TAHA Engineering Toolsby TAHA Knowledge Lab

Mechanical Engineering

Pressure & Hydrostatic Pressure Calculator

Pressure from force over an area, or gauge and absolute pressure at a depth in a still liquid.

Inputs

Calculate from
A force F pressing down on a circular pad of diameter D resting on a surface.FD (area A = πD² ÷ 4)p
A force F pushes a circular pad of diameter D onto a surface. The average pressure under the pad is p = F ÷ A, with A = πD² ÷ 4. Diagram not to scale.

Result

Pressure
1.27324
Area used
7,853.98

A force of 10,000 N spread evenly over 7,853.98 mm² gives an average pressure of 1.27324 MPa.

Educational estimate — check the assumptions below.

About this calculator

Pressure is force spread over an area. The same force on a smaller area gives a higher pressure — which is why a knife cuts and a wide foot does not sink. The first mode finds the average pressure from a force and the area it acts on, such as a press ram, a column base or a pad on the floor.

The second mode finds the pressure inside a still liquid at a given depth, for example at the bottom of a water tank, in a dam or under the sea. It gives both gauge pressure (the extra pressure caused by the liquid, which is what most pressure gauges read) and absolute pressure (gauge pressure plus the pressure acting on the liquid surface).

Formula

Force ÷ area

p = F ÷ A    (circular face: A = πD² ÷ 4)

p = average pressure (Pa = N/m²), F = force at right angles to the surface (N), A = area (m²), D = diameter (m). 1 MPa = 1 N/mm² = 10 bar.

Liquid depth (hydrostatic)

pgauge = ρ × g × h

pabs = pgauge + psurface

ρ = liquid density (kg/m³), g = gravitational acceleration (m/s²), h = vertical depth below the surface (m), psurface = absolute pressure on the liquid surface (atmospheric pressure for an open tank).

Worked example

Force ÷ area: a press applies 10 kN through a round punch 100 mm in diameter. Area = π × 100² ÷ 4 = 7853.98 mm², so p = 10 000 ÷ 7853.98 = 1.273 N/mm² = 1.273 MPa (12.73 bar).

Hydrostatic: fresh water (ρ = 1000 kg/m³) at a depth of 10 m, with g = 9.80665 m/s²:

  • Gauge pressure = 1000 × 9.80665 × 10 = 98 066.5 Pa ≈ 98.07 kPa ≈ 0.981 bar (about 14.22 psi)
  • Absolute pressure, open tank at standard atmosphere = 98.07 + 101.325 = 199.39 kPa

Assumptions and limitations

  • Force ÷ area gives the average pressure, assuming the force is spread evenly and acts at right angles to the surface. Real contact pressure can peak at edges.
  • Hydrostatic mode assumes a still (static) liquid of constant density. It does not apply to flowing liquids, gases over large heights, or liquids that are accelerating.
  • Gauge pressure is measured relative to the pressure on the liquid surface; absolute pressure is measured relative to a perfect vacuum.
  • The result depends only on vertical depth, not on the shape or size of the container.

Safety note

Pressure vessels, tanks and hydraulic equipment must be designed and tested to the applicable standards. Do not use this result alone to judge whether equipment is safe.

References

  • Definition of pressure, p = F/A (ISO 80000-4); hydrostatic equation p = ρgh for a fluid at rest; standard gravity 9.80665 m/s² and standard atmosphere 101 325 Pa.