Mathematical operators and symbols in Unicode

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Template:Short description

File:0009-cmls-2012 preview ecran.jpg
Blackboard at the Laurent Schwartz Center for Mathematics, École Polytechnique

Template:SpecialChars The Unicode Standard encodes almost all standard characters used in mathematics.[1] Unicode Technical Report #25 provides comprehensive information about the character repertoire, their properties, and guidelines for implementation.[1] Mathematical operators and symbols are in multiple Unicode blocks. Some of these blocks are dedicated to, or primarily contain, mathematical characters while others are a mix of mathematical and non-mathematical characters. This article covers all Unicode characters with a derived property of "Math".[2][3]

Dedicated blocks

Mathematical Operators block

Script error: No such module "Labelled list hatnote". The Mathematical Operators block (U+2200–U+22FF) contains characters for mathematical, logical, and set notation.

Mathematical Operators<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+220x
U+221x
U+222x
U+223x
U+224x
U+225x
U+226x
U+227x
U+228x
U+229x
U+22Ax
U+22Bx
U+22Cx
U+22Dx
U+22Ex
U+22Fx
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Supplemental Mathematical Operators block

Script error: No such module "Labelled list hatnote". The Supplemental Mathematical Operators block (U+2A00–U+2AFF) contains various mathematical symbols, including N-ary operators, summations and integrals, intersections and unions, logical and relational operators, and subset/superset relations.

Supplemental Mathematical Operators<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+2A0x
U+2A1x
U+2A2x
U+2A3x ⨿
U+2A4x
U+2A5x
U+2A6x
U+2A7x ⩿
U+2A8x
U+2A9x
U+2AAx
U+2ABx ⪿
U+2ACx
U+2ADx
U+2AEx
U+2AFx ⫿
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Mathematical Alphanumeric Symbols block

Script error: No such module "Labelled list hatnote". The Mathematical Alphanumeric Symbols block (U+1D400–U+1D7FF) contains Latin and Greek letters and decimal digits that enable mathematicians to denote different notions with different letter styles. The reserved code points (the "holes") in the alphabetic ranges up to U+1D551 duplicate characters in the Letterlike Symbols block. In order, these are: Template:Not a typo.

Template:Unicode chart Mathematical Alphanumeric Symbols

Letterlike Symbols block

Script error: No such module "Labelled list hatnote". The Letterlike Symbols block (U+2100–U+214F) includes variables. Most alphabetic math symbols are in the Mathematical Alphanumeric Symbols block shown above.

The math subset of this block is U+2102, U+2107, U+210A–U+2113, U+2115, U+2118–U+211D, U+2124, U+2128–U+2129, U+212C–U+212D, U+212F–U+2131, U+2133–U+2138, U+213C–U+2149, and U+214B.[4]

Letterlike Symbols<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+210x
U+211x
U+212x
U+213x
U+214x
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Miscellaneous Mathematical Symbols-A block

Script error: No such module "Labelled list hatnote". The Miscellaneous Mathematical Symbols-A block (U+27C0–U+27EF) contains characters for mathematical, logical, and database notation.

Miscellaneous Mathematical Symbols-A<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+27Cx
U+27Dx
U+27Ex
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Miscellaneous Mathematical Symbols-B block

Script error: No such module "Labelled list hatnote". The Miscellaneous Mathematical Symbols-B block (U+2980–U+29FF) contains miscellaneous mathematical symbols, including brackets, angles, and circle symbols.

Miscellaneous Mathematical Symbols-B<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+298x
U+299x
U+29Ax
U+29Bx ⦿
U+29Cx
U+29Dx
U+29Ex
U+29Fx ⧿
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Miscellaneous Technical block

Script error: No such module "Labelled list hatnote". The Miscellaneous Technical block (U+2300–U+23FF) includes braces and operators.

The math subset of this block is U+2308–U+230B, U+2320–U+2321, U+237C, U+239B–U+23B5, 23B7, U+23D0, and U+23DC–U+23E2.

Miscellaneous Technical<templatestyles src="Citation/styles.css"/>[1]<templatestyles src="Citation/styles.css"/>[2]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+230x
U+231x
U+232x
U+233x
U+234x
U+235x
U+236x
U+237x
U+238x
U+239x
U+23Ax
U+23Bx
U+23Cx
U+23Dx
U+23Ex
U+23Fx
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version
2.<templatestyles src="Citation/styles.css"/>^ Unicode code points U+2329 and U+232A are deprecated as of Unicode version 5.2

Geometric Shapes block

Script error: No such module "Labelled list hatnote". The Geometric Shapes block (U+25A0–U+25FF) contains geometric shape symbols.

The math subset of this block is U+25A0–25A1, U+25AE–25B7, U+25BC–25C1, U+25C6–25C7, U+25CA–25CB, U+25CF–25D3, U+25E2, U+25E4, U+25E7–25EC, and U+25F8–25FF.

Geometric Shapes<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+25Ax
U+25Bx
U+25Cx
U+25Dx
U+25Ex
U+25Fx
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Arrows block

Script error: No such module "Labelled list hatnote". The Arrows block (U+2190–U+21FF) contains line, curve, and semicircle arrows and arrow-like operators.

