This article is about pressure in the physical sciences. For the psychological meaning, see Peer pressure. For the Billy Joel song, see Pressure (Billy Joel song). For the Paramore song, see Pressure (Paramore song). For Under Pressure, see Under Pressure (disambiguation).

Pressure (symbol: p or P) is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.

## Definition

Pressure is an effect which occurs when a force is applied on a surface. The symbol of pressure is  P.

### Formula

Mathematically:

where:

p is the pressure,
F is the normal force,
A is the area.

Pressure is a scalar quantity, and has SI units of pascals; 1 Pa = 1 N/m2, and has EES units of psi; 1 psi = 1 lb/in2.

Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. It is a fundamental parameter in thermodynamics and it is conjugate to volume.

### Units

Mercury column

The SI unit for pressure is the pascal (Pa), equal to one newton per square meter (N·m-2 or kg/m·s2). This special name for the unit was added in 1971; before that, pressure in SI was expressed simply as N/m2.

Non-SI measures such as pound per square inch (psi) and bar are used in parts of the world. The cgs unit of pressure is the barye (ba), equal to 1 dyn·cm-2. Pressure is sometimes expressed in grams-force/cm2, or as kg/cm2 and the like without properly identifying the force units. But using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as units of force is expressly forbidden in SI. The technical atmosphere (symbol: at) is 1 kgf/cm2. In US Customary units, it is 14.696 psi.

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 most other fields, where the hecto prefix is rarely used. The unit inch of mercury (inHg, see below) is still used in the United States. Oceanographers usually measure underwater pressure in decibars (dbar) because an increase in pressure of 1 dbar is approximately equal to an increase in depth of 1 meter. Scuba divers often use a manometric rule of thumb: the pressure exerted by ten metres depth of water is approximately equal to one atmosphere.

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

standard atmosphere = 101325 Pa = 101.325 kPa = 1013.25 hPa.

Because pressure is commonly measured by its ability to displace a column of liquid in a manometer, pressures are often expressed as a depth of a particular fluid (e.g., inches of water). The most common choices are mercury (Hg) and water; water is nontoxic and readily available, while mercury’s high 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 p = ρgh. 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. These manometric units are still encountered in many fields. Blood pressure is measured in millimeters of mercury in most of the world, and lung pressures in centimeters of water are still common.

Gauge pressure is often given in units with ‘g’ appended, eg ‘kPag’ or ‘psig’, and units for measurements of absolute pressure are sometimes given a suffix of ‘a’, to avoid confusion, for example ‘kPaa’, ‘psia’.

Presently or formerly popular pressure units include the following:

• atmosphere (atm)
• manometric units:
• centimeter, inch, and millimeter of mercury (torr)
• millimeter, centimeter, meter, inch, and foot of water
• customary units:
• kip, ton-force (short), ton-force (long), pound-force, ounce-force, and poundal per square inch
• pound-force, ton-force (short), and ton-force (long)
• non-SI metric units:
• bar, decibar, millibar
• kilogram-force, or kilopond, per square centimetre (technical atmosphere)
• gram-force and tonne-force (metric ton-force) per square centimetre
• barye (dyne per square centimetre)
• kilogram-force and tonne-force per square metre
• sthene per square metre (pieze)