Units of Pressure

07th Aug 2019 @ 30 min read

What is pressure? The pressure is the force to perpendicular to a unit surface. In other words, it is the perpendicular force per unit area. The pressure is a scalar quantity and has the dimension of the force divided by the area.

$P =\frac{F}{A}$

The pressure is a widely used quantity; it is found in physics, chemistry, engineering, and biology. Because of the wide usage of pressure, it has adopted various units to express it. And it is necessary for us to know the relationship between various units of pressure.

Pressure Converter

Enter a value and choose desired pressure units.

List of Important Pressure Units

The table below list important units of pressure with its symbols.

Table 1: Units of Pressure
Symbol	Unit	Comment
atm	atmosphere	a standard unit of pressure
at	technical atmosphere	It is a non-SI unit and a unit value of it is equivalent to 1 kilogram-force per square centimetre
N m⁻² or Pa	newton per square metre or Pascal	the SI unit of pressure
µPa	micropascal	a metric unit, derived from the pascal
hPa	hectopascal	a metric unit, derived from the pascal
MPa	megapascal	a metric unit, derived from the pascal
GPa	gigapascal	a metric unit, derived from the pascal
bar	bar	a non-SI metric unit
mbar	millibar	a non-SI metric unit, derived from the bar
dbar	decibar	a non-SI metric unit, derived from the bar
Torr	torr	a non-SI standard unit of pressure
mmHg	millimetre of mercury	a manometric unit based on mercury
cmHg	centimetre of mercury	a manometric unit based on mercury
inHg	inch of mercury	a manometric unit based on mercury
ftHg	foot of mercury	a manometric unit based on mercury
mmH₂O	millimetre of water	a manometric unit based on water
cmH₂O	centimetre of water	a manometric unit based on water
inH₂O	inch of water	a manometric unit based on water
ftH₂O	foot of water	a manometric unit based on water
msw	metre sea water	an underwater diving unit
fsw	foot sea water	an underwater diving unit

Other Units of Pressure

The other nonstandard units of pressure are listed below.

Table 2: List of Nonstandard Units of Pressure
Symbol	Unit	Comment
kg_f cm⁻²	kilogram-force per square centimetre	a gravitational metric unit
g_f cm⁻²	gram-force per square centimetre	a gravitational metric unit
dyne cm⁻² or Ba	barye	the CGS unit of pressure
psi or lb_f in⁻²	pound per square inch or pound-force per square inch	the most used imperial unit of pressure
ksi	kilopound per square inch	an imperial unit of pressure, derived from psi
Mpsi	megapound per square inch	an imperial unit of pressure, derived from psi
lb_f ft⁻²	pound-force per square foot	an imperial unit of pressure
kip in⁻²	kip per square inch	an imperial unit of pressure, derived from psi
oz_f in⁻²	ounce-force per square inch	a US customary unit
oz_f ft⁻²	ounce-force per square foot	an imperial unit of pressure
pdl in⁻²	poundal per square inch	an imperial unit of pressure
pdl ft⁻²	poundal per square foot	an imperial unit of pressure
tf m⁻²	tonne-force per square metre	a metric unit based on tonne
tf cm⁻²	tonne-force per square centimetre	a metric unit based on tonne
tf in⁻²	long ton-force per square inch	a UK (imperial) unit based on ton
tf ft⁻²	long ton-force per square foot	a UK (imperial) unit based on ton
tf in⁻²	short ton-force per square inch	a US (customary) unit based on ton
tf ft⁻²	short ton-force per square foot	a US (customary) unit based on ton
pz	pieze	a unit in metre-tonne-second system

Conversion Table

The conversion table below gives the relationship between some important units of pressure.

