Calculator · Fluid Mechanics
Hydrostatic Pressure Calculator
In a fluid at rest, pressure changes only with height. Work down from a free surface at a known pressure, or take the pressure difference between two elevations in the same continuous fluid.
Inputs
Positive downward. A depth of 0 is the free surface itself.
Type 101.325 kPa if you want the standard atmosphere here.
Gauge pressure is measured relative to the ambient pressure, so 0 kPa means ambient. It may legitimately be negative. No atmospheric pressure is added anywhere in this calculation.
h is depth below the free surface, positive downward, so a larger h means a higher pressure. z is elevation above the datum, positive upward. They are different quantities and are never mixed.
Results
Pressure at depth (gauge)
49.033 kPa, stated in the gauge reference you selected.
| Surface pressure p₀ | 0 Pa |
|---|---|
| Hydrostatic rise ρgh | 49.0333 kPa |
| Pressure p at h = 5 m | 49.0333 kPa |
| Pressure reference | Gauge |
Assumptions
- · Static fluid of constant density.
- · The result uses the same pressure reference kind as the stated surface pressure.
Pressure with depth
Pressure grows linearly with depth from 0 Pa at the free surface to 49.0333 kPa at a depth of 5 m.
Explore in the Lab
Same fluid, same surface pressure, with the manometer path, submerged surface and buoyancy alongside.
Technical reference
p = p₀ + ρ g h
p₂ − p₁ = ρ g (z₁ − z₂)
dp/dz = −ρ g
- p
- pressure at the point of interest[Pa]
- p₀
- pressure at the free surface[Pa]
- ρ
- fluid density, constant here[kg/m³]
- g
- gravity, 9.80665 m/s²[m/s²]
- h
- depth below the free surface, positive downward[m]
- z
- elevation above the datum, positive upward[m]
The fluid is at rest and its density is constant. With any motion, or with a compressible gas over a large height, this relation no longer holds on its own.
Pressure at a point acts equally in all directions, and every point at the same depth in the same connected fluid is at the same pressure. The shape of the container does not matter.
Gauge and absolute differ by the ambient pressure. This calculator reports whichever reference you selected and never converts between them silently.
The two elevations must lie in the same continuous fluid of that density. Crossing an interface into a different fluid needs the Manometer calculator instead.