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Science

Hydrostatic Pressure Calculator

Enter the fluid density, depth and gravity to compute the hydrostatic pressure P = ρ·g·h instantly, with conversions to kPa, bar, psi, atm, mmHg and metres of water. Add a surface pressure to get absolute pressure too.

Gauge pressure P = ρgh

Pressure exerted by the fluid column alone (relative to the surface). This is what diving tables and tank designs typically use.

Absolute pressure

Gauge pressure plus the surface pressure — the total pressure something at depth actually feels.

Gauge pressure in other units

kPa kilopascals
bar bar
psi pounds per square inch
atm atmospheres
mmHg millimetres of mercury
mH₂O metres of water

Formula

P_gauge = ρ · g · h · P_abs = P_surface + ρ·g·h

From Pascal's principle: in a static fluid, pressure depends only on depth and density — not on the shape of the container.

Formula

P_gauge = ρ · g · h P_abs = P_surface + ρ · g · h

Frequently asked

Why does every 10 m of water depth add roughly one atmosphere?

Fresh water has density 1000 kg/m³, so ρ·g·h with g ≈ 9.80665 and h = 10 m gives 98 067 Pa — essentially one standard atmosphere (101 325 Pa). Seawater is a bit denser (1025 kg/m³), giving about 1.005 atm per 10 m. That is where the diver "1 atm per 10 m" rule of thumb comes from.

What is the difference between gauge and absolute pressure?

Gauge pressure reads relative to the surface (usually atmospheric) — that is what most pressure dials show. Absolute pressure reads relative to vacuum. At 10 m beneath the ocean surface, gauge ≈ 1 atm but absolute ≈ 2 atm. Use gauge pressure for diving and pipe/tank stress; use absolute pressure in gas laws like PV = nRT.

Does the shape of the container change the pressure at the bottom?

No — that is the classic "hydrostatic paradox". For a static, connected fluid, the bottom pressure is always ρ·g·h regardless of whether the container is a narrow-necked bottle or a wide tank; pressure depends only on depth. Shape changes the total force on the bottom (because force = pressure × area), not the pressure itself.

Why does this matter in engineering?

It sets the wall thickness needed for tanks and dams, the working pressure of dive gear, the flow rate of IV drips, the water pressure available on each storey of a building, and the design loads on offshore platforms. Any time you have a standing column of fluid, this formula is the starting point.

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