Hydrostatic Pressure Calculator
Gauge and absolute pressure at depth in water, seawater, oil or any liquid (p = ρgh), plus the force and centre of pressure on a vertical rectangular gate.
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About this toolWhat is the Hydrostatic Pressure Calculator?
In a liquid at rest, pressure grows in a straight line with depth: p = ρgh. It does not depend on the shape of the container, only on the density of the liquid and how far below the surface you are. This calculator gives the gauge pressure (above atmosphere) and the absolute pressure at any depth, in kPa, bar, psi, Pa or MPa, plus as a water column and in atmospheres. Ten metres of fresh water at 1000 kg/m³ gives 98.07 kPa gauge, and with standard air pressure on top, 199.4 kPa absolute.
Fluid presets cover fresh water at 4 and 20 °C, typical seawater at 1025 kg/m³, saturated brine, diesel, gasoline, hydraulic oil and mercury, and you can type any density. The atmospheric pressure is editable, which matters at altitude or for a pressurised tank.
The second panel answers the question that usually follows: how hard does the liquid push on a wall or gate? Enter the width, height and depth of the top edge of a vertical rectangle and you get the resultant force, the depth of the centroid and the depth of the centre of pressure where that force acts, with a diagram of the pressure distribution. A 2 m wide, 3 m tall wall holding water to its top edge carries 88.3 kN acting 2 m down, at two-thirds of the height.
- Gauge and absolute pressure at any depth, p = ρgh
- Presets for fresh water, seawater, brine, fuels, oil and mercury, plus custom density
- Editable atmospheric pressure and a choice of Pa, kPa, bar, MPa or psi
- Force and centre of pressure on a vertical rectangular wall or gate, with a diagram
- Metric and US units with in-place conversion, copy and share
How to use the Hydrostatic Pressure Calculator
- Choose metric or US units. Lengths switch between metres and feet and the inputs convert in place.
- Pick a fluid preset or enter a density.
- Enter the depth below the free surface and, if needed, change the atmospheric pressure on the surface.
- Choose the pressure unit you want to read, then see gauge pressure, absolute pressure, the pressure gradient and the equivalent water column.
- For a wall or gate, enter its width, height and the depth of its top edge to get the force, the centre of pressure and the edge pressures.
Worked examples
Diver at 10 m in the sea
Input
Seawater 1025 kg/m³, depth 10 m
Output
100.5 kPa gauge, about 201.8 kPa absolute (roughly 2 atmospheres)
Every 10 m of seawater adds about one atmosphere, which is why dive tables work in 10 m (33 ft) steps.
Retaining wall or tank side
Input
Water 1000 kg/m³, wall 2 m wide, 3 m tall, filled to the top
Output
F = 88.26 kN acting 2.0 m below the surface; bottom pressure 29.4 kPa
The pressure triangle averages to the mid-height pressure, 14.7 kPa, over 6 m².
Submerged sluice gate, US units
Input
62.4 lb/ft³ water, gate 4 ft wide, 6 ft tall, top 2 ft below the surface
Output
F ≈ 7,490 lbf, centre of pressure 5.6 ft below the surface
The centroid is at 5 ft; the force acts 0.6 ft lower because the bottom of the gate sees more pressure.
Background and insight
The relation comes from a force balance on a small column of fluid: the pressure at the bottom must support the weight of the column above it, so dp/dz = ρg. With constant density this integrates to p = p_atm + ρgh. Pascal described the consequences in the 1640s, including the hydrostatic paradox that a tall thin column exerts the same bottom pressure as a wide tank of the same depth.
For a plane surface, the resultant force equals the pressure at the centroid times the area, F = ρg h_c A. The force acts lower than the centroid, at y_cp = h_c + I_c/(h_c A), because pressure is higher at the bottom. For a rectangle starting at the surface that is two-thirds of the way down. Gauge pressure is used because atmospheric pressure usually acts on both faces of a wall and cancels.
Seawater density depends on salinity and temperature, usually between about 1020 and 1030 kg/m³ at the surface, so 1025 kg/m³ is a common design value. Standard gravity is 9.80665 m/s² and a standard atmosphere is 101.325 kPa (14.696 psi).
Common use cases
Tank and pipe pressure ratings
Find the static pressure at the bottom of a tank, a riser or a vertical pipe run.
Walls, gates and hatches
Get the resultant force and where it acts for structural or hinge design.
Level and pressure sensors
Convert a transmitter reading to liquid depth for a known density, or the reverse.
Diving and marine work
Pressure at depth in seawater in bar, psi and atmospheres absolute.
Tips and limitations
- Gauge pressure is relative to the air above the liquid. Absolute pressure adds the atmosphere. Instruments and ratings usually say which one with "g" or "a".
- In a closed or pressurised tank, replace the atmospheric value with the gas pressure above the liquid.
- Density changes with temperature and dissolved solids. For a precise level reading, measure the density of your actual liquid.
- Layered liquids (oil over water, for example) need p = Σρᵢghᵢ summed layer by layer. Run the calculator once per layer and add the results.
- Inclined or curved surfaces need the horizontal and vertical force components treated separately; this tool covers vertical rectangles.
Frequently asked questions
How do you calculate hydrostatic pressure?
Multiply density, gravity and depth: p = ρgh. For water at 1000 kg/m³ and 9.81 m/s², every metre adds 9.81 kPa. Add atmospheric pressure, 101.325 kPa at sea level, for absolute pressure.
How much pressure is there per foot of water?
About 0.433 psi per foot of fresh water, or 2.31 ft of water per psi. In metric, about 9.8 kPa (0.098 bar) per metre.
What is the difference between gauge and absolute pressure?
Gauge pressure is measured relative to the local atmosphere, so an open tank surface is 0 gauge. Absolute pressure is measured from a perfect vacuum, so the same surface is about 101.3 kPa or 14.7 psi absolute at sea level.
Does the shape of the tank affect the pressure at the bottom?
No. Pressure at a depth depends only on density, gravity and the vertical distance below the surface. A narrow standpipe and a wide tank with the same depth have the same bottom pressure, though the total force on the base differs with area.
Where does the hydrostatic force act on a vertical wall?
At the centre of pressure, below the centroid. For a rectangle starting at the free surface it is at two-thirds of the depth. In general y_cp = h_c + I_c/(h_c A).
What is the pressure at 10 m depth in the ocean?
With seawater at about 1025 kg/m³, the gauge pressure is 100.5 kPa (about 1.0 bar or 14.6 psi). Adding the atmosphere gives about 202 kPa absolute, roughly two atmospheres.
Is there an in-depth guide to the Hydrostatic Pressure Calculator?
Yes. “Hydrostatic Pressure at Depth and the Force on Walls and Gates” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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