for Roman Arithmetic with Fractions |url=http://dmaher.org/Publications/romanarithmetic.pdf |journal=Classical Philology |volume=96 |issue=4 |pages=376–399 |doi=10.1086/449557 |s2cid=15162149 |archive-url=https://web.archive.org/web/20130827220707/http://dmaher.org/Publications/romanarithmetic.pdf |archive-date=27 August 2013}}</ref> The arrangement of the dots was variable and not necessarily [[Linearity|linear]]. Five dots arranged like ('''⁙''') (as on the face of a [[dice|die]]) are known as a [[quincunx]], from the name of the Roman fraction/coin. The Latin words {{lang|la|sextans}} and {{lang|la|quadrans}} are the source of the English words ''[[sextant]]'' and ''[[Quadrant (plane geometry)|quadrant]]''.

Each fraction from {{frac|1|12}} to {{frac|12|12}} had a name in Roman times; these corresponded to the names of the related coins:

{| class="wikitable"
! Fraction
! Roman numeral
! Name (nominative and genitive singular)
! Meaning
|-
| {{frac|1|12}}
| '''·'''
| {{lang|la|[[Uncia (coin)|Uncia]], unciae}}
| "Ounce"
|-
| {{frac|2|12}} = {{frac|1|6}}
| '''··''' or ''':'''
| {{lang|la|[[Sextans (coin)|Sextans]], sextantis}}
| "Sixth"
|-
| {{frac|3|12}} = {{frac|1|4}}
| '''···''' or '''∴'''
| {{lang|la|[[Quadrans]], quadrantis}}
| "Quarter"
|-
| {{frac|4|12}} = {{frac|1|3}}
| '''····''' or '''∷'''
| {{lang|la|[[Triens]], trientis}}
| "Third"
|-
| {{frac|5|12}}
| '''·····''' or '''⁙'''
| {{lang|la|[[Quincunx (Roman coin)|Quincunx]], quincuncis}}
| "Five-ounce" ({{lang|la|quinque unciae}} → {{lang|la|quincunx}})
|-
| {{frac|6|12}} = {{frac|1|2}}
| {{rn|S}}
| {{lang|la|[[Semis]], semissis}}
| "Half"
|-
| {{frac|7|12}}
| {{rn|S}}'''·'''
| {{lang|la|Septunx, septuncis}}
| "Seven-ounce" ({{lang|la|septem unciae}} → {{lang|la|septunx}})
|-
| {{frac|8|12}} = {{frac|2|3}}
| {{rn|S}}'''··''' or {{rn|S}}''':'''
| {{lang|la|[[Bes (coin)|Bes]], bessis}}
| "Twice" (as in "twice a third")
|-
| {{frac|9|12}} = {{frac|3|4}}
| {{Rn|S}}'''···''' or {{rn|S}}'''∴'''
| {{lang|la|[[Dodrans]], dodrantis}}<br />'''or''' {{lang|la|nonuncium, nonuncii}}
| "Less a quarter" ({{lang|la|de-quadrans}} → {{lang|la|dodrans}})<br />'''or''' "ninth ounce" ({{lang|la|nona uncia}} → {{lang|la|nonuncium}})
|-
| {{frac|10|12}} = {{frac|5|6}}
| {{Rn|S}}'''····''' or {{rn|S}}'''∷'''
| {{lang|la|Dextans, dextantis}}<br />'''or''' {{lang|la|decunx, decuncis}}
| "Less a sixth" ({{lang|la|de-sextans}} → {{lang|la|dextans}})<br />'''or''' "ten ounces" ({{lang|la|decem unciae}} → {{lang|la|decunx}})
|-
| {{frac|11|12}}
| {{Rn|S}}'''·····''' or {{rn|S}}'''⁙'''
| {{lang|la|Deunx, deuncis}}
| "Less an ounce" ({{lang|la|de-uncia}} → {{lang|la|deunx}})
|-
| {{frac|12|12}} = 1
| {{rn|I}}
| {{lang|la|[[As (Roman coin)|As]], assis}}
| "Unit"
|}

Other Roman fractional notations included the following:

{| class="wikitable"
! Fraction
! Roman numeral
! Name (nominative and genitive singular)
! Meaning
|-
| {{frac|1|1728}}=12<sup>−3</sup>
| {{rn|𐆕}}
| {{lang|la|[[Siliqua]], siliquae}}
| <!-- translation needed -->
|-
| {{frac|1|288}}
| {{rn|{{Roman|1/288|fraction=yes}}}}
| {{lang|la|Scripulum, scripuli}}
| "[[Apothecaries' system|scruple]]"
|-
| {{frac|1|144}}=12<sup>−2</sup>
| {{rn|<s>Ƨ</s>}}
| {{lang|la|Dimidia sextula, dimidiae sextulae}}
| "half a sextula"
|-
| {{frac|1|72}}
| {{rn|Ƨ}}
| {{lang|la|[[Sextula]], sextulae}}
| "{{frac|6}} of an uncia"
|-
| {{frac|1|48}}
| {{rn|Ↄ}}
| {{lang|la|Sicilicus, sicilici}}
| <!-- translation needed -->
|-
| {{frac|1|36}}
| {{rn|ƧƧ}}
| {{lang|la|Binae sextulae, binarum sextularum}}<br>(Exceptionally, these are plural forms.)
| "two sextulas" ({{lang|la|[[duella]], duellae}})
|-
| {{frac|1|24}}
| {{rn|Σ}} or {{rn|𐆒}} or {{rn|Є}}
| {{lang|la|[[Semuncia]], semunciae}}
| "{{frac|2}} uncia" ({{lang|la|semi-}} + {{lang|la|uncia}})
|-
| {{frac|1|8}}
| {{rn|Σ}}'''·''' or {{rn|𐆒}}'''·''' or {{rn|Є}}'''·'''
| {{lang|la|Sescuncia, sescunciae}}
| "{{frac|1|1|2}} uncias" ({{lang|la|[[Numeral prefix|sesqui]]-}} + {{lang|la|uncia}})
|}

Fractions could also be indicated with a slash through the last letter in a numeral (e.g. {{rn|Ɨ}}), which subtracted the number by an amount less than one (usually {{frac|1|2}}).<ref name=cappelli/>

===Large numbers===

The modern form can only write numbers up to 3999, and without M in early Roman times only numbers up to 899 could be written. Various schemes have been used over time to write larger numbers.

====Apostrophus====
[[File:Westerkerk MDCXXX.jpg|thumb|upright=0.9| "1630" on the [[Westerkerk]] in Amsterdam. "{{rn|M}}" and "{{rn|D}}" are given archaic {{lang|la|apostrophus}} form.]]

