View source for Pascal (unit)

{{Short description|SI derived unit of pressure}}
{{redirect|Pascals|other uses|Pascal (disambiguation)}}
{{Redirect|Hectopascal|the song|Hectopascal (song)}}
{{Use dmy dates|date=December 2020}}
{{Infobox Unit
| bgcolour =
| name = pascal
| image = [[File:Psidial.jpg|250px]]
| caption = A [[pressure gauge]] reading in [[Pounds per square inch|psi]] (red scale) and kPa (black scale)
| standard = [[SI]]
| quantity = [[pressure]] or [[Stress (physics)|stress]]
| symbol = Pa
| namedafter = [[Blaise Pascal]]
| units1 = [[SI base unit]]s:
| inunits1 = [[Kilogram|kg]]&sdot;[[metre|m]]<sup>−1</sup>&sdot;[[second|s]]<sup>−2</sup>
| units2 = [[US customary units]]:
| inunits2 = {{cvt|1e0|Pa|psi|sigfig=6|disp=out|lk=out|comma=gaps}}
| units3 = [[Atmosphere (unit)|atmosphere]]:
| inunits3 = {{convert|1|Pa|atm|sigfig=6|disp=out|comma=gaps}}
| units4 = [[Bar (unit)|bar]]:
| inunits4 = 10<sup>−5</sup> bar
| units5 = [[barye]] (CGS unit)
| inunits5 = 10 Ba
}}

The '''pascal''' (symbol: '''Pa''') is the unit of [[pressure]] in the [[International System of Units|International System of Units (SI)]]. It is also used to quantify [[internal pressure]], [[stress (physics)|stress]], [[Young's modulus]], and [[ultimate tensile strength]]. The unit, named after [[Blaise Pascal]], is an [[SI coherent derived unit]] defined as one [[Newton (unit)|newton]] per [[square metre]] (N/m<sup>2</sup>).<ref>{{SIbrochure8th|page=118}}</ref> It is also equivalent to 10 [[barye]] (10 Ba) in the [[Centimetre–gram–second system of units|CGS]] system. Common multiple units of the pascal are the hectopascal (1&nbsp;hPa = 100&nbsp;Pa), which is equal to one [[Bar (unit)#Usage|millibar]], and the kilopascal (1&nbsp;kPa = 1000&nbsp;Pa), which is equal to one centibar.

The unit of measurement called ''[[Standard atmosphere (unit)|standard atmosphere (atm)]]'' is defined as {{val|101,325|u=Pa}}.<!-- not kPa - the comma here separates the thousands in 101325 per [[WP:DIGITS]], it's not a decimal separator --><ref name="BIPM">{{cite web|url=http://www.bipm.org/jsp/en/ViewCGPMResolution.jsp?CGPM=10&RES=4 |publisher=[[BIPM]] |title=Definition of the standard atmosphere|access-date=2015-02-16}}</ref>
[[Meteorology|Meteorological]] observations typically report [[atmospheric pressure]] in hectopascals per the recommendation of the [[World Meteorological Organization]], thus a standard atmosphere (atm) or typical sea-level air pressure is about 1013&nbsp;hPa. Reports in the United States typically use [[inches of mercury]]<ref>{{Cite web|url=https://w1.weather.gov/glossary/index.php?word=inches+of+mercury|title=National Weather Service glossary page on inches of mercury}}</ref> or millibars (hectopascals).<ref>{{Cite web|url=https://www.wpc.ncep.noaa.gov/sfc/90fwbg.gif|title=US government atmospheric pressure map}}</ref><ref>{{Cite web|url=https://s.w-x.co/util/image/map/WEB_Current_Weather_Map_1280x720.jpg?v=ap&w=1280&h=720&api=7db9fe61-7414-47b5-9871-e17d87b8b6a0|title=The Weather Channel}}</ref> In Canada, these reports are given in kilopascals.<ref>{{Cite web|url=https://weather.gc.ca/canada_e.html|title=Canadian Weather – Environment Canada|first=Environment|last=Canada|date=16 April 2013|website=weather.gc.ca}}</ref>

