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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kg/m³
m/s²
m
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: Pabs = Pgauge + 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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