Pascal (Pa)
Definition, derivation and practical pressure measurement in the International System of Units
Pressure is found everywhere: in the atmosphere, in liquids, in tyres, in pipelines and in the bloodstream. Yet everyday pressure is stated in a motley collection of units, from bar and atmosphere to millimetres of mercury and psi. The International System of Units (SI) has only one unit of pressure: the pascal, symbol Pa. The pascal is a derived SI unit, built from the base units kilogram, metre and second with no definition of its own beside them.
To understand how the pascal is used in practice, it is necessary, as with the base units, to distinguish between definition, realization and practical pressure measurement.
The definition of the pascal in the SI system
The pascal is defined within the SI as:
one pascal is the pressure exerted by a force of one newton distributed uniformly over an area of one square metre.
In other SI units, 1 Pa = 1 N/m² = 1 J/m³, and in base units 1 Pa = 1 kg·m⁻¹·s⁻². The definition therefore rests on three base units:
- the kilogram, defined via the Planck constant,
- the metre, defined via the speed of light in vacuum,
- the second, defined via the hyperfine transition of the caesium-133 atom.
Since force is measured in newtons, the pascal is in practice newtons per square metre. The same unit serves for mechanical stress in materials, usually as megapascals.
Fact box: the history of the pascal
| Year | Event |
| 1648 | Blaise Pascal (1623-1662) has the air pressure measured on the summit of the Puy de Dôme and shows that pressure falls with altitude. |
| 1653 | Pascal’s principle is formulated: a pressure applied to an enclosed fluid is transmitted undiminished in every direction. |
| 1954 | The 10th CGPM fixes the standard atmosphere at exactly 101 325 Pa. |
| 1971 | The 14th CGPM adopts the name pascal for the unit newton per square metre. |
The pascal is thus the youngest of the common derived units with a name of its own.
How much is one pascal?
One pascal is a very small pressure. A sheet of A4 paper lying on a table exerts about 1 Pa. Atmospheric pressure at sea level is around 101 000 Pa, roughly 101 kPa or 1 013 hPa. Some reference values:
- sound pressure at the threshold of hearing: 20 µPa,
- standard atmospheric pressure: 101 325 Pa (1 013.25 hPa),
- the pressure in a car tyre: about 220 kPa gauge,
- water pressure at a depth of 10 metres: about 100 kPa on top of atmospheric pressure,
- blood pressure of 120/80 mmHg: about 16/10.7 kPa,
- yield strength of structural steel: a few hundred MPa.
This is why the pascal is almost always used with a prefix: hectopascals in meteorology, kilopascals and megapascals in engineering.
Definition, realization and use
Pressure metrology keeps three levels apart:
- The definition states what the pascal is in principle: one newton per square metre.
- The realization refers to the experimental methods that produce a pressure of known value, traceable to the kilogram, the metre and the second.
- The use refers to pressure measurement in industry, meteorology, medicine and everyday life.
That the pascal has no definition of its own does not mean it lacks a realization. Pressure is realized with dedicated primary standards, which give manometers and transducers their traceability.
How the pascal is realized
The primary method from about 10 kPa up to several hundred megapascals is the pressure balance, also called a piston gauge or deadweight tester. A piston with an accurately measured effective area A is loaded with masses m in the local gravitational field g, so the pressure under the piston is p = m·g/A. The masses are traceable to the kilogram, the area to the metre, and g is measured on site with an absolute gravimeter.
For lower pressures, mercury manometers are used, where the pressure difference follows from the height and density of the mercury column and g. In the vacuum range, pressure is realized by static expansion of a known amount of gas into a known volume. Up towards one gigapascal, controlled-clearance pistons are used, with the piston’s deformation controlled and corrected for.
Practical pressure measurement and sources of error
In practice, pressure is measured with transducers calibrated against a pressure balance or a secondary standard. Sources of error to handle:
- The reference level: absolute pressure is counted from vacuum, gauge pressure from the surrounding air, differential pressure between two points. A tyre’s 220 kPa is gauge; the absolute pressure is around 320 kPa.
- Temperature affects both the sensitivity of the transducer and the density of gases and liquids.
- A height difference between transducer and measuring point adds a hydrostatic head, about 10 kPa per metre in water.
- The acceleration of gravity varies with latitude and altitude, which matters when a pressure balance is moved.
The pascal and other derived units
The pascal belongs to a web of derived units that all rest on the same base units:
| Unit | Quantity | Relation to the pascal |
| newton (N) | Force | 1 Pa = 1 N/m² |
| joule (J) | Energy | 1 Pa = 1 J/m³ (energy density) |
| watt (W) | Power | 1 W = 1 Pa·m³/s (pressure times volume flow) |
| bar | Pressure (outside the SI) | 1 bar = 100 000 Pa exactly |
Pascal, bar and atmosphere: multiples and common conversions
The common multiples are the hectopascal (1 hPa = 100 Pa, identical to the millibar), the kilopascal (1 kPa = 1 000 Pa), the megapascal (1 MPa = 10⁶ Pa) and the gigapascal (1 GPa = 10⁹ Pa). The bar is accepted for use with the SI and equals exactly 100 000 Pa, so 1 bar = 100 kPa = 1 000 hPa. Other common units:
- 1 atm (standard atmosphere) = 101 325 Pa exactly,
- 1 mmHg = 133.322 Pa,
- 1 psi = 6 894.76 Pa.
Conversions between these are done directly in the pressure converter on Konvertera.nu, for example pascal to bar. The unit pascal and all pressure units are collected there.
Summary
The pascal is the SI unit of pressure, one newton per square metre, or kg·m⁻¹·s⁻² in base units. It is small in everyday terms and is therefore almost always used with a prefix, while the bar and the atmosphere live on as accepted or customary alternatives.
Through pressure balances and manometers, the pascal is realized with traceability to the kilogram, the metre and the second. This chain, from the base-unit definitions to a calibrated transducer, is what makes a measured pressure mean the same thing in the weather forecast, the workshop and the hospital.