Calculators
Hydrostatic Pressure Calculator
Solve liquid pressure, depth, or density with p = ρgh.
Hydrostatic Pressure Calculator tool
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About This Tool
A stationary liquid creates pressure because the liquid above a point has weight. For a liquid whose density is approximately constant, the pressure increase with vertical depth is p = ρgh, where ρ is density, g is gravitational acceleration, and h is vertical depth below the free surface. This calculator solves gauge pressure, depth, or density and converts common units locally in your browser.
How To Use It
- Choose whether to calculate gauge pressure, vertical liquid depth, or liquid density.
- Enter the two known quantities and select their units. Use vertical depth below the liquid surface rather than the length of a sloped pipe or container.
- Leave gravity at standard gravity (9.80665 m/s²) for a conventional Earth reference, or enter another positive value when the problem specifies it.
- Choose the result unit. Remember that p = ρgh gives the pressure increase relative to pressure at the liquid surface.
Examples
Water at 10 metres
Using ρ = 1000 kg/m³, g = 9.80665 m/s², and h = 10 m gives p = 98,066.5 Pa, or about 98.07 kPa gauge.
Find water depth from pressure
A gauge pressure of 98.0665 kPa in water at standard gravity corresponds to a vertical depth of 10 m.
A denser liquid
At the same depth and gravity, a liquid with twice the density produces twice the hydrostatic gauge pressure in this constant-density model.
Useful Notes
Hydrostatic pressure formula
The pressure difference between two elevations in a stationary constant-density liquid is Δp = ρgΔh. Taking the free surface as the reference gives p = ρgh. Rearranging gives h = p/(ρg) and ρ = p/(gh).
Gauge pressure versus absolute pressure
The calculated p is gauge pressure relative to the pressure acting on the liquid surface. If the surface is exposed to an atmosphere and you need absolute pressure, add the local atmospheric pressure. Do not automatically add a standard atmosphere when the actual surface pressure is different.
Depth means vertical height
Hydrostatic pressure depends on vertical elevation difference, not container shape, total water volume, pipe length, or distance along a slope. Points at the same elevation in the same connected static liquid have the same hydrostatic pressure under the model assumptions.
Density and gravity assumptions
The simple p = ρgh form treats density and gravity as constant over the depth. Liquid density can change with temperature, composition, salinity, and pressure. Very large depth ranges or compressible fluids may require integration with a varying density model.
Units and interpretation
The calculator converts pressure through pascals, depth through metres, and density through kg/m³. A result in psi, bar, or kPa is still the same pressure difference expressed in another unit; unit conversion does not change the physical assumptions.
What this model does not calculate
This tool is for static-fluid pressure differences. It does not calculate flowing-pipe losses, pump head losses, water hammer, buoyancy force, vessel-wall stress, dynamic pressure, or pressure changes caused by acceleration of the container.
FAQ
How much does water pressure increase with depth?
Using 1000 kg/m³ and standard gravity, the hydrostatic increase is about 9.80665 kPa per metre of vertical depth. Actual water density and local gravity can change the value slightly.
Does the shape of the tank affect pressure at a given depth?
Not in the basic hydrostatic model. With the same surface pressure, liquid density, gravity, and vertical depth, the pressure is the same regardless of tank shape.
Is the result gauge or absolute pressure?
It is gauge pressure relative to the pressure at the liquid surface. Add the actual surface pressure if an absolute pressure is required.
Can I use pipe length as depth?
Only when that length is also the vertical elevation difference. For a sloped or horizontal pipe, use the vertical height difference instead.
Can I use this for gases?
The constant-density equation can describe limited cases, but gas density often changes significantly with pressure and height. This page is intended primarily for approximately incompressible liquids.