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×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.

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.

Enter a value and choose desired pressure units.

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

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 |

mmH_{2}O | millimetre of water | a manometric unit based on water |

cmH_{2}O | centimetre of water | a manometric unit based on water |

inH_{2}O | inch of water | a manometric unit based on water |

ftH_{2}O | 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 |

The other nonstandard units of pressure are listed below.

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 |

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

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 × 10^{5}^{†} | 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. |

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.

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.

Similarly for Pa to Torr,

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.

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

The International Union of Pure and Applied Chemistry recommends 1 × 10^{5} 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:

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.

The bar is another common unit used to measure pressure. It is a metric non-SI unit and defined exactly to 1 × 10^{5} Pa.

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).

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.

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

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:

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 ℃.

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).

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.

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.

The centimetre of water (cmH_{2}O) 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 ℃.

Other related units to it are the millimetre of water (mmH_{2}O), the foot of water (ftH_{2}O), the inch of water (inH_{2}O).

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.

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

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

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 cm^{2}.

The technical atmosphere is a deprecated metric unit. The gram per square centimetre (g_{f} cm^{−2}) is a derived unit of it.

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.

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.

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}.

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

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