The math subset of this block is U+2190–U+21A7, U+21A9–U+21AE, U+21B0–U+21B1, U+21B6–U+21B7, U+21BC–U+21DB, U+21DD, U+21E4–U+21E5, U+21F4–U+21FF.[5]

Arrows<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+219x
U+21Ax
U+21Bx
U+21Cx
U+21Dx
U+21Ex
U+21Fx
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Supplemental Arrows-A block

Script error: No such module "Labelled list hatnote". The Supplemental Arrows-A block (U+27F0–U+27FF) contains arrows and arrow-like operators.

Supplemental Arrows-A<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+27Fx
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Supplemental Arrows-B block

Script error: No such module "Labelled list hatnote". The Supplemental Arrows-B block (U+2900–U+297F) contains arrows and arrow-like operators (arrow tails, crossing arrows, curved arrows, and harpoons).

Supplemental Arrows-B<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+290x
U+291x
U+292x
U+293x ⤿
U+294x
U+295x
U+296x
U+297x ⥿
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Miscellaneous Symbols and Arrows block

Script error: No such module "Labelled list hatnote". The Miscellaneous Symbols and Arrows block (U+2B00–U+2BFF Arrows) contains arrows and geometric shapes with various fills.

The math subset of this block is U+2B30–U+2B44, U+2B47–U+2B4C.[6]

Miscellaneous Symbols and Arrows<templatestyles src="Citation/styles.css"/>[1]<templatestyles src="Citation/styles.css"/>[2]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+2B0x
U+2B1x
U+2B2x
U+2B3x ⬿
U+2B4x
U+2B5x
U+2B6x
U+2B7x ⭿
U+2B8x
U+2B9x
U+2BAx
U+2BBx ⮿
U+2BCx
U+2BDx
U+2BEx
U+2BFx ⯿
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version
2.<templatestyles src="Citation/styles.css"/>^ Grey areas indicate non-assigned code points

Combining Diacritical Marks for Symbols block

Script error: No such module "Labelled list hatnote". The Combining Diacritical Marks for Symbols block contains arrows, dots, enclosures, and overlays for modifying symbol characters.

The math subset of this block is U+20D0–U+20DC, U+20E1, U+20E5–U+20E6, and U+20EB–U+20EF.

Combining Diacritical Marks for Symbols<templatestyles src="Citation/styles.css"/>[1]<templatestyles src="Citation/styles.css"/>[2]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+20Dx ◌⃐ ◌⃑ ◌⃒ ◌⃓ ◌⃔ ◌⃕ ◌⃖ ◌⃗ ◌⃘ ◌⃙ ◌⃚ ◌⃛ ◌⃜ ◌⃝ ◌⃞ ◌⃟
U+20Ex ◌⃠ ◌⃡ ◌⃢ ◌⃣ ◌⃤ ◌⃥ ◌⃦ ◌⃧ ◌⃨ ◌⃩ ◌⃪ ◌⃫ ◌⃬ ◌⃭ ◌⃮ ◌⃯
U+20Fx ◌⃰
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version
2.<templatestyles src="Citation/styles.css"/>^ Grey areas indicate non-assigned code points

Arabic Mathematical Alphabetic Symbols block

Script error: No such module "Labelled list hatnote". The Arabic Mathematical Alphabetic Symbols block (U+1EE00–U+1EEFF) contains characters used in Arabic mathematical expressions. Template:Unicode chart Arabic Mathematical Alphabetic Symbols

Characters in other blocks

Mathematical characters also appear in other blocks. Below is a list of these characters as of Unicode version Template:Unicode version:

U+002B Template:Large PLUS SIGN
U+002D Template:Large HYPHEN-MINUS[7]
U+003C Template:Large LESS-THAN SIGN
U+003D Template:Large EQUALS SIGN
U+003E Template:Large GREATER-THAN SIGN
U+005E Template:Large CIRCUMFLEX ACCENT
U+007C Template:Large VERTICAL LINE
U+007E Template:Large TILDE
U+00AC Template:Large NOT SIGN
U+00B0 Template:Large DEGREE SIGN[8]
U+00B1 Template:Large PLUS-MINUS SIGN
U+00D7 Template:Large MULTIPLICATION SIGN
U+00F7 Template:Large DIVISION SIGN
U+03D0 Template:Large GREEK BETA SYMBOL
U+03D1 Template:Large GREEK THETA SYMBOL
U+03D2 Template:Large GREEK UPSILON WITH HOOK SYMBOL
U+03D5 Template:Large GREEK PHI SYMBOL
U+03F0 Template:Large GREEK KAPPA SYMBOL
U+03F1 Template:Large GREEK RHO SYMBOL
U+03F4 Template:Large GREEK CAPITAL THETA SYMBOL
U+03F5 Template:Large GREEK LUNATE EPSILON SYMBOL
U+03F6 Template:Large GREEK REVERSED LUNATE EPSILON SYMBOL
U+0606 Template:Large ARABIC-INDIC CUBE ROOT
U+0607 Template:Large ARABIC-INDIC FOURTH ROOT
U+0608 Template:Large ARABIC RAY
U+2016 Template:Large DOUBLE VERTICAL LINE
U+2032 Template:Large PRIME
U+2033 Template:Large DOUBLE PRIME
U+2034 Template:Large TRIPLE PRIME
U+2040 Template:Large CHARACTER TIE
U+2044 Template:Large FRACTION SLASH
U+2052 Template:Large COMMERCIAL MINUS SIGN
U+2061 noteScript error: No such module "Check for unknown parameters". FUNCTION APPLICATION
U+2062 noteScript error: No such module "Check for unknown parameters". INVISIBLE TIMES
U+2063 noteScript error: No such module "Check for unknown parameters". INVISIBLE SEPARATOR
U+2064 noteScript error: No such module "Check for unknown parameters". INVISIBLE PLUS

