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Hydrostatic Pressure & Pascal’s Principle Calculator

Calculate gauge pressure at depth in a fluid or model force multiplication in an ideal hydraulic system.

Formula shown Runs locally Reviewed Aug 11, 2026
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Equation guide

Static uniform fluid and ideal hydraulic transmission

Pressure increase with depth

p = ρgh

Pascal’s principle

F₁/A₁ = F₂/A₂

Ideal force multiplication

F₂/F₁ = A₂/A₁
Fluid pressure

Explore depth and hydraulic force

Depth is measured vertically downward from the fluid surface. The result is gauge pressure, not absolute pressure.

Inputs and displayed values use at most three decimal places.

p = ρgh

Enter the fluid properties and vertical depth.

Hydrostatic pressure on a horizontal areaA fluid column of height h presses on area S. Its weight G supplies force F, so pressure equals force divided by area.hSGp = F / SF is the weight of the fluidcolumn above area S.F = G
The pressure at depth comes from the weight of the fluid column above the selected horizontal area.

Using the model

Symbols, assumptions and limitations

Interpretation notes

Hydrostatic gauge pressure assumes a fluid at rest with uniform density and gravitational acceleration. Zero depth gives zero gauge pressure. The hydraulic model accepts a non-negative input-force magnitude and assumes an enclosed incompressible fluid, equal transmitted pressure, negligible friction, and no height difference between pistons.

Worked examples

See the method in practice

01

Water below the surface

At 5 m depth in water with ρ = 1000 kg/m³ and g = 9.807 m/s², gauge pressure is about 49.035 kPa.

02

Hydraulic lift

A 200 N input on 0.01 m² transmitted to a 0.25 m² piston ideally produces 5000 N.

Questions

Frequently asked

Is hydrostatic pressure absolute pressure?

The result ρgh is gauge pressure above the pressure at the fluid surface. Add surface pressure to obtain absolute pressure.

Why can a hydraulic system multiply force?

The same pressure acts on both pistons, so the larger piston area produces a proportionally larger force. Its displacement is proportionally smaller, conserving work ideally.

Does the hydraulic model include losses?

No. Real systems lose energy through friction, fluid viscosity, deformation, leakage, and pressure differences caused by elevation.

Sources & review

Equations and examples are checked against the references below. Results are educational and should be independently verified for safety-critical work.

OpenStax University Physics — Pressure in a Static Fluid OpenStax University Physics — Pascal’s Principle and Hydraulics

Written by the STEM Hub editorial team · Reviewed August 11, 2026 · Review methodology