How to use it
- Choose the Formula: Force on an area: p = F ÷ A or Fluid at a depth: p = ρgh.
- Type the values you know into their boxes, for example Force F 500 and Area A 100 cm². Leave exactly one box empty, the one to find, such as Pressure p.
- Read the Solved value, then the same pressure in each unit in The same pressure in other units.
The two formulas
Pressure is force per unit area. A force F spread over an area A gives p = F ÷ A, and the SI unit is the pascal (Pa), which is one newton per square metre. In a liquid at rest, the pressure grows with depth: p = ρgh, where ρ is the density of the liquid, g = 9.80665 m/s² is standard gravity and h is the depth below the surface.
p = F ÷ A (1 Pa = 1 N/m²)
p = ρ × g × h (hydrostatic, a gauge pressure)
p_absolute = p_gauge + p_air- Halving the area doubles the pressure for the same force, which is why a sharp nail or a knife cuts more easily.
- In water, the pressure rises by about 9.8 kPa for each metre of depth, and about 10.3 m of water gives one atmosphere.
The units and their factors
The table converts the result. Bar and standard atmosphere are fixed multiples of the pascal. The psi comes from the pound-force and the inch, and the millimetre of mercury is defined by the density of mercury. Each factor is the number of pascals in one unit.
| Unit | Pa in one unit | How it is fixed |
|---|---|---|
| Pascal (Pa) | 1 | the SI unit, one newton per square metre |
| Kilopascal (kPa) | 1,000 | one thousand pascals |
| Bar | 100,000 | exact: 1 bar = 100 000 Pa |
| Standard atmosphere (atm) | 101,325 | exact by the 10th CGPM (1954) |
| Pound-force per square inch (psi) | 6,894.757 | 0.45359237 kg × 9.80665 m/s² ÷ (0.0254 m)² |
| Millimetre of mercury (mmHg) | 133.3224 | 13595.1 kg/m³ × 9.80665 m/s² × 1 mm, exact by definition |
What the calculator does not cover
- Pressure in a moving fluid, such as the dynamic pressure of wind or water in a pipe, which adds ½ρv² to the static pressure.
- Gases: their pressure depends on temperature and volume, through the gas laws, and the depth formula does not apply to them.
- Compression of the liquid at great depth, where its density changes. The formula uses one density for the whole depth.
Worked example: 500 N on 100 cm² and 10 m of water
A force of 500 N on 100 cm² (0.01 m²) gives p = 500 ÷ 0.01 = 50 000 Pa, which is 50 kPa, 0.5 bar, 0.4935 atm, 7.252 psi or 375 mmHg.
Ten metres of fresh water (ρ = 1000 kg/m³) give p = 1000 × 9.80665 × 10 = 98 066.5 Pa, which is 98.07 kPa above the air pressure at the surface.
| Unit | 50 000 Pa is |
|---|---|
| Pa | 50,000 |
| kPa | 50 |
| bar | 0.5 |
| atm | 0.4935 |
| psi | 7.252 |
| mmHg | 375 |
Frequently asked questions
What is the difference between Pa and kPa?
They are the same kind of unit, with the kilo prefix meaning one thousand: 1 kPa is 1000 Pa. Atmospheric pressure is about 101.3 kPa, or 101 325 Pa.
How many atmospheres is 10 m of water?
About one. Ten metres of fresh water add 98.07 kPa to the air pressure, close to one standard atmosphere of 101.325 kPa. The depth that gives exactly one atmosphere is 10.33 m.
Why are psi and mmHg not exact multiples of the pascal?
The psi is defined from the pound and the inch, and its value in pascals is 6894.757, a number with many digits. The millimetre of mercury is defined from the density of mercury, so 1 mmHg is 133.322387415 Pa. Both are exact by their definitions.
What does gauge pressure mean?
It is the pressure measured above the surrounding air. The formula p = ρgh gives gauge pressure. A tyre gauge also reads gauge pressure, so 220 kPa on a gauge is about 320 kPa absolute.
Can the pressure be negative?
Yes, a pressure can be below the air pressure, as in a partial vacuum. The calculator accepts a negative pressure only when you enter it; a force, an area, a density and a depth cannot be negative.
Why does a sharp knife cut better?
The same force on a smaller area gives a larger pressure: halving the area doubles the pressure. The blade's edge is so thin that a small push is enough to exceed the strength of the material.
Sources
- Wikipedia: Pressure (p = F/A, hydrostatic p = ρgh)
- Wikipedia: Bar (unit), 1 bar = 100 000 Pa
- Wikipedia: Standard atmosphere (unit), 101 325 Pa
- Wikipedia: Pound per square inch (psi)
- Wikipedia: Millimetre of mercury (133.322387415 Pa)
Figures and text last checked on Tuesday, November 10, 2026.