Gas Pressure at Depth Calculator
Calculate absolute and gauge pressure at any depth using P = ρgh + P_atm.
Returns pressure in PSI, bar, atm, and kPa for scuba and hydraulic engineering.
Hydrostatic pressure is the pressure a column of fluid exerts because of its own weight. It depends on only three things: how deep you are, how dense the fluid is, and gravity. The shape of the container does not enter into it at all.
The formula: P_absolute = ρ × g × h + P_atmospheric
- ρ (rho) = fluid density in kg/m³
- g = 9.81 m/s², acceleration due to gravity
- h = depth below the surface in metres
- P_atmospheric = 101,325 Pa at sea level
The ρgh part on its own is the gauge pressure, which is what a pressure gauge reads because the gauge is already sitting in atmospheric pressure and measures the difference. Add the atmosphere back and you have absolute pressure, which is what matters for gas laws and for anything involving a sealed volume.
Worked example: A diver at 30 m in seawater (ρ = 1,025 kg/m³):
Gauge = 1,025 × 9.81 × 30 = 301,658 Pa (about 3.0 atm) Absolute = 301,658 + 101,325 = 402,983 Pa, which is about 4.0 atm or 58.4 psi
A useful rule of thumb: every 10 m of seawater adds almost exactly 1 atmosphere. So at 10 m you are at 2 atm total, at 20 m you are at 3, at 30 m you are at 4. Divers memorise this because it also tells them how much their air supply compresses.
Why the container shape does not matter
This surprises people the first time they meet it. A pressure reading at the bottom of a narrow pipe and at the bottom of a wide lake is identical if the depth is the same. Pressure depends on the height of the column above you, not on how much fluid there is. It is the reason a small header tank on a roof can pressurise an entire building’s plumbing, and the reason a dam’s thickness is determined by the depth of the reservoir rather than its surface area.
Where this comes up:
- Diving: decompression planning, and why a breath taken at depth expands dangerously on ascent
- Plumbing and irrigation: a tank 10 m above the outlet gives roughly 1 bar of static head
- Hydraulic and civil engineering: dam wall thickness, submarine hull rating, tank design
- Manometers: mercury’s density of 13,600 kg/m³ is exactly why a short mercury column balances a whole atmosphere
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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