Pressure Head Calculator
Pressure head is the height of a fluid column that would produce a given pressure at its base, and it is the natural way to express pressure when you are dealing with pumps, tanks and pipework. Converting a pressure into a head lets you compare it directly with elevation changes and with the heads quoted on pump curves. The conversion divides the pressure by the fluid density times gravitational acceleration, which yields a height in meters. A higher pressure gives a taller equivalent column, while a denser fluid gives a shorter one for the same pressure, because each meter of a dense fluid weighs more. This calculator takes a pressure in pascals and a fluid density in kilograms per cubic meter, then returns the pressure head in meters to two decimal places. Using SI units throughout keeps the answer in meters of head. The relationship is the standard hydrostatic one taught in fluid mechanics and used throughout hydraulic engineering. Fluid mechanics conventions and related engineering standards are published by US federal agencies including the National Highway Traffic Safety Administration. Every figure is computed deterministically from the formula, shown in full below, with a worked example that reconciles exactly to the calculator so you can verify each step yourself.
Pressure head is pressure divided by density times gravity: h = P / (rho g). A pressure of 200,000 Pa in water (1,000 kg/m3) gives a head of 20.39 m. A denser fluid gives a shorter column.
Pressure head formula
h = P / (rho g)
h = pressure head (m)
P = pressure (Pa)
rho = fluid density (kg/m3), g = 9.81 m/s^2
Divide the pressure by the product of fluid density and gravitational acceleration. The result is the height of a column of that fluid which would create the given pressure at its base. Gravitational acceleration g is taken as 9.81 m/s^2.
Worked example
A gauge reads 200,000 Pa (2 bar) of pressure in water, which has a density of 1,000 kg/m3.
- Compute rho g: 1,000 x 9.81 = 9,810
- Divide pressure by rho g: 200,000 / 9,810 = 20.3874
- Round to two decimal places: 20.39
- The pressure head is 20.39 m of water
So 200,000 Pa corresponds to about 20.39 m of water head. These are the calculator's default inputs, so the result above matches the widget exactly.
Pressure Head Calculator: frequently asked questions
How do you convert pressure to head?
Divide the pressure by the fluid density times gravitational acceleration: h = P / (rho g). For 200,000 Pa in water, h = 200,000 / (1,000 x 9.81) = 20.39 m. The result is the equivalent column height of that fluid.
Why does fluid density matter?
A denser fluid weighs more per meter of column, so it takes a shorter column to create the same pressure. That is why the same pressure converts to a smaller head in mercury than in water; mercury is about 13.6 times denser.
What is pressure head used for?
Pressure head lets engineers add pressure, elevation and velocity contributions on a common basis of meters when applying the Bernoulli equation, and it makes pump curves, which are quoted in meters of head, directly comparable with system requirements.
How do I convert head back to pressure?
Multiply the head by the fluid density and gravitational acceleration: P = rho g h. This is the exact inverse of the pressure head formula.
What is the pressure head formula?
Pressure head equals h = P / (rho g), where P is pressure, rho is fluid density and g is 9.81 m/s^2.
Official sources
- Fluid mechanics and engineering standards reference: US National Highway Traffic Safety Administration (NHTSA). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.