== Etymology ==
The unit is named after [[Blaise Pascal]], noted for his contributions to hydrodynamics and hydrostatics, and experiments with a [[barometer]]. The name ''pascal'' was adopted for the SI unit newton per square metre (N/m<sup>2</sup>) by the 14th [[General Conference on Weights and Measures]] in 1971.<ref>[http://www.bipm.fr/en/convention/cgpm/14/pascal-siemens.html bipm.fr]. {{webarchive|url=https://web.archive.org/web/20070630020548/http://www.bipm.fr/en/convention/cgpm/14/pascal-siemens.html |date=30 June 2007 }}.</ref><ref name="CGPM14">[http://www.bipm.org/utils/common/pdf/CGPM/CGPM14.pdf#page=78 Minutes of the 14. General Conference on Weights and Measures], 1971, p. 78.</ref>

== Definition ==
The pascal can be expressed using [[SI derived unit]]s, or alternatively solely [[SI base unit]]s, as:
: <math>{\rm 1~Pa = 1~N/m^2 =  1~kg/(m {\cdot} s^2) = 1~J/m^3 }</math>
where N is the [[Newton (unit)|newton]], m is the [[metre]], kg is the [[kilogram]], s is the [[second]], and J is the [[joule]].<ref>[http://www.bipm.org/en/si/si_brochure/chapter2/2-2/table3.html Table 3 (Section 2.2.2)]. {{webarchive|url=https://web.archive.org/web/20070618123613/http://www.bipm.org/en/si/si_brochure/chapter2/2-2/table3.html |date=18 June 2007 }}. ''SI Brochure''. [[International Bureau of Weights and Measures]].</ref>

One pascal is the pressure exerted by a force of one newton perpendicularly upon an area of one square metre.

== Standard units ==
The unit of measurement called an [[standard atmosphere (unit)|atmosphere or a standard atmosphere]] (atm) is {{convert|101325|Pa|kPa|abbr=on|comma=gaps}}.<ref>{{cite web |url=http://www.bipm.org/jsp/en/ViewCGPMResolution.jsp?CGPM=10&RES=4 |title = Resolution 4 of the 10th meeting of the CGPM |publisher=[[General Conference on Weights and Measures|Conférence Générale des Poids et Mesures]] |year = 1954 |access-date = 2010-04-05 |archive-url=https://web.archive.org/web/20210330142301/http://www.bipm.org/jsp/en/ViewCGPMResolution.jsp?CGPM=10&RES=4 |archive-date=30 March 2021 |url-status=dead }}</ref> This value is often used as a reference pressure and specified as such in some national and international standards, such as the [[International Organization for Standardization]]'s ISO 2787 (pneumatic tools and compressors), [[ISO 2533]] (aerospace) and ISO&nbsp;5024 (petroleum). In contrast, [[International Union of Pure and Applied Chemistry]] (IUPAC) recommends the use of 100&nbsp;kPa as a standard pressure when reporting the properties of substances.<ref>IUPAC.org, Gold Book, [http://goldbook.iupac.org/S05921.html ''Standard Pressure'']</ref>

[[Unicode]] has dedicated code-points {{Unichar|33a9|Square Pa}} and {{Unichar|33AA|Square kPa}} in the [[CJK Compatibility]] block, but these exist only for backward-compatibility with some older ideographic character-sets and are therefore [[deprecate]]d.<ref>{{cite web|url=https://www.unicode.org/charts/PDF/U3300.pdf|title=CJK Compatibility|access-date=2016-02-21|date=2015}}</ref><ref>{{cite book|publisher=The Unicode Consortium|title=The Unicode Standard, Version 8.0.0|location=Mountain View, CA|date=2015|isbn=978-1-936213-10-8|url=https://www.unicode.org/versions/Unicode8.0.0|access-date=2016-02-21}}</ref>

== Uses ==
The pascal (Pa) or kilopascal (kPa) as a unit of pressure measurement is widely used throughout the world and has largely replaced the [[pounds per square inch]] (psi) unit, except in some countries that still use the [[imperial measurement system]] or the [[US customary system]], including the United States.

[[Geophysics|Geophysicists]] use the gigapascal (GPa) in measuring or calculating [[Tectonophysics|tectonic stresses]] and pressures within the [[Earth]].

Medical [[elastography]] measures tissue stiffness non-invasively with [[medical ultrasonography|ultrasound]] or [[magnetic resonance imaging]], and often displays the [[Young's modulus]] or [[shear modulus]] of tissue in kilopascals.

In [[materials science]] and [[engineering]], the pascal measures the [[Young's modulus|stiffness]], [[tensile strength]] and [[compressive strength]] of materials. In engineering the megapascal (MPa) is the preferred unit for these uses, because the pascal represents a very small quantity.

