Pressure Calculator
Solve P = F ÷ A for pressure, force or area — in pascals, psi, bar or atmospheres — and work out hydrostatic pressure at depth in any fluid.
P = F ÷ A (hydrostatic: P = ρ·g·h)
Pressure
Formula used for this direction
P = F ÷ A
Your values
F = 500 N, A = 0.5
Area cannot be zero.
Force Spread Over Area
Pressure is not a force — it is a force divided by the area carrying it. That distinction explains why a person can lie safely on a bed of nails but not stand on a single one. The weight is identical; only the area changes.
All three directions are solvable here: P = F ÷ A, F = P·A for the total force a pressure exerts on a surface, and A = F ÷ P for the area needed to keep a pressure within a limit. There is also a hydrostatic mode, P = ρ·g·h, for pressure at depth in a fluid.
Worked example — the same force, two areas
Press with 50 N through a knife edge of 1 mm² (0.000001 m²):
P = 50 ÷ 0.000001 = 5.000e+7 Pa, about 493.5 atmospheres.
Press with the same 50 N through a flat hand of 100 cm² (0.01 m²): 5,000 Pa. Ten thousand times less pressure from exactly the same push.
A second example — pressure at depth. Fresh water at 10 m: P = 1000 × 9.80665 × 10 = 98,070 Pa, which is 0.9678 atmospheres of water pressure on top of the atmosphere already there. At 30 m it is 294,200 Pa.
Solving the other way: to keep 50 N below 200 kPa you need at least 0.00025 m² of contact area.
Gauge versus absolute
Standard atmospheric pressure is 101,325 Pa exactly — 14.7 psi. A tyre gauge reading 32 psi means 32 psi above that, so the absolute pressure inside is about 46.7 psi. The hydrostatic figures above are likewise water pressure alone, before adding the atmosphere.
Water Pressure by Depth
Computed with P = ρ·g·h at a fresh-water density of 1,000 kg/m³ and exact standard gravity.
| Depth | Water pressure | In atmospheres | Total incl. air |
|---|---|---|---|
| 0 m | 0 Pa | 0 atm | 1 atm |
| 5 m | 49,033 Pa | 0.484 atm | 1.48 atm |
| 10 m | 98,067 Pa | 0.968 atm | 1.97 atm |
| 20 m | 196,130 Pa | 1.94 atm | 2.94 atm |
| 50 m | 490,330 Pa | 4.84 atm | 5.84 atm |
| 100 m | 980,670 Pa | 9.68 atm | 10.7 atm |
Standard atmosphere of 101,325 Pa is exact by definition (NIST CODATA). Sea water is denser than the fresh water used here, around 1,025 kg/m³, so real ocean pressures run a few percent higher at the same depth.
Keep going
- Pressure is force spread over an area, so the two are the same quantity viewed differently; the force calculator solves for the force itself. Force Calculator
- Hydrostatic pressure depends on the fluid's density, so a density figure is the input that calculation needs; the density calculator finds it from mass and volume. Density Calculator
Frequently Asked Questions
What is the pressure formula?
P = F ÷ A — force divided by the area it is spread over, giving pascals. One pascal is one newton per square metre, which is a very small pressure: standard atmospheric pressure is 101,325 Pa, defined exactly by international agreement.
Why do sharp knives cut better?
Because pressure is force divided by area, and a sharp edge has a tiny contact area. The same hand force concentrated into a hundredth of the area produces a hundred times the pressure. Nothing about the force changes — only the geometry.
How does pressure increase with depth in water?
P = ρ·g·h, so it rises linearly with depth. In fresh water pressure increases by roughly one atmosphere for every 10 metres, which is why divers must equalise frequently near the surface where the proportional change is steepest.
What is the difference between gauge and absolute pressure?
Gauge pressure is measured relative to the surrounding atmosphere; absolute pressure includes it. A tyre reading 32 psi on a gauge is at about 46.7 psi absolute, because atmospheric pressure of roughly 14.7 psi is already pressing on everything. Mixing the two is a common and consequential error.
How do pascals, psi, bar and atmospheres compare?
One atmosphere is exactly 101,325 Pa by definition, one bar is exactly 100,000 Pa, and one psi is about 6,894.76 Pa. So a bar is very slightly less than an atmosphere, which is why weather reports in millibars and in hectopascals show near-identical numbers.
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