Using the {{lang|la|apostrophus}} method,<ref name="merriam-webster">{{Cite web |url=https://www.merriam-webster.com/dictionary/apostrophus |title=Definition of Apostrophus |website=www.merriam-webster.com}}</ref> 500 is written as {{rn|IↃ}}, while 1,000 is written as {{rn|CIↃ}}.<ref name="asimov on numbers 12" /> This system of encasing numbers to denote thousands (imagine the {{rn|C}}s and {{rn|Ↄ}}s as parentheses) had its origins in Etruscan numeral usage.

Each additional set of {{rn|C}} and {{rn|Ↄ}} surrounding {{rn|CIↃ}} raises the value by a factor of ten: {{rn|CCIↃↃ}} represents 10,000 and {{rn|CCCIↃↃↃ}} represents 100,000. Similarly, each additional {{rn|Ↄ}} to the right of {{rn|IↃ}} raises the value by a factor of ten: {{rn|IↃↃ}} represents 5,000 and {{rn|IↃↃↃ}} represents 50,000. Numerals larger than {{rn|CCCIↃↃↃ}} do not occur.<ref name=PropN3218/>

[[File:Roman numerals Bungus 1584-1585.png|thumb|upright=0.9|Page from a 16th-century manual, showing a mixture of {{lang|la|apostrophus}} and {{lang|la|vinculum}} numbers (see in particular the ways of writing 10,000).]]
* '''{{rn|IↃ}}''' = 500 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'''{{rn|CIↃ}}''' = 1,000
* '''{{rn|IↃↃ}}''' = 5,000 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'''{{rn|CCIↃↃ}}''' = 10,000
* '''{{rn|IↃↃↃ}}''' = 50,000 &nbsp;&nbsp;&nbsp;'''{{rn|CCCIↃↃↃ}}''' = 100,000

Sometimes {{rn|CIↃ}} (1000) is reduced to {{rn|ↀ}}, {{rn|IↃↃ}} (5,000) to {{rn|ↁ}}; {{rn|CCIↃↃ}} (10,000) to {{rn|ↂ}}; {{rn|IↃↃↃ}} (50,000) to {{rn|ↇ}}; and {{rn|CCCIↃↃↃ}} (100,000) to {{rn|ↈ}}.<ref name="Ifrah2000">{{Cite book |last=Ifrah |first=Georges |title=The Universal History of Numbers: From Prehistory to the Invention of the Computer |date=2000 |publisher=John Wiley & Sons |others=Translated by David Bellos, E. F. Harding, Sophie Wood, Ian Monk}}</ref> It is likely {{rn|IↃ}} (500) reduced to {{rn|D}} and {{rn|CIↃ}} (1000) influenced  the later {{rn|M}}.

[[John Wallis]] is often credited with introducing the symbol for [[infinity]] {{angbr|∞}}, and one conjecture is that he based it on {{rn|ↀ}}, since 1,000 was [[hyperbole|hyperbolically]] used to represent very large numbers.

====Vinculum====
Using the {{lang|la|[[Vinculum (symbol)|vinculum]]}}, conventional Roman numerals are multiplied by 1,000 by adding a "bar" or "overline", thus:<ref name="Ifrah2000" />
* '''{{rn|IV|border=t}}''' = 4,000
* '''{{rn|XXV|border=t}}''' = 25,000
The ''vinculum ''came into use in the [[Roman Republic|late Republic]],<ref name=Dilke>{{Cite book |last=Dilke |first=Oswald Ashton Wentworth |title=Mathematics and measurement |date=1987 |publisher=British Museum Publications |isbn=978-0-7141-8067-0 |series=Reading the past |location=London|page=15}}</ref> and it was a common alternative to the apostrophic ↀ during the Imperial era around the Roman world (M for '1000' was not in use until the Medieval period).<ref name="Chrisomalis01">{{Cite book |last=Chrisomalis |first=Stephen |title=Numerical Notation: A Comparative History |title-link=Numerical Notation: A Comparative History |date=2010 |publisher=Cambridge University Press |isbn=978-0-521-87818-0 |pages=102–109}}</ref><ref name="gordon01">{{Cite book |last=Gordon |first=Arthur E. |title=Illustrated Introduction to Latin Epigraphy |date=1982 |publisher=University of California Press |isbn=0-520-05079-7 |location=Berkeley |pages=122–123}}</ref> It continued in use in the Middle Ages, though it became known more commonly as {{lang|la|titulus}},<ref name="Chrisomalis02">{{Cite book |last=Chrisomalis |first=Stephen |title=Numerical Notation: A Comparative History |title-link=Numerical Notation: A Comparative History |date=2010 |publisher=Cambridge University Press |isbn=978-0-521-87818-0 |pages=119}}</ref> and it appears in modern editions of classical and medieval Latin texts.<ref>{{Cite book |last=Boethius |url=https://archive.org/download/aniciimanliitor00friegoog/aniciimanliitor00friegoog.pdf |title=De Institutione Arithmetica, libri duo |date=1867 |publisher=B.G.Teubner |pages=42 |author-link=Boethius |access-date=18 January 2023 |orig-date=6th century AD}}</ref><ref name="PlinyNH" />

In an extension of the {{lang|la|vinculum}}, a three-sided box (now sometimes printed as two vertical lines and a {{lang|la|vinculum}}) is used to multiply by 100,000,<ref name="Chrisomalis03">{{Cite book |last=Chrisomalis |first=Stephen |title=Numerical Notation: A Comparative History |title-link=Numerical Notation: A Comparative History |date=2010 |publisher=Cambridge University Press |isbn=978-0-521-87818-0 |pages=402–403}}</ref><ref name=Dilke /> thus:
* '''{{rn|XIII|border=vt}}{{nbsp}}{{rn|XXXII|border=t}} p.''' = 1,332,000 paces (1,332 [[Mile#Roman|Roman miles]]).{{efn|1={{rn|XIII|border=vt}} = 13 × 100,000 = 1,300,000 and {{rn|XXXII|border=t}} = 32 × 1000 = 32,000, so '{{rn|XIII|border=vt}}{{nbsp}}{{rn|XXXII|border=t}} = 1,332,000. '''p.''' is a common abbreviation for {{lang|la|passus}}, paces, the Romans counting a pace as two steps.}}<ref name="PlinyNH">{{Cite book |last=Pliny |url=https://archive.org/details/L352PlinyNaturalHistoryII37/page/n429/mode/2up |title=Natural History |date=1961 |publisher=Harvard University Press |series=Loeb Classical Library |volume=L352 |at=Book VI, XXVI, 100 (pp 414-415) |orig-date=1st century AD}}</ref>