{| class="wikitable"
|+ Approximate Young's modulus for common substances<ref>{{cite web|url=http://www.engineeringtoolbox.com/young-modulus-d_417.html|title=Tensile Modulus – Modulus of Elasticity or Young's Modulus – for some common Materials|access-date=2015-02-16}}</ref>
! Material !! Young's modulus {{br}}(GPa)
|-
| [[Nylon 6]] ||align="right"| 2–4 
|-
| [[Hemp]] fibre ||align="right"| 35 
|-
| [[Aluminium]] ||align="right"| 69 
|-
| [[Tooth enamel]] ||align="right"| 83 
|-
| [[Copper]] ||align="right"| 117 
|-
| Structural [[steel]] ||align="right"| 200 
|-
| [[Diamond]] ||align="right"| 1220 
|}

The pascal is also equivalent to the SI unit of [[energy density]], the joule per cubic metre. This applies not only to the thermodynamics of pressurised gases, but also to the energy density of [[electric potential energy|electric]], [[magnetic field#Energy stored in magnetic fields|magnetic]], and [[gravitational energy|gravitational]] fields.

The pascal is used to measure [[sound pressure]]. [[Loudness]] is the subjective experience of sound pressure and is measured as a [[Sound pressure#Sound pressure level|sound pressure level]] (SPL) on a logarithmic scale of the sound pressure relative to some reference pressure. For sound in air, a pressure of 20 μPa is considered to be at the [[threshold of hearing]] for humans and is a common reference pressure, so that its SPL is zero.

[[Blower door|The airtightness of buildings]] is measured at 50&nbsp;Pa.<ref>
{{cite web
 |url         = http://www.resnet.us/hotnews/revised_chapter_seven_final_9-16-10.pdf
 |title       = Chapter 7 ResNet Standards: ResNet National Standard for Home Energy Audits
 |publisher   = ResNet
 |year        = 2010
 |access-date  = 2011-03-03
 |url-status     = dead
 |archive-url  = https://web.archive.org/web/20110726045004/http://www.resnet.us/hotnews/revised_chapter_seven_final_9-16-10.pdf
 |archive-date = 26 July 2011
}}</ref>

In medicine, [[Blood pressure|blood pressure]] is measured in [[Millimetre of mercury|millimeters of mercury]] (mmHg, very close to one [[Torr]]).  The normal adult blood pressure is less than 120&nbsp;mmHg systolic BP (SBP) and less than 80&nbsp;mmHg diastolic BP (DBP).<ref>{{cite web |title=BP Guideline {{!}} Target:BP |url=https://targetbp.org/guidelines17/ |website=American Heart Association |access-date=18 May 2020}}</ref> Convert mmHg to SI units as follows: {{nowrap|1= 1 mmHg = {{val|0.13332|u=kPa}}}}. Hence the normal blood pressure in SI units is less than 16.0&nbsp;kPa SBP and less than 10.7&nbsp;kPa DBP. These values are similar to the pressure of water column of average human height; so pressure has to be measured on arm roughly at the level of the heart.