Table 3: Pressure Units Conversion Table
Units	Pa	bar	Torr	psi	at (≡ kg_f cm⁻²)	atm
1 Pa	1	1 × 10⁻⁵^†	7.500 62 × 10⁻³	1.450 38 × 10⁻⁴	1.019 72 × 10⁻⁵	9.869 23 × 10⁻⁶
1 bar	1 × 10⁵^†	1	750.062	14.503 8	1.019 72	0.986 923
1 Torr	133.322	1.333 22 × 10⁻³	1	1.933 68 × 10⁻²	1.359 51 × 10⁻³	1.315 79 × 10⁻³
1 psi	6 894.76	6.894 76 × 10⁻²	51.714 9	1	7.030 70 × 10⁻²	6.804 60 × 10⁻²
1 at (≡ kg_f cm⁻²)	98 066.5^†	0.980 665^†	735.559	14.223 3	1	0.967 841
1 atm	101 325^†	1.013 25^†	760^†	14.695 9	1.033 23	1
Note: The above values are accurate up to six significant digits, and the values marked by † are exact values.

How to use the conversion table?

The above table is divided into units and values; the values are conversion factors. The first row and the first column represent the units and the remaining cells are the values. A unit in the first column has a unit value (e.g., 1 Pa, 1 bar) while a unit in the first row have a value of its conversion factor.

Consider an example of Torr to Pa.

$1 \,\text{Torr} =133.322 \,\text{Pa}$

In the above equation, 1 Torr is the unit from the first column has a unit value, and the right-hand side of the equation, 133.322 Pa, is formed from the first-row unit and the conversion factor.

$\underbrace{1 \,\text{Torr}}_{\text{1}^\text{st} \,\text{column}} = \underbrace{133.322}_{\text{conversion} \, \text{factor}} \,\underbrace{\text{Pa}}_{\text{1}^\text{st} \,\text{row}}$

Similarly for Pa to Torr,

$\underbrace{1 \,\text{Pa}}_{\text{1}^\text{st} \,\text{column}} =\underbrace{7.500\,62 \times 10^{-3}}_{\text{conversion} \,\text{factor}} \,\underbrace{\text{Torr}}_{\text{1}^\text{st} \,\text{row}}$

Conversion Scales

mmHg to atm

psi to bar

psi to kPa

Pascal

The SI unit of pressure is the pascal (Pa) or the newton per square metre (N m⁻²) or (kg m⁻¹ s⁻²). The unit pascal is christened after French mathematician Blaise Pascal. One pascal is a force of one-newton perpendicular to a surface of one square metre.

The pascal is the recognised SI derived unit of pressure and can also be expressed in terms of SI base units.

$1\,\text{Pa} =\frac{1\,\text{N}}{1 \,\text{m}^{2}} =\frac{\text{kg}\,\text{m}\,\text{s}^{-2}}{1 \,\text{m}^{2}} =\text{kg} \,\text{m}^{-1}\,\text{s}^{-2}$

The pascal can also be expressed in terms of the joule, which is the SI unit of energy.

$1 \,\text{Pa} =\frac{1 \,\text{N}}{1 \,\text{m}^{2}} =\frac{1 \,\text{N} \,\text{m}}{1 \,\text{m}^{3}} =\frac{\text{J}}{\text{m}^3}$

The International Union of Pure and Applied Chemistry recommends 1 × 10⁵ Pa as a reference standard pressure.

The common derivatives of the pascal are the micropascal, the hectopascal, the kilopascal, the megapascal, and the gigapascal. The relationship among all follows as:

$1 \,\text{Pa} &=1 \times 10^{3} \mu\text{Pa} \\ &=1 \times 10^{-2} \,\text{hPa} \\ &=1 \times 10^{-3} \,\text{kPa} \\ &=1 \times 10^{-6} \,\text{MPa} \\ &=1 \times 10^{-9} \,\text{GPa}$

The pascal is a very small unit, the micropascal is the smallest among them. The kilopascal is a widely used unit often atmospheric pressures are reported in kPa. The mechanical quantities like Young’s modulus, shear modulus, tensile strength, stiffness are displayed in the kilopascal (kPa) and the megapascal (MPa). The gigapascal (GPa) is preferred by geophysicists since the stresses and pressures within the Earth are in a large order of magnitude.

The hectopascal (hPa) is used by meteorologists to measure the pressure of air.

Note: one hectopascal is equivalent to one minibar.

$1 \,\text{hPa}= 1 \,\text{mbar}$

Bar

The bar is another common unit used to measure pressure. It is a metric non-SI unit and defined exactly to 1 × 10⁵ Pa.