{{lang|la|Vinculum}} notation is distinct from the custom of adding an overline to a numeral simply to indicate that it is a number. Both usages can be seen on Roman inscriptions of the same period and general location, such as on the [[Antonine Wall]].<ref>{{Cite web |title=RIB 2208. Distance Slab of the Twentieth Legion |url=https://romaninscriptionsofbritain.org/inscriptions/2208 |access-date=9 November 2020 |website=Roman Inscriptions in Britain}}</ref><ref>{{Cite web |title=RIB 2171. Building Inscription of the Second and Twentieth Legions |url=https://romaninscriptionsofbritain.org/inscriptions/2171 |access-date=9 November 2020 |website=Roman Inscriptions in Britain}}</ref>

==== Other ====

* There are some examples of year numbers after 1000 written as two Roman numerals 1–99, e.g. 1613 as {{rn|XVIXIII}}, corresponding to the common reading "sixteen thirteen" of such year numbers in English, or 1519 as {{rn|X{{Overset|C|V}}XIX}} as in [[French language|French]] ''quinze-cent-dix-neuf'' (fifteen-hundred and nineteen), and similar readings in other languages.<ref name="gach1862">{{Cite journal |last=Gachard |first=M. |date=1862 |title=II. Analectes historiques, neuvième série (n<sup>os</sup> CCLXI-CCLXXXIV) |url=https://www.persee.fr/doc/bcrh_0770-6707_1862_num_31_3_3033 |journal=Bulletin de la Commission royale d'Historie |volume=31 |issue=3 |pages=345–554 |doi=10.3406/bcrh.1862.3033}} <br />Page 347: {{lang|fr|Lettre de Philippe le Beau aux échevins..., quote: "Escript en nostre ville de Gand, le XXIIII<sup>me</sup> de febvrier, l'an IIII<sup>XX</sup>XIX [quatre-vingt-dix-neuf {{=}} 99].}}" <br />Page 356: {{lang|fr|Lettre de l'achiduchesse Marguerite au conseil de Brabant..., quote: "... Escript à Bruxelles, le dernier jour de juing anno XV<sup>c</sup>XIX [1519].}}" <br />Page 374: {{lang|fr|Letters patentes de la rémission ... de la ville de Bruxelles, quote}}: "{{lang|nl|... Op heden, tweentwintich ['twenty-two'] daegen in decembri, anno vyfthien hondert tweendertich}} ['fifteen hundred thirty-two'] {{lang|nl|... Gegeven op ten vyfsten dach in deser jegewoirdige maent van decembri anno XV tweendertich [1532] vorschreven.}}" <br />Page 419: {{lang|fr|Acte du duc de Parme portant approbation..., quote: "Faiet le XV<sup>me</sup> de juillet XV<sup>c</sup> huytante-six [1586].}}".</ref>

* In some French texts from the 15th century and later, one finds constructions like {{rn|IIII<sup>XX</sup>XIX}} for 99, reflecting the French reading of that number as {{lang|fr|quatre-vingt-dix-neuf}} (four-score and nineteen).<ref name=gach1862/> Similarly, in some English documents one finds, for example, 77 written as "{{rn|iii<sup>xx</sup>xvii}}" (which could be read "three-score and seventeen").<ref name=salt1923>{{Cite book |last=Salter |first=Herbert Edward |url=https://books.google.com/books?id=dfNAAAAAYAAJ&q=iiixx |title=Registrum Annalium Collegii Mertonensis 1483–1521 |date=1923 |publisher=Oxford Historical Society |volume=76}} 544 pages. Page 184 has the computation in pounds:shillings:pence (li:s:d) x:iii:iiii + xxi:viii:viii + xlv:xiiii:i = iii<sup>xx</sup>xvii:vi:i, i.e. 10:3:4 + 21:8:8 + 45:14:1 = 77:6:1.</ref>

* A medieval accounting text from 1301 renders numbers like 13,573 as "{{rn|{{sc|XIII. M. V. C. III. XX. XIII}}}}", that is, "13×1000 + 5×100 + 3×20 + 13".<ref name="wade1865">{{Cite encyclopedia |chapter=E Duo Codicibus Ceratis Johannis de Sancto Justo |url=https://books.google.com/books?id=NrxuEwPNWD4C&pg=PA530 |date=1865 |orig-date=1301 |last1=de Wailly |last2=Delisle | title=Recueil des historiens des Gaules et de la France. Par Martin Bouquet: Contenant la deuxieme livraison des monumens des regnes de saint Louis, de Philippe le Hardi, de Philippe le bel, de Louis X, de Philippe V et de Charles IV ... Jusqu'en MCCCXXVIII. Tome Vingt-Deuxième |trans-chapter=From Two Texts in Wax by John of St Just |encyclopedia=Recueil des Historiens des Gaules et de la France |lang=la |volume=22 |quote-page=530 |quote= SUMMA totalis, XIII. M. V. C. III. XX. XIII. l. III s. XI d. |trans-quote=Sum total, 13 thousand 5 hundred 3 score 13 livres, 3 sous, 11 deniers.}}</ref>

==Origin==
The system is closely associated with the ancient [[city-state]] of Rome and the Empire that it created. However, due to the scarcity of surviving examples, the origins of the system are obscure and there are several competing theories, all largely conjectural.

===Etruscan numerals===
{{Main|Etruscan numerals}}
Rome was founded sometime between 850 and 750 BC. At the time, the region was inhabited by diverse populations of which the Etruscans were the most advanced. The ancient Romans themselves admitted that the basis of much of their civilization was Etruscan. Rome itself was located next to the southern edge of the Etruscan domain, which covered a large part of north-central Italy.