=== Hectopascal and millibar units ===
{{main|Bar (unit)}}
The units of [[Atmospheric pressure|atmospheric pressure]] commonly used in [[meteorology]] were formerly the [[Bar (unit)|bar]] ({{val|100,000|u=Pa}}), which is close to the average air pressure on Earth, and the millibar. Since the introduction of [[International System of Units|SI units]], meteorologists generally measure atmospheric pressure in hectopascals (hPa), equal to 100 pascals or 1 millibar.<ref>{{cite web|url=http://www.knmi.nl/actueel/|title=KNMI – Weer – Waarnemingen|access-date=4 December 2016}}</ref><ref>{{cite web|url=http://www.meteo.be/meteo/view/fr/68771-FAQ%20sur%20le%20temps.html?view=195695|title=Comment convertir la pression? – IRM|access-date=4 December 2016}}</ref><ref>{{Cite web|url=http://www.dwd.de/de/WundK/W_aktuell/Beobachtungen.htm|title=DWD|access-date=20 December 2006|archive-url=https://web.archive.org/web/20080210040845/http://www.dwd.de/de/WundK/W_aktuell/Beobachtungen.htm|archive-date=10 February 2008|url-status=dead}}</ref><ref>{{cite web|url=http://www.jma.go.jp/en/g3/index.html|title=Japan Meteorological Agency – Weather Maps|access-date=4 December 2016}}</ref><ref>{{Cite web|url=http://www.meteoam.it/modules.php?name=analisiPrevisioniSuolo|archive-url=https://web.archive.org/web/20060506192242/http://www.meteoam.it/modules.php?name=analisiPrevisioniSuolo|url-status=dead|title=MDD|archive-date=6 May 2006}}</ref><ref>[http://weather.noaa.gov/weather/current/KDCA.html NOAA]</ref><ref>{{cite web|url=http://www.metoffice.gov.uk/guide/weather/symbols#units|title=Key to symbols and terms|first=Met Office|last=United Kingdom|access-date=4 December 2016}}</ref> Exceptions include Canada, which uses kilopascals (kPa). In many other fields of science, prefixes that are a power of 1000 are preferred, which theoretically excludes hectopascal from use.<ref>{{Cite web|url=http://www.ctv.ca/servlet/HTMLTemplate/!ctvDynNews/Weather/Weather?City=Montreal|archive-url=https://web.archive.org/web/20110604131321/http://www.ctv.ca/servlet/HTMLTemplate/!ctvDynNews/Weather/Weather?City=Montreal|url-status=dead|title=CTV News, weather; current conditions in Montreal|archive-date=4 June 2011}}</ref><ref>{{cite web|url=http://www.weatheroffice.gc.ca/city/pages/qc-147_metric_e.html|title=Montréal, QC – 7 Day Forecast – Environment Canada|first=Environment|last=Canada|access-date=4 December 2016|archive-date=30 November 2017|archive-url=https://web.archive.org/web/20171130163853/http://www.weatheroffice.gc.ca/city/pages/qc-147_metric_e.html|url-status=dead}}</ref>

Many countries still use millibars to measure atmospheric pressure. In practically all other fields, the kilopascal is used instead.<ref>Ambler Thompson (Editor) {{google books|pTw-SCI7EkoC|Guide for the Use of the International System of Units (SI) (rev. ): The ...|page=66}}</ref>

== Multiples and submultiples ==
Decimal multiples and submultiples are formed using standard [[metric prefixes]].
{| class="wikitable"
|+
! colspan="3" |Multiples
! colspan="3" |Submultiples
|-
!Value
!Name
!Symbol
!Value
!Name
!Symbol
|-
|10<sup>1</sup> Pa
|decapascal
|daPa
|10<sup>−1</sup> Pa
|decipascal
|dPa
|-
|10<sup>2</sup> Pa
|hectopascal
|hPa
|10<sup>−2</sup> Pa
|centipascal
|cPa
|-
|10<sup>3</sup> Pa
|kilopascal
|kPa
|10<sup>−3</sup> Pa
|millipascal
|mPa
|-
|10<sup>5</sup> Pa
|bar (non-SI unit)
|bar
|
|
|
|-
|10<sup>6</sup> Pa
|megapascal
|MPa
|10<sup>−6</sup> Pa
|micropascal
|μPa
|-
|10<sup>9</sup> Pa
|gigapascal
|GPa
|10<sup>−9</sup> Pa
|nanopascal
|nPa
|-
|10<sup>12</sup> Pa
|terapascal
|TPa
|10<sup>−12</sup> Pa
|picopascal
|pPa
|-
|10<sup>15</sup> Pa
|petapascal
|PPa
|10<sup>−15</sup> Pa
|femtopascal
|fPa
|-
|10<sup>18</sup> Pa
|exapascal
|EPa
|10<sup>−18</sup> Pa
|attopascal
|aPa
|-
|10<sup>21</sup> Pa
|zettapascal
|ZPa
|10<sup>−21</sup> Pa
|zeptopascal
|zPa
|-
|10<sup>24</sup> Pa
|yottapascal
|YPa
|10<sup>−24</sup> Pa
|yoctopascal
|yPa
|-
|10<sup>27</sup> Pa
|ronnapascal
|RPa
|10<sup>−27</sup>Pa
|rontopascal
|rPa
|-
|10<sup>30</sup> Pa
|quettapascal
|QPa
|10<sup>−30</sup> Pa
|quectopascal
|qPa
|}

== See also ==
* [[Atmospheric pressure]] which gives the usage of the hbar and the mbar
* [[Centimetre of water]]
* [[Meteorology]]
* [[Metric prefix]]
* [[Orders of magnitude (pressure)]]
* [[Pascal's law]]
* [[Pressure measurement]]

== References ==
{{reflist|30em}}

{{SI units}}

[[Category:SI derived units]]
[[Category:Units of pressure]]
[[Category:Blaise Pascal]]