Hydrostatic Pressure Calculator

Created by Krishna Nelaturu
Last updated: Jun 22, 2022

Whether you want to calculate the ocean pressure your favorite diver or a submarine experiences, or you just want to complete that one problem in your homework, this hydrostatic pressure calculator is here for you.

Hydrostatic pressure may seem an elusive concept, but we shall break it down to show you how simple it is. Specifically, let's answer some fundamental questions:

  • What is hydrostatic pressure or fluid pressure?
  • What is the formula for hydrostatic pressure?

If you're exclusively interested in calculating pressure, try our pressure calculator.

What is hydrostatic pressure or fluid pressure?

Consider a fluid at rest. Under the influence of gravity, every layer in the liquid would apply a certain pressure on the layer below it. The deeper we go, the more liquid volume is present above, and hence higher this pressure. It depends on the strength of the gravity, the density of the fluid, and the depth inside the fluid. We call this fluid pressure the hydrostatic pressure. The size and shape of the container has no affect on this pressure.

Notice how the hydrostatic pressure stems from the influence of gravity. To learn more about its effects on you and the things around you, visit our gravitational force calculator.

Hydrostatic pressure formula

The equation for hydrostatic pressure is given by:

p=ρgh+p0p = \rho g h + p_0

where:

  • pp is the hydrostatic pressure;
  • ρ\rho is the density of the liquid;
  • gg is the gravitational acceleration, equals 9.81 m/s on Earth;
  • hh is the depth inside the liquid body; and
  • p0p_0 is the pressure at the surface of the liquid, usually the atmospheric pressure (equal to 1 atm or 1.013 MPa).

We can use this hydrostatic pressure equation to calculate the pressure at any depth for any fluid, given we know its density.

For example, let's calculate the water head pressure at the bottom of a 40 feet freshwater lake. Using the fluid pressure equation above, we have:

p=ρgh+p0=62.43 lb/ft332.15 ft/s240 ft+1 atm=220.9 kPa=2.18 atm\footnotesize\begin{align*} p &= \rho g h + p_0\\ &= 62.43 \text{ lb/ft}^3 \cdot 32.15 \text{ ft/s}^2 \cdot 40 \text{ ft} + 1 \text{ atm} \\ & = 220.9 \text{ kPa}\\ & = 2.18 \text{ atm} \end{align*}

Now that you've a good grasp of the concept, challenge yourself to use this fluid pressure equation to calculate the water pressure at the bottom of your favorite ocean. Verify your calculated ocean pressure with this calculator. You'll love its versatility with unit conversions!

Want to calculate water head pressure in a manometer? Then drop what you're doing and head over to our manometer calculator!

How to use this hydrostatic pressure calculator

This hydrostatic pressure calculator is a versatile tool ready to help you calculate pressure at depth of any fluid:

  1. Select any fluid from the Fluid field and the calculator will look up its density. You can skip this step if you want to enter a custom density value instead.
  2. Enter the value of the depth where you want to calculate water pressure or fluid pressure. This calculator will show you the result in the hydrostatic pressure field.

Note that by default, this calculator takes the values g = 9.801 m/s and p₀ = 1 atm, but you can change these values by selecting advanced mode.

Krishna Nelaturu
Fluid (optional)
Water (pure)
Density of fluid
kg/m³
Depth
m
Hydrostatic pressure
atm
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