The Roman numerals, in particular, are directly derived from the [[Etruscan numerals|Etruscan number symbols]]: {{angbr|𐌠}}, {{angbr|𐌡}}, {{angbr|𐌢}}, {{angbr|𐌣}}, and {{angbr|𐌟}} for 1, 5, 10, 50, and 100 (they had more symbols for larger numbers, but it is unknown which symbol represents which number). As in the basic Roman system, the Etruscans wrote the symbols that added to the desired number, from higher to lower value. Thus, the number 87, for example, would be written 50 + 10 + 10 + 10 + 5 + 1 + 1 = 𐌣𐌢𐌢𐌢𐌡𐌠𐌠 (this would appear as 𐌠𐌠𐌡𐌢𐌢𐌢𐌣 since [[Etruscan language|Etruscan]] was written from right to left.)<ref name="heem2009">{{Cite journal |last=Van Heems |first=Gilles |date=2009 |title=Nombre, chiffre, lettre: Formes et réformes. Des notations chiffrées de l'étrusque |trans-title=Between Numbers and Letters: About Etruscan Notations of Numeral Sequences |url=https://www.cairn.info/revue-de-philologie-litterature-et-histoire-anciennes-2009-1-page-103.htm |journal=Revue de philologie, de littérature et d'histoire anciennes |language=fr |volume=83 |issue=1 |pages=103–130 |issn=0035-1652}}</ref>

The symbols {{angbr|𐌠}} and {{angbr|𐌡}} resembled letters of the Etruscan alphabet, but {{angbr|𐌢}}, {{angbr|𐌣}}, and {{angbr|𐌟}} did not. The Etruscans used the subtractive notation, too, but not like the Romans. They wrote 17, 18, and 19 as 𐌠𐌠𐌠𐌢𐌢, 𐌠𐌠𐌢𐌢, and 𐌠𐌢𐌢, mirroring the way they spoke those numbers ("three from twenty", etc.); and similarly for 27, 28, 29, 37, 38, etc. However, they did not write 𐌠𐌡 for 4 (nor 𐌢𐌣 for 40), and wrote 𐌡𐌠𐌠, 𐌡𐌠𐌠𐌠 and 𐌡𐌠𐌠𐌠𐌠 for 7, 8, and 9, respectively.<ref name=heem2009/>

===Early Roman numerals===
The early Roman numerals for 1, 10, and 100 were the Etruscan ones: {{angbr|𐌠}}, {{angbr|𐌢}}, and {{angbr|𐌟}}. The symbols for 5 and 50 changed from {{angbr|𐌡}} and {{angbr|𐌣}} to {{angbr|V}} and {{angbr|ↆ}} at some point. The latter had flattened to {{angbr|⊥}} (an inverted T) by the time of [[Augustus]], and soon afterwards became identified with the graphically similar letter {{angbr|{{rn|L}}}}.<ref name=PropN3218/>

The symbol for 100 was written variously as {{angbr|𐌟}} or {{angbr|ↃIC}}, and was then abbreviated to {{angbr|{{rn|Ↄ}}}} or {{angbr|{{rn|C}}}}, with {{angbr|{{rn|C}}}} (which matched the Latin letter ''C'') finally winning out. It might have helped that ''C'' was the initial letter of {{lang|la|CENTUM}}, Latin for "hundred".

The numbers 500 and 1000 were denoted by {{rn|V}} or {{rn|X}} overlaid with a box or circle. Thus, 500 was like a {{rn|Ɔ}} superimposed on a {{rn|⋌}} or {{rn|⊢}}, making it look like {{rn|<s>Þ</s>}}. It became {{rn|<s>D</s>}} or {{rn|Ð}} by the time of Augustus, under the graphic influence of the letter {{rn|D}}. It was later identified as the letter {{rn|D}}; an alternative symbol for "thousand" was a {{rn|CIↃ}}, and half of a thousand or "five hundred" is the right half of the symbol, {{rn|IↃ}}, and this may have been converted into {{rn|D}}.<ref name="asimov on numbers 12" />

The notation for 1000 was a circled or boxed {{rn|X}}: Ⓧ, {{rn|⊗}}, {{rn|⊕}}, and by Augustan times was partially identified with the Greek letter {{rn|Φ}} ''[[phi]]''. Over time, the symbol changed to {{rn|Ψ}} and {{rn|ↀ}}. The latter symbol further evolved into {{rn|∞}}, then {{rn|⋈}}, and eventually changed to {{rn|M}} under the influence of the Latin word ''mille'' "thousand".<ref name=PropN3218/>

According to Paul Kayser, the basic numerical symbols were {{rn|I}}, {{rn|X}}, {{rn|𐌟}} and {{rn|Φ}} (or {{rn|⊕}}) and the intermediate ones were derived by taking half of those (half an {{rn|X}} is {{rn|V}}, half a {{rn|𐌟}} is {{rn|ↆ}} and half a {{rn|Φ/⊕}} is {{rn|D}}). Then 𐌟 and ↆ developed as mentioned above.<ref>{{Cite journal |last=Keyser |first=Paul |date=1988 |title=The Origin of the Latin Numerals 1 to 1000 |journal=American Journal of Archaeology |volume=92 |issue=4 |pages=529–546 |doi=10.2307/505248 |jstor=505248 |s2cid=193086234}}</ref>

[[File:Colosseum-Entrance LII.jpg|thumb|upright=1.1|Entrance to section {{rn|LII}} (52) of the [[Colosseum]], with numerals still visible]]

===Classical Roman numerals===
The [[Colosseum]] was constructed in Rome in CE 72–80,<ref name="Hopkins p.2">{{Cite book |last=Hopkins |first=Keith |title=The Colosseum |date=2005 |publisher=[[Harvard University Press]] |isbn=978-0-674-01895-2 |location=Cambridge, MA}}</ref> and while the original perimeter wall has largely disappeared, the numbered entrances from {{rn|XXIII}} (23) to {{rn|LIIII}} (54) survive,<ref name="Claridge pp. 276–282">{{Cite book |last=Claridge |first=Amanda |title=Rome: An Oxford Archaeological Guide (First ed.) |date=1998 |publisher=[[Oxford University Press]] |isbn=978-0-19-288003-1 |location=Oxford}}</ref> to demonstrate that in Imperial times Roman numerals had already assumed their classical form: [[Roman numerals#Standard form|as largely standardised in current use]]. The most obvious anomaly ([[Roman numerals#Other additive forms|a common one that persisted for centuries]]) is the inconsistent use of subtractive notation - while {{rn|XL}} is used for 40, {{rn|IV}} is avoided in favour of {{rn|IIII}}: in fact, gate 44 is labelled {{rn|XLIIII}}.

==Use in the Middle Ages and Renaissance==
[[Lower case]], or ''minuscule'', letters were developed in the Middle Ages, well after the demise of the [[Western Roman Empire]], and since that time lower-case versions of Roman numbers have also been commonly used: {{rn|i}}, {{rn|ii}}, {{rn|iii}}, {{rn|iv}}, and so on.

[[File:Excerpt from BnF ms. 23112 fr., fol. 343v.png|thumb|upright=1.1|13th century example of {{rn|iiij}}.]]

