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Hydraulic Cylinder Calculator (Force, Speed and Flow)

Hydraulic cylinder push and pull force from bore, rod and pressure, plus extend and retract speed and time from pump flow, oil volume per stroke and the hydraulic power needed.

Units

Bore (piston) diameter (mm or in)

Rod diameter (mm or in)

Working pressure (bar or psi)

Stroke length (mm or in)

Pump flow (L/min or gpm)

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How it works

Bore area A = π·D² ÷ 4 · annulus area Aᵣ = π·(D² − d²) ÷ 4 · push F = p × A, pull F = p × Aᵣ · speed = pump flow ÷ area · time = stroke ÷ speed · oil volume = area × stroke · hydraulic power = p × Q (US: hp = psi × gpm ÷ 1,714)

A double-acting hydraulic cylinder pushes with the full piston area and pulls with the smaller annulus left around the rod, so it is stronger extending and faster retracting. Speed depends only on the pump flow and the area being filled, while force depends only on pressure and area. Real cylinders lose a few percent to seal friction (about 90–95% mechanical efficiency), and the relief valve setting caps the pressure, so size with some margin.

Worked example

An 80 mm bore cylinder with a 45 mm rod at 160 bar pushes with 16 MPa × 0.005027 m² = 80.42 kN (8.20 tonnes-force) and pulls with 54.98 kN. Fed by 40 L/min it extends at 132.6 mm/s, taking 3.77 s for a 500 mm stroke, and retracts in 2.58 s. Extending uses 2.51 L of oil, and the hydraulic power at full pressure is 10.67 kW.

Sources: Engineering ToolBox — Hydraulic cylinder force · Wikipedia — Hydraulic cylinder

Frequently asked questions

How do I calculate hydraulic cylinder force?

Multiply pressure by the piston area: F = p × π·D² ÷ 4. In metric, kN = bar × D(mm)² × π ÷ 40,000; in US units, lbf = psi × π·D(in)² ÷ 4. For the pulling force, subtract the rod area first.

Why does the cylinder retract faster than it extends?

On the rod side the oil fills only the annulus, a smaller volume per millimetre of travel, so the same pump flow moves the piston faster — but with less force.

How do I size the pump for a target speed?

Flow = area × speed. For an 80 mm bore extending at 100 mm/s you need 0.005027 m² × 0.1 m/s = 0.503 L/s, or about 30 L/min.

How much hydraulic power does the cylinder need?

Hydraulic power = pressure × flow: 160 bar × 40 L/min = 10.7 kW (US: psi × gpm ÷ 1,714 = hp). Divide by the pump and motor efficiencies (about 0.85 combined) to size the electric motor.

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This calculator is for educational purposes. Double-check important results before acting on them.