Pressure Calculator
Calculate pressure, force, or area using P = F/A. Supports Pa, kPa, MPa, bar, psi, and atm.
Pressure: force spread over area
Pressure is force divided by the area it acts on. The same force concentrated onto a smaller area produces a larger pressure — which is why a drawing pin pierces wood under a thumb push that would do nothing through a flat coin.
The SI unit is the pascal, one newton per square metre. A pascal is tiny: atmospheric pressure is about 101,325 of them. That is why practical work uses kilopascals, bars, psi, or atmospheres instead.
The one distinction worth getting right early is gauge versus absolute pressure. A tyre gauge reading 32 psi means 32 psi above the surrounding air. In absolute terms the tyre is at about 46.7 psi. Thermodynamic formulas almost always want absolute pressure.
Formula Reference Table
P = F / A · Phydrostatic = ρgh · Pabs = Pgauge + Patm| Symbol | Meaning |
|---|---|
| P | pressure (Pa = N/m²) |
| F | force acting perpendicular to the surface (N) |
| A | area over which the force is distributed (m²) |
| ρ | fluid density (kg/m³) — water is 1000 |
| g | gravitational acceleration = 9.81 m/s² |
| h | depth below the fluid surface (m) |
Only the component of force perpendicular to the surface counts. A force applied at an angle θ to the normal contributes F·cos θ.
3 Worked Examples
A 70 kg person stands with a total sole contact area of 0.030 m². What pressure do they exert on the floor?
- F = mg = 70 × 9.81 = 686.7 N
- P = F / A = 686.7 / 0.030
- P = 22,890 Pa ≈ 22.9 kPa
Standing on one foot doubles it to 45.8 kPa. In stiletto heels with a 1 cm² tip the same weight produces nearly 7 MPa — comparable to the pressure under a car tyre, and enough to dent softwood floors.
Find the gauge and absolute pressure 10 m below the surface of fresh water.
- P_gauge = ρgh = 1000 × 9.81 × 10
- P_gauge = 98,100 Pa ≈ 98.1 kPa
- P_abs = P_gauge + P_atm = 98,100 + 101,325
Roughly every 10 m of water adds one atmosphere. This is the basis of the diving rule that lung volume halves at 10 m and thirds at 20 m.
A tyre gauge reads 32 psi. Express this in pascals and bar, both gauge and absolute.
- 1 psi = 6894.76 Pa
- P_gauge = 32 × 6894.76 = 220,632 Pa = 2.21 bar
- P_abs = 220,632 + 101,325 = 321,957 Pa = 3.22 bar
European tyre placards usually quote bar gauge, US placards psi gauge. They agree once converted — a 2.2 bar and a 32 psi spec are the same tyre pressure.
Pressure unit conversions
| Unit | In pascals | Notes |
|---|---|---|
| 1 Pa | 1 | SI unit; 1 N/m² |
| 1 kPa | 1,000 | Common in engineering and weather |
| 1 bar | 100,000 | Close to, but not equal to, 1 atm |
| 1 atm | 101,325 | Standard atmosphere, exact by definition |
| 1 psi | 6,894.76 | Pounds per square inch; US standard |
| 1 mmHg (torr) | 133.322 | Medical blood pressure, vacuum work |
| 1 inHg | 3,386.39 | US barometric readings |
| 1 kgf/cm² | 98,066.5 | Older industrial unit, ≈ 1 bar |
Reference pressures
| Situation | Pressure | In atmospheres |
|---|---|---|
| Best laboratory vacuum | ≈ 10⁻¹² Pa | ≈ 10⁻¹⁷ atm |
| Summit of Everest (8,849 m) | ≈ 33,700 Pa | 0.33 atm |
| Sea level standard | 101,325 Pa | 1.00 atm |
| Car tyre (32 psi gauge) | 322,000 Pa absolute | 3.18 atm |
| Deepest ocean (Mariana Trench) | ≈ 1.09 × 10⁸ Pa | ≈ 1,070 atm |
| Centre of the Earth | ≈ 3.6 × 10¹¹ Pa | ≈ 3.6 million atm |
Fluid densities for ρgh calculations
| Fluid | Density (kg/m³) | Pressure per metre of depth |
|---|---|---|
| Fresh water (4 °C) | 1,000 | 9.81 kPa/m |
| Seawater | 1,025 | 10.05 kPa/m |
| Petrol / gasoline | ≈ 740 | 7.26 kPa/m |
| Mercury | 13,534 | 132.8 kPa/m |
| Air (sea level) | 1.225 | 0.012 kPa/m |
Common Mistakes to Avoid
Tyre gauges, blood pressure cuffs, and most industrial sensors read gauge pressure — the excess over ambient. Gas law calculations (PV = nRT) need absolute. Add 101,325 Pa unless you know the reading is already absolute.
P = F/A only gives pascals when A is in square metres. Dividing by an area in cm² inflates the answer by 10,000. Convert first: 1 cm² = 10⁻⁴ m².
Hydrostatic pressure depends only on depth, density and gravity — never on the width of the vessel or the total volume of liquid. A narrow tube 10 m tall produces the same bottom pressure as a 10 m deep lake.
In a static fluid, pressure at a point is the same in every direction. It is a scalar, not a vector, so 'the pressure pushing down' and 'the pressure pushing sideways' at the same depth are equal.
Frequently Asked Questions
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Formula Explorer connections
Interpretation: This relationship connects pressure, velocity, density, viscosity, geometry or transport in a fluid system. Assumption: Check whether flow is steady, incompressible, laminar, fully developed or one-dimensional. Reynolds and Mach regimes determine whether simplified formulas are valid.