Since the Middle Ages, a "{{rn|j}}" has sometimes been substituted for the final "{{rn|i}}" of a "lower-case" Roman numeral, such as "{{rn|iij}}" for 3 or "{{rn|vij}}" for 7. This "{{rn|j}}" can be considered a [[Swash (typography)|swash]] variant of "{{rn|i}}". Into the early 20th century, the use of a final "{{rn|j}}" was still sometimes used in [[medical prescription]]s to prevent tampering with or misinterpretation of a number after it was written.<ref>Bastedo, Walter A. [https://archive.org/details/materiamedica00bastgoog/page/n604 <!-- pg=582 --> Materia Medica: Pharmacology, Therapeutics and Prescription Writing for Students and Practitioners, 2nd ed. (Philadelphia, PA: W.B. Saunders, 1919) p582]. Retrieved 15 March 2010.</ref>

Numerals in documents and inscriptions from the Middle Ages sometimes include additional symbols, which today are called "medieval Roman numerals". Some simply substitute another letter for the standard one (such as "{{rn|A}}" for "{{rn|V}}", or "{{rn|Q}}" for "{{rn|D}}"), while others serve as abbreviations for compound numerals ("{{rn|O}}" for "{{rn|XI}}", or "{{rn|F}}" for "{{rn|XL}}"). Although they are still listed today in some dictionaries, they are long out of use.<ref name=cappelli>{{Cite book |last=Capelli |first=Adriano |title=Lexicon abbreviaturarum : dizionario di abbreviature Latine ed Italiane |date=1912|chapter-url=https://archive.org/details/pbc.gda.pl.Lexicon_abbreviaturarum_Cappelli_A_90447/page/413/mode/1up|access-date=2025-03-21|pages=413–421|chapter=Numerazione romana|publisher=Ulrico Hoepli |lang=it}}</ref>

A superscript "o" (sometimes written directly above the symbol) was sometimes used as an [[ordinal indicator]].<ref>{{Cite web |url=http://agad.archiwa.gov.pl/prezentacje/foto08m.jpg |title=Example of superscript 'o' used as an ordinal indicator |access-date=2014-01-25 |archive-date=2016-03-04 |archive-url=https://web.archive.org/web/20160304055339/http://agad.archiwa.gov.pl/prezentacje/foto08m.jpg |url-status=dead}}</ref>

{| class="sortable wikitable"
|-
! Number
! Medieval<br />abbreviation
! Notes and etymology
|-
| 5
| {{rn|A}}
| Resembles an upside-down V. Also said to equal 500.
|-
| 6
|ↅ
| Either from a [[typographic ligature|ligature]] of {{rn|VI}}, or from [[digamma]] (ϛ), the Greek numeral 6 (sometimes conflated with the [[Stigma (letter)|στ]] ligature).<ref name="PropN3218">{{Cite web |last=Perry |first=David J. |title=Proposal to Add Additional Ancient Roman Characters to UCS |url=http://std.dkuug.dk/jtc1/sc2/wg2/docs/N3218.pdf |archive-url=https://web.archive.org/web/20110622065211/http://std.dkuug.dk/jtc1/sc2/wg2/docs/n3218.pdf |archive-date=22 June 2011}}.</ref>
|-
| 7
| {{rn|S}}, {{rn|Z}}
| Presumed abbreviation of ''{{lang|la|septem}}'', Latin for 7.
|-
| 11
| {{rn|O}}
| Presumed abbreviation of ''{{lang|fr|onze}}'', French for 11.
|-
| 40
| {{rn|F}}
| Presumed abbreviation of English ''forty''.
|-
| 70
| {{rn|S}}
| Also could stand for 7, with the same derivation.
|-
| 80
| {{rn|R}}
|
|-
| 90
| {{rn|N}}
| Presumed abbreviation of ''{{lang|la|nonaginta}}'', Latin for 90. (Ambiguous with {{rn|N}} for "nothing" (''nihil'')).
|-
| 150
| {{rn|Y}}
| Possibly derived from the lowercase y's shape.
|-
| 151
| {{rn|K}}
| Unusual, origin unknown; also said to stand for 250.<ref>{{Cite book |last=Bang |first=Jørgen |title=Fremmedordbog |date=1962 |publisher=Berlingske Ordbøger |language=da}}</ref>
|-
| 160
| {{rn|T}}
| Possibly derived from Greek ''tetra'', as 4 × 40 = 160.
|-
| 200
| {{rn|H}}
| Could also stand for 2 (see also 𐆙, the symbol for the [[dupondius]]). From a barring of two {{rn|I}}'s.
|-
| 250
| {{rn|E}}
|
|-
| 300
| {{rn|B}}
|
|-
| 400
| {{rn|P}}, {{rn|G}}
|
|-
| 500
| {{rn|Q}}
| Redundant with {{rn|D}}; abbreviates ''{{lang|la|quingenti}}'', Latin for 500. Also sometimes used for 500,000.<ref>{{Cite book |last=Gordon |first=Arthur E. |url=https://archive.org/details/illustratedintro0000gord |title=Illustrated Introduction to Latin Epigraphy |date=1983 |publisher=[[University of California Press]] |isbn=9780520038981 |pages=44 |access-date=3 October 2015 |url-access=registration}}</ref>
|-
| 800
| {{rn|Ω}}
| Borrowed from [[Gothic alphabet|Gothic]].
|-
| 900
| {{rn|ϡ}}
| Borrowed from Gothic.
|-
| 2000
| {{rn|Z}}
|
|-
| 9000
| {{rn|Ṫ}}
| Cappelli notes that the T with [[umlaut (diacritic)|double dot]] is only attested for [[Spanish-suited playing cards]].
|}

[[Chronogram]]s, messages with dates encoded into them, were popular during the [[Renaissance]] era. The chronogram would be a phrase containing the letters {{rn|I}}, {{rn|V}}, {{rn|X}}, {{rn|L}}, {{rn|C}}, {{rn|D}}, and {{rn|M}}. By putting these letters together, the reader would obtain a number, usually indicating a particular year.

