Hydrostatic Pressure Calculator

The pressure exerted by a static fluid increases linearly with depth. Every metre you descend in water adds the weight of a one-metre column of water on top of you. The formula that describes this is P equals rho times g times h, where P is the gauge pressure in pascals, rho is the density of the fluid in kilograms per cubic metre, g is the gravitational acceleration in metres per second squared, and h is the depth below the surface in metres. For fresh water (density 1000 kg/m3) on Earth (g = 9.81 m/s2), pressure increases by about 9810 Pa, or roughly 0.097 atm, for every metre of depth. At 10 metres depth the gauge pressure is therefore about 98,100 Pa, which is close to one full atmosphere. This is why scuba divers must be careful about pressure changes and gas laws, and why deep-sea equipment requires specialised pressure-resistant design. Hydrostatic pressure also explains Archimedes' principle, the design of water towers, and the operation of hydraulic systems. This calculator takes fluid density, gravitational acceleration, and depth as inputs and returns the gauge pressure (above atmospheric), the absolute pressure (including standard atmospheric pressure at sea level), and equivalent pressures in kilopascals, atmospheres, and bar. You can change the gravity value for calculations on other planets or adjust the fluid density for seawater, oil, mercury, or other fluids using the presets provided.

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Fluid preset

Fluid density ρ

kg/m³

Gravity g

m/s²

Depth h

98,100 Pa

gauge pressure (P = ρgh)

Gauge in kPa98.10 kPa

Gauge in atm0.968 atm

Absolute pressure199,425 Pa

Absolute in atm1.968 atm

Atmospheric pressure is taken as 101,325 Pa (1 atm) at sea level. Gauge pressure is relative to that surface value.

How it works

Gauge pressure is P = ρ × g × h, where ρ is fluid density in kg/m³, g is gravity in m/s², and h is depth in metres. Absolute pressure adds standard atmospheric pressure: P_abs = P_gauge + 101,325 Pa. To convert: 1 atm = 101,325 Pa; 1 bar = 100,000 Pa. Pressure increases linearly with depth and is independent of the container shape or horizontal area.

Worked example

Fresh water has a density of 1000 kg/m³. At a depth of 10 m on Earth (g = 9.81 m/s²): gauge pressure P = 1000 × 9.81 × 10 = 98,100 Pa = 98.10 kPa = 0.969 atm. Adding atmospheric pressure: absolute pressure = 98,100 + 101,325 = 199,425 Pa = 1.969 atm. These match the default values pre-filled in the calculator above.

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Frequently asked questions

What is hydrostatic pressure?

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the weight of the fluid above it. It is calculated as P = rho times g times h, where rho is the fluid density in kg per cubic metre, g is gravitational acceleration in m per second squared (9.81 on Earth), and h is the depth below the fluid surface in metres. Hydrostatic pressure increases linearly with depth and depends on the fluid density and gravity, but not on the horizontal area of the container.

What is the difference between gauge and absolute pressure?

Gauge pressure is the pressure above atmospheric pressure and is what a typical pressure gauge reads. Absolute pressure is the total pressure including atmospheric pressure (approximately 101,325 Pa at sea level). Absolute pressure = gauge pressure + atmospheric pressure. Gauge pressure is positive for pressures above atmospheric and negative for pressures below (vacuum). Hydrostatic pressure from the P = rho g h formula is a gauge pressure measured relative to the surface of the fluid.

How much pressure is there at 10 metres depth in water?

At 10 metres depth in fresh water (density 1000 kg per cubic metre), the gauge pressure is rho times g times h = 1000 times 9.81 times 10 = 98,100 Pa, which is approximately 0.97 atm or 0.981 bar. Adding atmospheric pressure of 101,325 Pa gives an absolute pressure of about 199,425 Pa, or roughly 1.97 atm. This is why every 10 metres of water depth adds approximately one atmosphere (about 101,325 Pa) to the absolute pressure on a diver.