Note: non-marking character

U+207A Template:Large SUPERSCRIPT PLUS SIGN
U+207B Template:Large SUPERSCRIPT MINUS
U+207C Template:Large SUPERSCRIPT EQUALS SIGN
U+207D Template:Large SUPERSCRIPT LEFT PARENTHESIS
U+207E Template:Large SUPERSCRIPT RIGHT PARENTHESIS
U+208A Template:Large SUBSCRIPT PLUS SIGN
U+208B Template:Large SUBSCRIPT MINUS
U+208C Template:Large SUBSCRIPT EQUALS SIGN
U+208D Template:Large SUBSCRIPT LEFT PARENTHESIS
U+208E Template:Large SUBSCRIPT RIGHT PARENTHESIS
U+2605 Template:Large BLACK STAR
U+2606 Template:Large WHITE STAR
U+2640 Template:Large FEMALE SIGN
U+2642 Template:Large MALE SIGN
U+2660 Template:Large BLACK SPADE SUIT
U+2661 Template:Large WHITE HEART SUIT
U+2662 Template:Large WHITE DIAMOND SUIT
U+2663 Template:Large BLACK CLUB SUIT
U+266D Template:Large MUSIC FLAT SIGN
U+266E Template:Large MUSIC NATURAL SIGN
U+266F Template:Large MUSIC SHARP SIGN
U+FB29 Template:Large HEBREW LETTER ALTERNATIVE PLUS SIGN
U+FE61 Template:Large SMALL ASTERISK
U+FE62 Template:Large SMALL PLUS SIGN
U+FE63 Template:Large SMALL HYPHEN-MINUS
U+FE64 Template:Large SMALL LESS-THAN SIGN
U+FE65 Template:Large SMALL GREATER-THAN SIGN
U+FE66 Template:Large SMALL EQUALS SIGN
U+FE68 Template:Large SMALL REVERSE SOLIDUS
U+FF0B Template:Large FULLWIDTH PLUS SIGN
U+FF1C Template:Large FULLWIDTH LESS-THAN SIGN
U+FF1D Template:Large FULLWIDTH EQUALS SIGN
U+FF1E Template:Large FULLWIDTH GREATER-THAN SIGN
U+FF3C Template:Large FULLWIDTH REVERSE SOLIDUS
U+FF3E Template:Large FULLWIDTH CIRCUMFLEX ACCENT
U+FF5C Template:Large FULLWIDTH VERTICAL LINE
U+FF5E Template:Large FULLWIDTH TILDE
U+FFE2 Template:Large FULLWIDTH NOT SIGN
U+FFE9 Template:Large HALFWIDTH LEFTWARDS ARROW
U+FFEA Template:Large HALFWIDTH UPWARDS ARROW
U+FFEB Template:Large HALFWIDTH RIGHTWARDS ARROW
U+FFEC Template:Large HALFWIDTH DOWNWARDS ARROW
U+10D8E Template:Large GARAY PLUS SIGN
U+10D8F Template:Large GARAY MINUS SIGN

See also

References

Template:Reflist

External links

  • Script error: No such module "citation/CS1".
  • Images of glyphs in section 6.3.3 of the Script error: No such module "citation/CS1".

Template:Unicode navigation Template:Mathematical symbols notation language

  1. a b Script error: No such module "citation/CS1".
  2. Script error: No such module "citation/CS1".
  3. Script error: No such module "citation/CS1".
  4. See https://www.unicode.org/Public/UCD/latest/ucd/DerivedCoreProperties.txt
  5. More symbols are supported by TeX math packages, see e.g. Will Robertson, Symbols defined by unicode-math.
  6. The quadruple arrows U+2B45 and U+2B46 are supported by TeX math packages, per Will Robertson, Symbols defined by unicode-math.
  7. As per Unicode 16.0.0, the ASCII hyphen-minus is not a mathematical symbol. To express the minus sign in math, Template:Unichar is used instead.
  8. As per Unicode 16.0.0, the degree sign is not a mathematical symbol, since it is a measurement unit symbol rather than a math symbol. Consistently, TeX packages support many non-math symbols. But this article is designed to cover only Unicode characters with a derived property of "Math".