==Modern use==
By the 11th century, Arabic numerals had been introduced into Europe from [[al-Andalus]], by way of [[Arab]] traders and arithmetic treatises. Roman numerals, however, proved very persistent, remaining in common use in the West well into the 14th and 15th centuries, even in accounting and other business records (where the actual calculations would have been made using an [[abacus]]). Replacement by their more convenient "Arabic" equivalents was quite gradual, and Roman numerals are still used today in certain contexts. A few examples of their current use are:

[[File:Carlos IV Coin.jpg|thumb|upright=1.1|Spanish [[Spanish real|Real]] using {{rn|IIII}} instead of {{rn|IV}} as regnal number of [[Charles IV of Spain|Charles {{Rn|IV}} of Spain]].|alt=]]
* Names of monarchs and popes, e.g. [[Elizabeth II]] of the United Kingdom, [[Pope Leo XIV]]. These are referred to as [[regnal number]]s and are usually read as [[Ordinal numbers (linguistics)|ordinals]]; e.g. {{rn|II}} is pronounced "the second". This tradition began in Europe sporadically in the [[Middle Ages]], gaining widespread use in England during the reign of [[Henry VIII]]. Previously, the monarch was not known by numeral but by an [[epithet]] such as [[Edward the Confessor]]. Some monarchs (e.g. [[Charles IV of Spain]], [[Louis XIV of France]] and [[William IV of the United Kingdom|William IV of Great Britain]]) seem to have preferred the use of {{rn|IIII}} instead of {{rn|IV}} on their coinage (see illustration).
* [[Suffix (name)#Generational titles|Generational suffixes]], particularly in the U.S., for people sharing the same name across generations, such as [[William Howard Taft IV]]. These are also usually read as ordinals.
* In the [[French Republican Calendar#Converting from the Gregorian Calendar|French Republican Calendar]], initiated during the [[French Revolution]], years were numbered by Roman numerals – from the year {{rn|I}} (1792) when this calendar was introduced to the year {{rn|XIV}} (1805) when it was abandoned.
* [[File:Cambridge Main Public Library 1888.jpg|thumb|upright=1.1|The year of construction of the [[Cambridge Public Library]] (Massachusetts, U.S.), 1888, displayed in "standard" Roman numerals on its facade.]]<!--
--> The year of production of films, television shows and other works of art within the work itself. Outside reference to the work will use regular Arabic numerals.
* Hour marks on [[timepiece]]s. In this context, 4 is often written {{rn|IIII}}.
* The year of construction on building [[façade]]s and [[cornerstone]]s.
* Page numbering of prefaces and introductions of books, and sometimes of appendices and annexes, too.
* Book volume and chapter numbers, as well as the several acts within a play (e.g. Act {{Rn|iii}}, Scene 2).
* [[Sequel]]s to some films, video games, and other works (as in ''[[Rocky II]]'', ''[[Grand Theft Auto V]]'', ''[[Myst III: Exile]]'').
* [[Outline (summary)|Outlines]] that use numbers to show hierarchical relationships.
* Occurrences of a recurring grand event, for instance:
** The [[Summer Olympic Games|Summer]] and [[Winter Olympic Games]] (e.g. the [[2010 Winter Olympics|XXI Olympic Winter Games]]; the [[2012 Summer Olympics|Games of the XXX Olympiad]]).
** The [[Super Bowl]], the annual championship game of the [[National Football League]] (e.g. [[Super Bowl XLII]]; [[Super Bowl 50]] was a one-time exception<ref>{{Cite web |last=Rosenthal |first=Gregg |date=June 4, 2014 |title=NFL won't use Roman numerals for Super Bowl 50 |url=https://www.nfl.com/news/nfl-won-t-use-roman-numerals-for-super-bowl-50-0ap2000000355943 |url-status=live |archive-url=https://web.archive.org/web/20151201194151/http://www.nfl.com/news/story/0ap2000000355943/article/nfl-wont-use-roman-numerals-for-super-bowl-50 |archive-date=1 December 2015 |access-date=5 November 2014 |publisher=National Football League}}</ref>).
** [[WrestleMania]], the annual [[professional wrestling]] event for [[WWE]] (e.g. [[WrestleMania XXX]]). This usage has also been inconsistent.

===Specific disciplines===
In [[astronautics]], [[List of orbital launch systems#United States|United States rocket]] model variants are sometimes designated by Roman numerals, e.g. [[Titan I]], [[Titan II]], [[Titan III]], [[Saturn I]], [[Saturn V]].

In [[astronomy]], the [[natural satellite]]s or "moons" of the [[planet]]s are [[Naming of moons#Roman numeral designations|designated]] by capital Roman numerals appended to the planet's name. For example, [[Titan (moon)|Titan]]'s designation is [[Saturn]] {{rn|VI}}.<ref name="jplsats-disc">{{Cite web |date=15 November 2021 |title=Planetary Satellite Discovery Circumstances |url=https://ssd.jpl.nasa.gov/sats/discovery.html |access-date=7 January 2022 |website=JPL Solar System Dynamics |publisher=NASA}}</ref>

In [[chemistry]], Roman numerals are sometimes used to denote the [[group (periodic table)|groups]] of the [[periodic table]], but this has officially been deprecated in favour of Arabic numerals.<ref name="Fluck 1988">{{Cite journal |last=Fluck |first=E. |date=1988 |title=New Notations in the Periodic Table |url=http://www.iupac.org/publications/pac/1988/pdf/6003x0431.pdf |journal=[[Pure and Applied Chemistry|Pure Appl. Chem.]] |publisher=[[International Union of Pure and Applied Chemistry|IUPAC]] |volume=60 |issue=3 |pages=431–436 |doi=10.1351/pac198860030431 |s2cid=96704008 |access-date=24 March 2012}}</ref> They are also used in the [[IUPAC nomenclature of inorganic chemistry]], for the [[oxidation number]] of [[cation]]s which can take on several different positive charges. They are also used for naming [[Phase (matter)|phases]] of [[Polymorphism (materials science)|polymorphic]] [[crystal]]s, such as [[ice]].

In [[education]], school grades (in the sense of year-groups rather than test scores) are sometimes referred to by a Roman numeral; for example, "grade {{rn|IX}}" is sometimes seen for "grade 9".

[[File:9th Aero Squadron AEF.jpg|thumb|upright=1.1|Stylised "{{rn|IX}}" represents "9" in unit emblem of [[9th Aero Squadron]] AEF, 1918.]]

In [[entomology]], the broods of the thirteen- and seventeen-year [[periodical cicadas]] are identified by Roman numerals.

In [[graphic design]], stylised Roman numerals may represent numeric values.

