Pressure at Depth Calculator: P = rho g h

The pressure in a liquid at a depth below the surface.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • P = \rho\,g\,h
  • h = \frac{P}{\rho\,g}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the gauge pressure: gauge pressure = density of the liquid x gravitational field strength x depth
  2. Put the values in (every value in its SI unit): gauge pressure = 1000 x 9.80665 x 10
  3. The answer: gauge pressure: 98066.5 Pa
  4. The same answer in other units: 98.0665 kPa; 0.980665 bar; 14.2233 psi; 0.967841 atm

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is the formula for pressure at depth?

Pressure equals density times gravity times depth. At 10 m in fresh water the gauge pressure is 98.1 kPa, or about 1 bar.

How much does pressure rise with depth in water?

About 9.8 kPa for every metre, so about 1 bar for every 10 m.

What is the absolute pressure?

The gauge pressure plus the atmospheric pressure on the surface.

Related calculators

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Further reading: Any school physics or fluid mechanics text (hydrostatic pressure).

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