Hydrostatic Pressure Calculator

About the Hydrostatic Pressure Calculator

Hydrostatic pressure is the pressure a fluid exerts at a given depth due to the weight of the fluid above. It increases linearly with depth.

Enter the fluid density (kg/m³), gravity (default 9.81) and depth (m). The gauge pressure is returned in pascals (Pa); add atmospheric pressure (~101,325 Pa) for absolute pressure.

How to use this calculator

1. Enter the fluid density \(\rho\) in units like \(\text{kg/m}^3\).
2. Enter gravity \(g\), usually \(9.8\,\text{m/s}^2\) on Earth.
3. Enter the depth \(h\) below the surface in meters.
4. Read the pressure \(P\) from the calculator, in pascals.

The formula explained

The formula \(P = \rho g h\) computes the hydrostatic pressure caused by a fluid at a given depth. It shows that pressure grows with density, gravity, and depth.

• P = hydrostatic pressure, in pascals \(\text{Pa}\)
• \(\rho\) = fluid density, in \(\text{kg/m}^3\)
• g = gravitational acceleration, in \(\text{m/s}^2\)
• h = depth below the fluid surface, in meters

Step by step method

1. Write down the density, gravity, and depth with matching units.
2. Multiply \(\rho\) by \(g\).
3. Multiply the result by \(h\) to get \(P\).

Worked example

Problem. Find the hydrostatic pressure in water with density \(1000\,\text{kg/m}^3\) at a depth of \(5\,\text{m}\), using \(g = 9.8\,\text{m/s}^2\).

1. Substitute into the formula: \(P = 1000 \times 9.8 \times 5\).
2. Compute the product: \(1000 \times 9.8 = 9800\), then \(9800 \times 5 = 49000\).
3. So the pressure is \(49000\,\text{Pa}\).

Tips and common mistakes

• Make sure depth \(h\) is measured vertically below the fluid surface, not along a slope.
• Use consistent units, because \(\rho\), \(g\), and \(h\) must match for the result to be in pascals.

Frequently asked questions