$1 \,\text{bar}=100 \,00 \,\text{Pa}$

Figure 5: Pressure Gauge Scaled in the bar

The bar is slightly less than an atomophere (1 bar ≈ 0.986 923 atm).

The most common derived units of the bar are the millibar (mbar), the centibar (cbar), the decibar (dbar) and the kilobar (kbar).

$1 \,\text{bar} &= 1 \times 10^{3} \,\text{mbar} \\ &= 1 \times 10^{2} \,\text{cbar} \\ &= 10 \,\text{dbar} \\ &= 1 \times 10^{-3} \,\text{kbar}$

The bar was introduced by Norwegian scientist Vilhelm Friman Koren Bjerknes. He was a well-known meteorologist and contributed to modern weather forecasting. Since then, the bar, precisely the minibar, remains a widely used unit in meteorology. The atmospheric pressures are reported mostly reported in mbar. Some scientists use the hectopascal hPa, the bar equivalent in SI, as a standard unit.

Figure 6: Pressures in the map is reported in mbar.

The bar is also an accepted unit in oceanography, engineering instead of the pascal.

Standard atmosphere

The standard atmosphere or one atmosphere (atm) is a standard pressure defined as 101 325 Pa. It is a standard reference pressure recommended by the National Institute of Standards and Technology (NIST). It is a widely used unit of pressure. The value of 1 atm approximately equals the atmospheric pressure at sea level.

The relation between 1 atm and other units are as follows:

$1\, \text{atm} &= 101 \,325 \,\text{Pa} \\ &= 101.325 \,\text{kPa} \\ &= 1.013 \,25 \,\text{bar} \\ &= 760 \,\text{Torr} \\ &= 1.013 \,25 \,\text{bar} \\ &= 14.695 \,9 \,\text{psi} \\ &= 1.033 \,23 \,\text{kg}_\text{f} \,\text{cm}^{-2} \\ &= 1 \,013 \,250 \,\text{dyne} \,\text{cm}^{-2}$

Millimetre of Mercury (mmHg)

The millimetre of mercury is a common unit of pressure. It is a manometric unit based on mercury. One millimetre of mercury is defined as the pressure exerted by one millimetre of a column of mercury at 0 ℃.

Figure 7: Mercury Manometer
[Image Source: Wikimedia]

$1 \,\text{mmHg} &= 1 \,\text{mm} \,\rho g \\ &= 10^{-3} \,\text{m} \times 13\, 595.1 \,\text{kg} \,\text{m}^{-3} \times9.806 \,65 \,\text{m} \,\text{s}^{-2} \\ &\approx 133.322 \,\text{Pa}$

It is often used in aviation, medicine, meteorology, vacuum system, refrigeration. Blood pressure is mostly measured by a sphygmomanometer, which is a mercury-based manometer.

Other related units to it are the centimetre of mercury (cmHg), the foot of water (ftHg), the inch of water (inHg).

$1 \,\text{mmHg} &=0.1 \,\text{cmHg} \\ &=0.003 \,280 \,83 \,\text{ftHg} \\ &=0.039 \,370 \,1 \,\text{inHg}$

mmHg vs Torr

There is a small difference between mmHg and Torr. This difference is very small and can be ignored for practical purposes. The table below distinguishes both.

Table 4: Difference between mmHg and Torr
mmHg	Torr
1 mmHg is defined as the pressure exerted by 1 mm of a column of mercury.	1 Torr is defined exactly equal to ¹⁄₇₆₀ of one standard atmosphere.
1 atm ≈ 759.999 891 7 mmHg	1 atm = 760 Torr

As we can see from the above table, the difference between mmHg and Torr is marginal, and it will not affect the practical calculations.

$1 \,\text{mmHg} &=1.000 \,000 \,142 \,466 \,32 \,\text{Torr} \\ &\approx 1 \,\text{Torr}$

Centimetre of Water (cmH₂O)

The centimetre of water (cmH₂O) is a unit of pressure calculated from a column of water. One centimetre of water is the pressure exerted by one centimetre of a column of water at 4 ℃.

