Hydraulic cylinder force calculator
Push and pull force in tonnes and kN, cylinder speed and power pack size, from bore, rod and pressure.
How it is calculated
Force is pressure times the area the oil pushes on. Pushing, the oil fills the full bore. Pulling, the rod takes up part of the area, so the pull force is always smaller.
Rod-side area = π × (D² − d²) ÷ 4
Force (N) = pressure (N/mm²) × area (mm²)
1 bar = 0.1 N/mm² · 1 kg/cm² = 0.0981 N/mm²
Tonnes = N ÷ 9,806.65
Speed (mm/s) = flow (L/min) × 1,000,000 ÷ 60 ÷ area
Power (kW) = pressure (bar) × flow (L/min) ÷ 600
Worked example
An 80 mm bore cylinder with a 45 mm rod at 160 bar: the bore area is 5,026.5 mm², so the push force is 80.4 kN, about 8.20 tonnes. The rod side has 3,436.1 mm², so it pulls with 55.0 kN, about 5.61 tonnes. With a 20 L/min pump it extends at 66.3 mm/s and retracts faster, at 97.0 mm/s. The hydraulic power is 5.33 kW.
Questions
How do I calculate hydraulic cylinder force?
Multiply the pressure by the piston area. In metric units: force in newtons = pressure in N/mm² × area in mm². 1 bar is 0.1 N/mm². Divide newtons by 9,806.65 for tonnes.
Why is the pull force less than the push force?
When the cylinder pulls, the oil presses on the ring around the rod, not on the full piston. The rod's area is missing, so the same pressure gives less force.
Is bar the same as kg/cm²?
Almost. 1 kg/cm² is 0.981 bar, so 160 kg/cm² is about 157 bar. Choose the unit your gauge shows and the calculator converts it.
How do I size the power pack motor?
Hydraulic power in kW is pressure in bar × flow in L/min ÷ 600. Pumps lose some power, so pick a motor about 15% larger than the result.
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