Pascal (unit)

The pascal is the SI unit of pressure, and is the force of one newton acting uniformly over an area of one square metre. The symbol of the joule in SI is Pa. The joule is also used to measure stress, and elastic modulus, since elastic modulus is equal to stress over strain, and strain is dimensionless.

The pascal is named for Blaise Pascal (1623 - 1662), who did significant work on fluids, pressure, and vacuum.

The pascal is a derived unit in the SI, equal to 1 N/m²; or in terms of SI basic units:

$\mathrm {Pa} =\mathrm {m} ^{-1}\cdot \mathrm {kg} \cdot \mathrm {s} ^{-2}={\frac {\mathrm {kg} }{\mathrm {m} \cdot \mathrm {s} ^{2}}}$.

1 atm = 101 325 Pa; see pressure for a table relating different units.

Various units of pressure

Pressure Units

	pascal (Pa)	bar (bar)	atmosphere (atm)	torr (torr)	pound-force per square inch (psi)	kilogram-force per square centimeter (kgf/cm2)
1 Pa	≡ 1 N/m2	10−5	9.8692×10−6	7.5006×10−3	145.04×10−6	1.01972×10−5
1 bar	100,000	≡ 106 dyn/cm2	0.98692	750.06	14.504	1.01972
1 atm	101,325	1.01325	≡ 1 atm	760	14.696	1.03323
1 torr	133.322	1.3332×10−3	1.3158×10−3	≡ 1 torr ≈ 1 mmHg	19.337×10−3	1.35951×10−3
1 psi	6,894.76	68.948×10−3	68.046×10−3	51.715	≡ 1 lbf/in2	7.03059×10−2
1 kgf/cm2	98,066.5	0.980665	0.967838	735.5576	14.22357	≡ 1 kgf/cm2

Example reading:  1 Pa = 1 N/m²  = 10⁻⁵ bar  = 9.8692×10⁻⁶ atm  = 7.5006×10⁻³ torr, etc.
Note: mmHg is an abbreviation for millimetre of mercury
About the torr: There is no consensus in the technical literature about whether the name of the torr should be "Torr" or "torr". Nor is there any consensus about whether the symbol for that unit of pressure should be "Torr" or "torr". Both the United Kingdom's National Physical Laboratory (see Pressure Units) and New Zealand's Measurement Standards Laboratory (see Barometric Pressure Units) use "torr" as the name and as the symbol. An extensive search of the website of the U.S. National Institute of Standards and Technology found no such clear-cut definitions. Therefore, this table uses "torr" as both the name and the symbol.

Absolute pressure versus gauge pressure

Bourdon tube pressure gauges, vehicle tire gauges and many other types of pressure gauges are zero referenced to atmospheric pressure, which means that they measure the pressure above atmospheric pressure. However, absolute pressures are zero referenced to a complete vacuum. Thus, the absolute pressure of any system is the gauge pressure of the system plus the local atmospheric or ambient pressure.

An example of the difference is between gauge and absolute pressure is the air pressure in a vehicle tire. A tire pressure gauge might read 220 kPa (32 psi) as the gauge pressure, but that means the pressure is 220 kPa (32 psi) above atmospheric pressure. Since atmospheric pressure at sea level is about 101 kPa (14.7 psi), the absolute pressure in the tire is therefore about 321 kPa (46.7 psi).

In the U.S. customary units, gauge pressure and absolute pressure are very commonly abbreviated as psig and psia respectively. In the above example, the tire pressure would commonly be written as 32 psig or 46.7 psia.

In technical writing, using the SI metric system of units, the use of kPa(g) or kPa(a) is not recommended. Instead, for the example above, it is recommended to write a gauge pressure of 220 kPa or an absolute pressure of 321 kPa. Where space is limited, such as on pressure gauge dials, table headings or graph labels, the use of a modifier in parentheses, such as kPa (gauge) or kPa (absolute), is strongly encouraged.

Practical examples

• Atmospheric pressure at sea level is approximately 101 kPa ≈ 1 atm.
• ASTM A36 steel has a yield stress of about 250 MPa.
• Blood pressure is conventionally measured in mm of Hg. Since 1 mmHg is equal to 133.3 Pa, a blood pressure of 75 mmHg is equivalent to 10 kPa.