In [[law]], Roman numerals are commonly used to help organize legal codes as part of an [[outline (list)#Alphanumeric outline|alphanumeric outline]]. 
* In numbering [[Act of Parliament (United Kingdom)|UK Acts of Parliament]] within a given year (a given [[parliamentary session|session]] until 1963), [[Local and personal acts of Parliament (United Kingdom)#Local acts|local act]]s have lowercase Roman numerals, whereas [[Act of Parliament (United Kingdom)#Public general acts|public act]]s have plain Arabic numerals and [[Local and personal acts of Parliament (United Kingdom)#Personal acts|personal act]]s have [[Italic type|italic]] Arabic numerals.<ref>{{cite web |title=Introduction to Private and Personal Acts |url=https://www.legislation.gov.uk/changes/chron-tables/private/intro#6ListingNumberingandAnnotationsofActs |website=[[legislation.gov.uk]] |access-date=22 July 2024 |page=6. Listing, Numbering and Annotations of Acts}}</ref>

In [[mathematics]] (including [[trigonometry]], [[statistics]], and [[calculus]]), when a graph includes negative numbers, its quadrants are named using {{rn|I}}, {{rn|II}}, {{rn|III}}, and {{rn|IV}}.<ref>{{Cite web |date=2020-08-04 |title=2.1: Definition and Label Quadrants |url=https://math.libretexts.org/Bookshelves/Applied_Mathematics/Calculus_for_Business_and_Social_Sciences_Corequisite_Workbook_(Dominguez_Martinez_and_Saykali)/02:_Cartesian_Coordinate_System/2.01:_Definition__and_Label_Quadrants |access-date=2025-01-31 |website=Mathematics LibreTexts |language=en}}</ref> These quadrant names signify positive numbers on both axes, negative numbers on the x-axis, negative numbers on both axes, and negative numbers on the y-axis, respectively. The use of Roman numerals to designate quadrants avoids confusion, since Arabic numerals are used for the actual data represented in the graph.

In [[military]] unit designation, Roman numerals are often used to distinguish between units at different levels. This reduces possible confusion, especially when viewing operational or strategic level maps. In particular, army corps are often numbered using Roman numerals (for example, the American XVIII Airborne Corps or the Nazi III Panzerkorps) with Arabic numerals being used for divisions and armies.

In [[music]], Roman numerals are used in several contexts:
* [[movement (music)|Movements]] are often numbered using Roman numerals.
* In [[Roman numeral analysis]], [[Function (music)|harmonic function]] is identified using Roman numerals.
* Individual strings of [[stringed instruments]], such as the [[violin]], are often denoted by Roman numerals, with higher numbers denoting lower strings.

In [[pharmacy]], Roman numerals were used with the now largely obsolete [[apothecaries' system]] of measurement: including {{rn|SS}} to denote "one half" and {{rn|N}} to denote "zero".<ref name="Bachenheimer" /><ref>{{Cite book |last1=Reddy |first1=Indra K. |url=https://books.google.com/books?id=U3QY7gz0C2cC |title=Essential Math and Calculations for Pharmacy Technicians |last2=Khan |first2=Mansoor A. |date=2003 |publisher=CRC Press |isbn=978-0-203-49534-6}}</ref>

In [[photography]], Roman numerals (with zero) are used to denote varying levels of brightness when using the [[Zone System]].

In [[seismology]], Roman numerals are used to designate degrees of the [[Mercalli intensity scale]] of earthquakes.

[[File:Eire Frankng I-IV-1986.jpg|thumb|Example of postage stamp from Ireland (Éire) franked using Roman numeral for the month]]

In [[team sport|sport]] the team containing the "top" players and representing a nation or province, a [[Sports club|club]] or a school at the highest level in (say) [[rugby union]] is often called the "1st {{rn|XV}}", while a lower-ranking [[cricket]] or [[American football]] team might be the "3rd {{rn|XI}}".

In [[tarot]], Roman numerals (with zero) are often used to denote the cards of the [[Major Arcana]].

In [[Republic_of_Ireland|Ireland]], Roman numerals were used until the late 1980s to indicate the month on postage [[Franking]]. In documents, Roman numerals are sometimes still used to indicate the month to avoid confusion over day/month/year or month/day/year formats.

In [[theology]] and [[biblical scholarship]], the [[Septuagint]] is often referred to as {{rn|LXX}}, as this translation of the [[Old Testament]] into Greek is named for the legendary number of its translators (''septuaginta'' being Latin for "seventy").

===Modern use in European languages other than English===
Some uses that are rare or never seen in English-speaking countries may be relatively common in parts of [[continental Europe]] and in other regions (e.g. [[Latin America]]) that use a European language other than English. For instance:

Capital or [[Small caps|small capital]] Roman numerals are widely used in [[Romance languages]] to denote {{strong|centuries}}, e.g. the French ''{{lang|fr|{{Smallcaps|xviii}}<sup>e</sup> siècle}}''<ref>{{Cite book |title=Lexique des règles typographiques en usage à l'imprimerie nationale |date=March 2011 |publisher=[[Imprimerie nationale]] |isbn=978-2-7433-0482-9 |edition=6th |location=Paris |pages=126 |language=fr}} ''On composera en chiffres romains petites capitales les nombres concernant : ↲ 1. Les siècles.''</ref> and the Spanish ''{{lang|es|siglo {{Smallcaps|xviii}}}}'' (not ''{{lang|es|{{Smallcaps|xviii}} siglo}}'') for "18th century". Some Slavic and Turkic languages (especially in and adjacent to Russia) similarly favour Roman numerals (e.g. Russian {{lang|ru|XVIII век}}, Azeri {{lang|az|XVIII əsr}} or Polish {{lang|pl|wiek XVIII}}<ref>{{Cite web |title=cyfry arabskie a zapis wieku |url=https://poradnia-jezykowa.uni.lodz.pl/faq/cyfry-arabskie-a-zapis-wieku/ |first=Katarzyna |last=Burska |website=Poradnia językowa Uniwersytetu Łódzkiego |publisher=University of Łódź |language=pl |trans-title=Arabic digits when formatting centuries}}</ref>). On the other hand, in [[Turkish language|Turkish]] and some [[Central Europe|Central European]] Slavic languages, like most [[Germanic languages]], one writes "18." (with a period) before the local word for "century" (e.g. Turkish {{lang|tr|18. yüzyıl}}, Czech {{lang|cs|18. století}}).

[[File:Yeltsin-authograph-1988.gif|thumb|upright=1.1|[[Boris Yeltsin]]'s signature, dated 10 November 1988, rendered as 10.{{rn|XI}}.'88.]]

Mixed Roman and Arabic numerals are sometimes used in numeric representations of dates (especially in formal letters and official documents, but also on tombstones). The {{strong|month}} is written in Roman numerals, while the day is in Arabic numerals: "4.{{rn|VI}}.1789" and "{{rn|VI}}.4.1789" both refer unambiguously to 4 June 1789.

[[File:DarboLaikas.jpg|thumb|upright=0.9|left|Business hours table on a shop window in [[Vilnius]], Lithuania.]]