$1 \,\text{cmH}_2\text{O} &= 1 \,\text{cm} \,\rho g \\ &= 10^{-2} \,\text{m} \times 999.972 \,0 \,\text{kg} \,\text{m}^{-3} \times9.806 \,65 \,\text{m} \,\text{s}^{-2} \\ &\approx 98.063 \,8 \,\text{Pa}$

Other related units to it are the millimetre of water (mmH₂O), the foot of water (ftH₂O), the inch of water (inH₂O).

$1 \,\text{cmH}_2\text{O} &=10 \,\text{mmH}_2\text{O} \\ &=0.032 \,808 \,3 \,\text{ftH}_2\text{O} \\ &=0.393 \,701 \,\text{inH}_2\text{O}$

Pound per Square Inch (psi)

The pound per square inch or the pound-force per square inch is denoted as psi or lb_f in⁻². It is an avoirdupois unit of pressure. It is defined as a force exerted by one pound-force on the surface of one square inch.

$1 \,\text{psi} &=\frac{1 \,\text{lb}_\text{f}}{1 \,\text{in}^2} \\ &=\frac{1 \,\text{lb} \times g}{1 \,\text{in}^2} \\ &=\frac{0.453 \,592 \,37 \,\text{kg} \times 9.806 \,65 \,\text{m} \,\text{s}^{-2}}{0.025 \,4^2} \\ &\approx 6 \,894.757 \,\text{Pa}$

The derived units of it are the kilopound per square inch (kpsi) and the megapound per square inch (Mpsi).

$1 \,\text{psi} =1 \times 10^{-3} \,\text{kpsi} =1 \times 10^{-6} \,\text{Mpsi}$

psi is usually used to measure gauge pressure i.e., pressure relative to atmospheric pressure.

Figure 9: Water Pressure Gauge in psi (Inner Scale) and bar (Outer Scale)

Technical Atmosphere (or Kilogram per Square Centimetre)

Technical atmosphere (at), also known as the kilogram per square centimetre or the kilogram-force per square centimetre (kg_f cm⁻²), is the force of 1 kg_f (one kilogram-force) exerted on the surface of 1 cm².

$1 \,\text{at} & = 1 \,\text{kg}_\text{f} \,\text{cm}^{-2} \\ & = \frac{1 \,\text{kg}_\text{f}} {1 \,\text{cm}^2} \\ & = \frac{1 \,\text{kg} \times 9.806 \,65 \,\text{m} \,\text{s}^{-2}}{1 \times 10^{-4} \,\text{m}^{2}} \\ & = 98 \,066.5 \,\text{Pa}$

The technical atmosphere is a deprecated metric unit. The gram per square centimetre (g_f cm⁻²) is a derived unit of it.

$1 \,\text{kg}_\text{f} \,\text{cm}^{-2} = 1 \times 10^{3} \,\text{g}_\text{f} \,\text{cm}^{-2}$

Barye

Barye is the CGS unit of pressure. It is also known as barad, bary, baryd, or baryed. One barye equals one dyne per square centimetre.

$1 \,\text{Ba} &=1 \,\text{dyne} \,\text{cm}^{-2} \\ &=1 \times 10^{-5} \,\text{N} \times 1 \times 10^4 \,\text{m}^{-2} \\ &=0.1 \,\text{N} \,\text{m}^2 \\ &=0.1 \,\text{Pa}$

Metre Sea Water (and Foot Sea Water)

The metre sea water (msw) is a unit of pressure and defined as 0.1 bar. Thus, one metre sea water is one-tenth of one bar.

Figure 10: The US navy drivers check the pressure gauge during a training dive.

$1 \,\text{msw} =0.1 \,\text{bar}$

It is a common unit used by drivers. Another common unit is the foot sea water (fsw). The value of 1 fsw is calculated using a depth of 1 ft and seawater density of 64 lb ft⁻³.

$1 \,\text{fsw} &= 1 \,\text{ft} \times 64\,\text{lb} \,\text{ft}^{-3} \times g\\ &= 0.3048 \,\text{m} \times 64 \times \frac{0.453 \,592 \,37}{0.304 \,8^3}\,\text{kg} \,\text{m}^{-3} \times g\\ &= 3064.34 \,\text{Pa}$

Note: The relation between msw and fsw is different from the metre and the foot.