# Pascal (unit)

The pascal (symbol: Pa) is the unit of pressure in the International System of Units (SI). It is also used to quantify internal pressure, stress, Young's modulus, and ultimate tensile strength. The unit, named after Blaise Pascal, is a SI coherent derived unit defined as one newton per square metre (N/m2).[1] It is also equivalent to 10 barye (10 Ba) in the CGS system. Common multiple units of the pascal are the hectopascal (1 hPa = 100 Pa), which is equal to one millibar, and the kilopascal (1 kPa = 1000 Pa), which is equal to one centibar.

pascal
A pressure gauge reading in psi (red scale) and kPa (black scale)
General information
Unit systemSI
Unit ofpressure or stress
SymbolPa
Named afterBlaise Pascal
Conversions
1 Pa in ...... is equal to ...
SI base units:   kgm−1s−2
US customary units:   1.45038×10−4 psi
atmosphere:   9.86923×10−6 atm
bar:   10−5 bar
barye (CGS unit)   10 Ba

The unit of measurement called standard atmosphere (atm) is defined as 101,325 Pa.[2]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 hPa. Reports in the United States typically use inches of mercury[3] or millibars (hectopascals).[4][5] In Canada these reports are given in kilopascals.[6]

## 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/m2) by the 14th General Conference on Weights and Measures in 1971.[7][8]

## Definition

The pascal can be expressed using SI derived units, or alternatively solely SI base units, as:

${\displaystyle {\rm {1~Pa=1~{\frac {N}{m^{2}}}=1~{\frac {kg}{m{\cdot }s^{2}}}=1~{\frac {J}{m^{3}}}}}}$

where N is the newton, m is the metre, kg is the kilogram, s is the second, and J is the joule.[9]

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

## Standard units

The unit of measurement called an atmosphere or a standard atmosphere (atm) is 101325 Pa (101.325 kPa).[10] 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 5024 (petroleum). In contrast, International Union of Pure and Applied Chemistry (IUPAC) recommends the use of 100 kPa as a standard pressure when reporting the properties of substances.[11]

Unicode has dedicated code-points U+33A9 SQUARE PA and U+33AA SQUARE KPA in the CJK Compatibility block, but these exist only for backward-compatibility with some older ideographic character-sets and are therefore deprecated.[12][13]

## 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.

Geophysicists use the gigapascal (GPa) in measuring or calculating tectonic stresses and pressures within the Earth.

Medical elastography measures tissue stiffness non-invasively with 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 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.

Approximate Young's modulus for common substances[14]
Material Young's modulus
(GPa)
Nylon 6 2–4
Hemp fibre 35
Aluminium 69
Tooth enamel 83
Copper 117
Structural steel 200
Diamond 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, magnetic, and 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 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.

The airtightness of buildings is measured at 50 Pa.[15]

In medicine, blood pressure is measured in millimeters of mercury (mmHg, very close to one Torr). The normal adult blood pressure is less than 120 mmHg systolic BP (SBP) and less than 80 mmHg diastolic BP (DBP).[16] Convert mmHg to SI units as follows: 1 mmHg = 0.13332 kPa. Hence normal blood pressure in SI units is less than 16.0 kPa SBP and less than 10.7 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

The units of atmospheric pressure commonly used in meteorology were formerly the bar, (100,000 Pa) which was close to the average air pressure on Earth, and the millibar. Since the introduction of SI units, meteorologists generally measure pressures in hectopascals (hPa) unit, equal to 100 pascals or 1 millibar.[17][18][19][20][21][22][23] Exceptions include Canada, which uses kilopascals (kPa). In many other fields of science, prefixes that are a power of 1000 are preferred, which excludes the hectopascal from use.[24][25]

Many countries also use millibars. In practically all other fields, the kilopascal (1000 pascals) is used instead.[26]

## Multiples and submultiples

Decimal multiples and sub-multiples are formed using standard SI units.

Multiples Sub-multiples
Value Name Symbol Value Name Symbol
101 Pa decapascal daPa 10−1 Pa decipascal dPa
102 Pa hectopascal hPa 10−2 Pa centipascal cPa
103 Pa kilopascal kPa 10−3 Pa millipascal mPa
105 Pa bar (non-SI unit) bar 10−6 Pa micropascal μPa
106 Pa megapascal MPa 10−9 Pa nanopascal nPa
109 Pa gigapascal GPa 10−12 Pa picopascal pPa
1012 Pa terapascal TPa 10−15 Pa femtopascal fPa
1015 Pa petapascal PPa 10−18 Pa attopascal aPa
1018 Pa exapascal EPa 10−21 Pa zeptopascal zPa
1021 Pa zettapascal ZPa 10−24 Pa yoctopascal yPa
1024 Pa yottapascal YPa 10−27Pa rontopascal rPa
1027 Pa ronnapascal RPa 10−30 Pa quectopascal qPa
1030 Pa quettapascal QPa

## References

1. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 118, ISBN 92-822-2213-6, archived (PDF) from the original on 4 June 2021, retrieved 16 December 2021
2. ^ "Definition of the standard atmosphere". BIPM. Retrieved 16 February 2015.
3. ^
4. ^
5. ^
6. ^ Canada, Environment (16 April 2013). "Canadian Weather - Environment Canada". weather.gc.ca.
7. ^ bipm.fr Archived 30 June 2007 at the Wayback Machine
8. ^
9. ^ Table 3 (Section 2.2.2) Archived 18 June 2007 at the Wayback Machine, SI Brochure, International Bureau of Weights and Measures
10. ^ "Resolution 4 of the 10th meeting of the CGPM". Conférence Générale des Poids et Mesures. 1954. Retrieved 5 April 2010.
11. ^ IUPAC.org, Gold Book, Standard Pressure
12. ^ "CJK Compatibility" (PDF). 2015. Retrieved 21 February 2016.
13. ^ The Unicode Standard, Version 8.0.0. Mountain View, CA: The Unicode Consortium. 2015. ISBN 978-1-936213-10-8. Retrieved 21 February 2016.
14. ^ "Tensile Modulus – Modulus of Elasticity or Young's Modulus – for some common Materials". Retrieved 16 February 2015.
15. ^ "Chapter 7 ResNet Standards: ResNet National Standard for Home Energy Audits" (PDF). ResNet. 2010. Archived from the original (PDF) on 26 July 2011. Retrieved 3 March 2011.
16. ^ "BP Guideline | Target:BP". American Heart Association. Retrieved 18 May 2020.
17. ^ "KNMI – Weer – Waarnemingen". Retrieved 4 December 2016.
18. ^ "Comment convertir la pression? – IRM". Retrieved 4 December 2016.
19. ^ "DWD". Archived from the original on 10 February 2008. Retrieved 20 December 2006.
20. ^ "Japan Meteorological Agency – Weather Maps". Retrieved 4 December 2016.
21. ^ "MDD". Archived from the original on 6 May 2006.
22. ^ NOAA
23. ^ United Kingdom, Met Office. "Key to symbols and terms". Retrieved 4 December 2016.
24. ^ "CTV News, weather; current conditions in Montreal". Archived from the original on 4 June 2011.
25. ^ Canada, Environment. "Montréal, QC – 7 Day Forecast – Environment Canada". Archived from the original on 30 November 2017. Retrieved 4 December 2016.
26. ^ Ambler Thompson (Editor) Guide for the Use of the International System of Units (SI) (rev. ): The ..., p. 66, at Google Books