In thermodynamics, pressure and volume are said to form a pair of conjugate variables (for nonviscous fluids). The pressure acts as a generalized force-pressure differences force a change in volume, and their product is the energy lost by the system due to mechanical work. Pressure is the driving force, and volume is the associated displacement.

Calculation of hydrostatic pressure

At a given spot within a fluid, the hydrostatic pressure (or "head pressure") is the pressure resulting from the weight of the fluid column above that spot. It may be calculated by the following formula:

  • ρ (rho) is the density of the fluid (for example, the density of freshwater is about 1000 kg/m3);
  • g is the acceleration due to gravity (approximately 9.81 m/s2 on Earth's surface);
  • h is the height of the fluid column (in meters).


The name for the unit of pressure, the (Pascal), was added in 1971. Before that, pressure in SI was expressed by using its units (N•m-2).

Non-SI measures (still in use in some parts of the world) include the pound-force per square inch (psi) and the bar.

The cgs unit of pressure is the barye (ba), which is equal to one dyne per square centimeter (dyn•cm-2).

The standard atmosphere (atm) of pressure is an established constant. It is approximately equal to typical air pressure at earth mean sea level and is defined as follows:

standard atmosphere = 101,325 Pa = 101.325 kPa = 1013.25 hPa.

Some meteorologists prefer the hectopascal (hPa) for atmospheric air pressure, which is equivalent to the older unit millibar (mbar). Similar pressures are given in kilopascals (kPa) in practically all other fields, where the hecto prefix is hardly ever used. In Canadian weather reports, the normal unit is kPa.

Because pressure may be measured by the displacement of a column of liquid in a manometer, it is sometimes expressed as the depth (in inches) of a particular fluid. The most common choices of fluid are mercury (Hg) and water, and pressure was once expressed in terms of inches of mercury (in Hg). Water is nontoxic and readily available, but mercury's density allows for a shorter column (and so a smaller manometer) to measure a given pressure. The pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation noted above: p = hgρ.

Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column does not define pressure precisely. When 'millimeters of mercury' or 'inches of mercury' are quoted today, these units are not based on a physical column of mercury; rather, they have been given precise definitions that can be expressed in terms of SI units. (The water-based units still depend on the density of water, a measured, rather than defined, quantity.)

Although no longer favored in physics, these manometric units are still encountered in certain fields. Blood pressure is measured in millimeters of mercury in most parts of the world, and lung pressure in centimeters of water is also common. Natural gas pipeline pressures are measured in inches of water, expressed as WC ('Water Column'). Scuba divers often use a manometric rule of thumb: the pressure exerted by ten meters depth of water is approximately equal to one atmosphere.

Pressure is still sometimes expressed in kgf/cm² or grams-force/cm² (sometimes as kg/cm² and g/cm² without properly identifying the force units). But using the terms kilogram, gram, kilogram-force, or gram-force (or their symbols) as a unit of force is expressly forbidden in SI. (The unit of force in SI is the newton, N).

Non-SI units presently or formerly in use include the following:

  • atmosphere.
  • manometric units:
    • centimeter, inch, and millimeter of mercury (Torr).
    • millimeter, centimeter, meter, inch, and foot of water.
  • imperial units:
    • kip, ton-force (short)3, ton-force (long)4, pound-force, ounce-force, and poundal per square inch.
    • pound-force, ton-force (short), and ton-force (long) per square foot.
  • non-SI metric units:
    • bar, millibar.
    • kilogram-force, or kilopond, per square centimeter (technical atmosphere) (symbol: at) is 1 kgf/cm².
    • gram-force and tonne-force (metric ton-force) per square centimeter.
    • barye (dyne per square centimeter).
    • kilogram-force and tonne-force (metric ton-force) per square meter.
    • sthene per square meter (pieze).

See also

  • Atmospheric pressure
  • Blood pressure
  • Kinetic theory Pressure
  • Combined gas law
  • Conversion of units
  • Ideal gas law
  • Partial pressure
  • Vacuum
  • Boyle's Law


  1. ↑ The "normal force" is the component of a force perpendicular to the surface of contact.
  2. ↑ Note that Bernoulli's equation applies only to incompressible flow.
  3. ↑ One short ton equals 2,000 pounds, or 90.72 percent of a metric ton.
  4. ↑ One long ton equals 2,240 pounds, or 101.605 percent of a metric ton.


  • Crowell, Benjamin. 2006. Simple Nature: Thermodynamics Retrieved December 3, 2007.
  • Nave, Carl R. 2007. Pressure Hyperphysics. Retrieved December 3, 2007.
  • Young, Hugh D., and Roger A. Freedman. 2003. Physics for Scientists and Engineers, 11th ed. San Francisco, CA: Pearson. ISBN 080538684X

External links

All links retrieved June 15, 2019.

  • HyperPhysics: Pressure Department of Physics and Astronomy, Georgia State University.
  • Gas Pressure Glenn Research Center, NASA.
  • Atmospheric Pressure Department of Atmospheric Sciences, University of Illinois at Urbana-Champaign.