Last updated: 2026-06-15

Hydrostatic Pressure

Dive to the bottom of a swimming pool and your ears feel the squeeze of the water above you. That squeeze is hydrostatic pressure — the pressure a fluid exerts because of its own weight. It grows steadily with depth, and at any point it depends only on how deep you are, the fluid's density and gravity: $P = \rho g h$. This calculator returns the gauge pressure from the fluid column and the absolute pressure once the pressure pushing on the surface is added.

Why pressure grows with depth

Every layer of fluid has to support the weight of all the fluid above it. Go deeper and there is more fluid overhead, so the pressure is greater. Because a fluid transmits pressure equally in all directions, the result depends only on the vertical depth — not on the shape of the container or how much fluid there is in total. A thin vertical pipe and a vast reservoir filled to the same height push with exactly the same pressure at the bottom.

Formula

The gauge pressure is measured relative to the surface; the absolute pressure adds the surface pressure $P_0$, which is normally one atmosphere ($101\,325\ \text{Pa}$) for an open container.

Worked example

How hard does the water press on a diver 10 m down in a fresh-water lake (density 1000 kg/m³)?

That is the gauge pressure — almost exactly one extra atmosphere. Adding the atmosphere already pressing on the surface gives an absolute pressure of about $101\,325 + 98\,067 = 199\,392\ \text{Pa}$, close to two atmospheres. This is the rule of thumb that every 10 m of water roughly doubles, then triples, the pressure a diver experiences.

Gauge versus absolute pressure

Gauge pressure is what you measure against the surrounding air, so it reads zero at the open surface. Absolute pressure is measured against a vacuum, so at the surface it equals atmospheric pressure. Which one you need depends on the problem: buoyancy and depth gauges work in gauge pressure, while gas laws and anything involving a sealed or evacuated space need absolute pressure. The calculator gives both.

Limitations

The formula assumes a single fluid of constant density at rest. That is excellent for liquids over ordinary depths, but gases compress and the atmosphere thins with height, so $P = \rho g h$ only approximates atmospheric pressure over small height changes. Very deep in the ocean, water density rises slightly under pressure, so true pressures run a little above this estimate. The model also ignores any motion of the fluid.