Roman numerals are sometimes used to represent the {{strong|days of the week}} in hours-of-operation signs displayed in windows or on doors of businesses,<ref>{{Cite web |title=Beginners latin |url=http://www.nationalarchives.gov.uk/latin/beginners/dating/default.htm |archive-url=https://web.archive.org/web/20131203092331/http://www.nationalarchives.gov.uk/latin/beginners/dating/default.htm |archive-date=3 December 2013 |access-date=1 December 2013 |website=nationalarchives.gov.uk}}</ref> and sometimes in railway and bus timetables. Monday, taken as the first day of the week, is represented by {{rn|I}}. Sunday is represented by {{rn|VII}}. The hours of operation signs are tables composed of two columns where the left column is the day of the week in Roman numerals and the right column is a range of hours of operation from starting time to closing time. In the example case (left), the business opens from 10 AM to 7 PM on weekdays, 10 AM to 5 PM on Saturdays and is [[Sunday shopping|closed on Sundays]]. Note that the listing uses 24-hour time.

[[File:S6002447 cropped.jpg|thumb|Sign at 17.9 km on route SS4 [[Via Salaria|Salaria]], north of Rome, Italy.]]

Roman numerals may also be used for [[floor numbering]].<ref>{{Cite web |title=Roman Arithmetic |url=http://turner.faculty.swau.edu/mathematics/materialslibrary/roman/ |archive-url=https://web.archive.org/web/20131122162120/http://turner.faculty.swau.edu/mathematics/materialslibrary/roman/ |archive-date=22 November 2013 |access-date=1 December 2013 |publisher=[[Southwestern Adventist University]]}}</ref><ref>{{Cite web |title=Roman Numerals History |url=http://romannumerals.info/roman-numerals-history/ |archive-url=https://web.archive.org/web/20131203091427/http://romannumerals.info/roman-numerals-history/ |archive-date=3 December 2013 |url-status=usurped |access-date=1 December 2013}}</ref> For instance, apartments in central [[Amsterdam]] are indicated as 138-{{rn|III}}, with both an Arabic numeral (number of the block or house) and a Roman numeral (floor number). The apartment on the ground floor is indicated as {{lang|nl|138-huis}}.

In Italy, where roads outside built-up areas have [[Milestone|kilometre signs]], major roads and motorways also mark 100-metre subdivisionals, using Roman numerals from {{rn|I}} to {{rn|IX}} for the smaller intervals. The sign {{sfrac|{{rn|IX}}|17}} thus marks 17.9&nbsp;km.

Certain romance-speaking countries use Roman numerals to designate assemblies of their national legislatures. For instance, the composition of the [[Italy|Italian]] [[Parliament of Italy|Parliament]] from 2018 to 2022 (elected in the [[2018 Italian general election]]) is called the [[Legislature XVIII of Italy|XVIII Legislature of the Italian Republic]] (or more commonly the "XVIII Legislature").

A notable exception to the use of Roman numerals in Europe is in Greece, where [[Greek numerals]] (based on the Greek alphabet) are generally used in contexts where Roman numerals would be used elsewhere.

==Unicode==
The "[[Number Forms]]" block of the [[Unicode]] computer character set standard has a number of [[Numerals in Unicode#Roman numerals|Roman numeral symbols]] in the range of [[Unicode code point|code points]] from U+2160 to U+2188.<ref name="UnicodeChartU2150">{{Cite web |url=https://www.unicode.org/charts/PDF/U2150.pdf |title=Unicode Number Forms}}</ref> This range includes both upper- and lowercase numerals, as well as pre-combined characters for numbers up to 12 (Ⅻ or {{rn|XII}}). One justification for the existence of pre-combined numbers is to facilitate the setting of multiple-letter numbers (such as VIII) on a single horizontal line in Asian vertical text. The Unicode standard, however, includes special Roman numeral code points for compatibility only, stating that "[f]or most purposes, it is preferable to compose the Roman numerals from sequences of the appropriate Latin letters".<ref>{{Cite web |date=2011 |title=The Unicode Standard, Version 6.0 – Electronic edition |url=https://www.unicode.org/versions/Unicode6.0.0/ch15.pdf |publisher=Unicode, Inc. |pages=486}}</ref> The block also includes some {{lang|la|apostrophus}} symbols for large numbers, an old variant of "{{rn|L}}" (50) similar to the Etruscan character, the [[Claudian letter]] "reversed C", etc.<ref>{{Cite web |title=Roman symbol |url=https://symbolonly.com/roman-symbols.html |website=symbolonly.com}}</ref>

==See also==
{{Columnslist|colwidth=23em|
* [[Biquinary]]
* [[Egyptian numerals]]
* [[Etruscan numerals]]
* [[Greek numerals]]
* [[Hebrew numerals]]
* [[Kharosthi numerals]]
* [[Maya numerals]]
* [[Chinese numerals]]
* [[Roman abacus]]
* [[Proto-writing]]
* [[Roman numerals in Unicode]]
}}
{{Clear}}

==References==

===Notes===
{{Notelist}}

===Citations===
{{Reflist}}

==Sources==
* {{Cite book |last=Menninger |first=Karl |title=Number Words and Number Symbols: A Cultural History of Numbers |date=1992 |publisher=[[Dover Publications]] |isbn=978-0-486-27096-8}}

==Further reading==
{{Library resources box |by=no |onlinebooks=yes |others=yes |about=yes |label=Roman numerals
|viaf= |lcheading= |wikititle= }}
* Aczel, Amir D. 2015. ''Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers.'' 1st edition. New York: Palgrave Macmillan.
* Goines, David Lance. ''A Constructed Roman Alphabet: A Geometric Analysis of the Greek and Roman Capitals and of the Arabic Numerals.'' Boston: D.R. Godine, 1982.
* Houston, Stephen D. 2012. ''The Shape of Script: How and Why Writing Systems Change.'' Santa Fe, NM: School for Advanced Research Press.
* Taisbak, Christian M. 1965. "Roman numerals and the abacus." ''Classica et medievalia'' 26: 147–60.

==External links==
* {{Cite web |title=Roman Numerals (Totally Epic Guide) |url=https://www.knowtheromans.co.uk/Categories/SubCatagories/RomanNumerals/ |website=Know The Romans}}

{{Latin alphabet}}
{{Ancient Rome topics}}
{{List of writing systems}}
{{Sister bar|auto=yes|wikt=Appendix:Roman numerals}}

[[Category:Numerals]]
[[Category:Numeral systems]]
[[Category:Ancient Roman mathematics]]
[[Category:Latin script]]
[[Category:Legacy of the Roman Empire]]