Introduction
The pressure in a still liquid grows steadily with depth, because each layer carries the weight of all the liquid above it. That simple rule sets the load on a tank bottom, the test pressure of a vertical pipe, the reading of a level gauge, the pressure on a diver, the load on a hatch below the waterline, and the static head a pump must overcome.
This calculator gives the gauge pressure at any depth in fresh water, sea water, marine fuel, lubricating oil or a liquid of your own, and the absolute pressure with the atmosphere or a tank pressure added on top. It also shows the head in metres of water, the pressure rise per metre, and the force on a horizontal surface such as a tank bottom or a hatch. It is for marine, civil, mechanical and process engineers, and for divers and students.
Formulas
Gauge and absolute pressure:
p_gauge = ρ × g × h
p_abs = p_surface + ρ × g × hHead in metres of water, and the force on a horizontal surface:
H = p_gauge / (1000 × g)
F = p_gauge × A- ρ — liquid density, kg/m³ (fresh water 998.2, sea water 1025.87)
- g — 9.806 65 m/s²
- h — depth below the free surface, m
- p_surface — pressure on the surface, Pa (101.325 kPa at sea level)
- A — horizontal area, m²
Assumptions and limitations
- The liquid is still and of uniform density. A tank with layers of different temperature, or a mixture, needs an average density.
- Standard gravity is used. Local gravity differs by up to 0.3 % with latitude and altitude.
- The surface pressure defaults to the standard atmosphere at sea level. For a pressurised tank, enter its absolute pressure; at altitude, enter the local atmospheric pressure.
- The force is on a horizontal surface, where the pressure is the same everywhere. On a vertical wall the pressure rises with depth, and the average acts at the centroid of the wall.
Worked example
What is the pressure on a hull plate 30 m below the sea surface?
- Sea water density at 15 °C: ρ = 1025.87 kg/m³.
- Gauge pressure: p = 1025.87 × 9.806 65 × 30 = 301 810 Pa = 301.8 kPa, which is 3.02 bar.
- Absolute pressure: 301.8 + 101.3 = 403.1 kPa, about four atmospheres.
- The pressure rises by 10.06 kPa for every metre of sea water.
In fresh water the same depth gives 293.7 kPa gauge, 2.7 % less, which is why draft and stability calculations must use the right water density.
FAQ
What is the difference between gauge and absolute pressure?
Gauge pressure is measured above the surrounding atmosphere, which is what most pressure gauges show. Absolute pressure adds the atmosphere on top and is measured from a perfect vacuum.
How much does pressure rise per metre of water?
About 9.8 kPa per metre in fresh water and 10.1 kPa in sea water. That is roughly one bar, or one atmosphere, for every ten metres.
Does the shape of the tank matter?
No. The pressure at a given depth depends only on the depth and the density, not on the tank's shape or width. This is the hydrostatic paradox.
What force acts on a tank bottom?
The gauge pressure at the bottom times its area. A 2 m × 3 m bottom under 4 m of fuel oil carries about 195 kN, the weight of the oil above it.
What is a metre of water column?
A pressure unit equal to the pressure at the bottom of 1 m of water, 9.81 kPa. Pump heads and low pressures are often given this way.
Does water compress at depth?
Slightly, about 0.5 % per 1000 m. For engineering depths the constant-density result is accurate; in the deep ocean it understates the pressure a little.
Related calculators
- Bernoulli's equation and venturi — the same pressure balance for a moving fluid.
- Tank volume and partial fill — how much liquid sits above the bottom.
- Pipe volume and mass of contents — the contents of a vertical pipe.
- Draft survey — water density in ship displacement.