Pressure Calculator (Force/Area & Fluid Depth)

About the Pressure Calculator (Force/Area & Fluid Depth)

Pressure is force spread over an area. This calculator works it out three ways:

• Force ÷ area: give two of the pressure, the force and the area, and get the third, with the pressure in pascals, kilopascals, megapascals, bar, psi, atmospheres and mmHg. Type an area, or choose a ⌀ unit and type the diameter of a round one.
• Depth in a liquid: the pressure at a depth, p = p₀ + ρ·g·h, both the gauge pressure (the liquid’s own) and the absolute pressure (with the air above), or the depth that gives a pressure, in fresh water, seawater, mercury, oils or a liquid of your own, on Earth or another world.
• Hydraulic press: Pascal’s principle multiplies a force by the ratio of the pistons’ areas; get the output force or the force needed to lift a load, the pressure in the liquid and how far the large piston rises.

With a Pro pass, copy the result or download it as a CSV, or unlock this one result. Without a pass the free preview shows the pressure, force, area or depth you solve for in full, with the first rows of the table and the first step of the working; every other figure is hidden.

Common uses

• Physics homework on pressure, fluids and Pascal’s principle
• Working out the water pressure at the bottom of a pool, a tank or a dive
• Comparing the pressure under a shoe, a tyre or a tool tip
• Sizing the pistons of a hydraulic jack or press for a force you need
• Turning a depth into a pressure in the unit a gauge shows, and back

The formulas

• Pressure p = F ÷ A: the force pressing straight onto an area, in pascals (1 Pa = 1 N/m²)
• The area of a circle A = π·d² ÷ 4, from its diameter d
• At a depth h in a liquid of density ρ: p = p₀ + ρ·g·h, where p₀ is the pressure at the surface; the liquid alone adds ρ·g·h
• The depth for a pressure: h = (p − p₀) ÷ (ρ·g), or the gauge pressure ÷ (ρ·g)
• Hydraulic press (Pascal’s principle): F₁ ÷ A₁ = F₂ ÷ A₂, so F₂ = F₁·A₂ ÷ A₁; the liquid’s volume stays the same, so the large piston moves d₂ = d₁·A₁ ÷ A₂ and the work out equals the work in

Gauge or absolute?

Gauge pressure is measured from the air’s pressure: a tyre gauge, a depth gauge or a blood-pressure cuff reads gauge pressure. Absolute pressure counts the air too: absolute = gauge + atmospheric. OpenStax’s example: a tyre gauge reading 34 psi means an absolute pressure of 34 + 14.7 = 48.7 psi.

For a depth, set the pressure at the surface to 1 atm (101.325 kPa, the standard atmosphere at sea level) for open water, to your local air pressure for more accuracy, or to 0 to see the gauge pressure alone.

Pressure units

• Pa (pascal): 1 N per m²; hPa = 100 Pa (weather), kPa = 1,000 Pa, MPa = 1,000,000 Pa
• bar = 100,000 Pa exactly
• atm, the standard atmosphere, = 101,325 Pa exactly
• psi, pounds-force per square inch, ≈ 6,894.757 Pa
• mmHg, the conventional millimetre of mercury, ≈ 133.322 Pa, so 760 mmHg ≈ 1 atm

For more units, gauge and absolute readings in barg and psig, use the Pressure Converter.

Sources

• OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure: p = F ÷ A, p = p₀ + ρ·g·h and the densities of Tables 14.1 and 14.2 (CC BY 4.0)
• OpenStax, University Physics Volume 1, §14.2 Measuring Pressure: gauge and absolute pressure (CC BY 4.0)
• OpenStax, University Physics Volume 1, §14.3 Pascal’s Principle and Hydraulics: F₁ ÷ A₁ = F₂ ÷ A₂ and Example 14.3 (CC BY 4.0)
• NIST Guide to the SI, Appendix B.8: the standard atmosphere (101,325 Pa) and the bar (100,000 Pa), both exact, and psi and mmHg in pascals
• NOAA: How does pressure change with ocean depth?: about one atmosphere more for every 10.06 m (33 ft) down

Limitations

• Liquids are taken as incompressible with a constant density: over great depths they are squeezed a little denser, so real pressures are slightly higher.
• The densities of the list are typical values at the temperatures given (seawater at 0 °C); warm or less salty seawater is a little lighter. Enter your own density when it matters.
• The hydraulic press is ideal: no friction, no leaks and both pistons at the same height.
• An educational calculator: for pressure vessels, diving plans or hydraulic equipment, follow the rated limits and standards that apply to them.

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