Calculators · Hydraulics and pneumatics
Hydraulic cylinder force, speed and volume calculator
A hydraulic cylinder turns fluid pressure into a straight-line push or pull. It pushes harder than it pulls, because on the return stroke the rod takes up part of the piston area, and for the same reason it retracts faster than it extends. These calculators give the force, the speed, the cycle time and the oil volume of a double-acting cylinder from its bore, rod diameter, stroke, pressure and pump flow.
Push and pull force
Multiplies system pressure by the effective piston area on each side. The extending (push) force uses the full bore; the retracting (pull) force uses the ring-shaped area around the rod. An efficiency factor covers seal friction.
F_push = P × π/4 × bore² × η F_pull = P × π/4 × (bore² − rod²) × η
Extension and retraction speed
Divides pump flow by the effective area to give piston speed. The cylinder retracts faster than it extends because less oil fills the smaller rod-side area.
v = Q / A
Cycle time
Calculates how long a full extension and retraction take at a given flow. Machine designers use this to check whether a loader arm, press or tipper will cycle fast enough.
t = A × stroke / Q
Oil volume
Gives the oil needed to fill each side of the cylinder over its stroke. The difference between the two is the rod volume — oil the tank must supply when the cylinder extends and receive back when it retracts.
V = A × stroke
Worked example: a 100/50 cylinder at 200 bar
- Piston area: π/4 × 100² = 7,854 mm². Annulus: 7,854 − 1,963 = 5,890 mm².
- Push force at 200 bar (20 N/mm²): 7,854 × 20 = 157,080 N, about 16 tonnes-force. Pull: 117,810 N.
- At 40 L/min the rod extends at 85 mm/s and retracts at 113 mm/s.
- A 500 mm stroke takes 5.9 s out and 4.4 s back, using 3.9 L and 2.9 L of oil.
Push force of common bores
| Bore | At 100 bar | At 200 bar |
|---|---|---|
| 40 mm | 12.6 kN | 25.1 kN |
| 63 mm | 31.2 kN | 62.3 kN |
| 80 mm | 50.3 kN | 100.5 kN |
| 100 mm | 78.5 kN | 157.1 kN |
| 125 mm | 122.7 kN | 245.4 kN |
Related
About these results
Results are theoretical estimates from standard engineering formulas. Real-world figures depend on conditions these formulas do not capture. Always follow the manufacturer's specifications for maintenance, loading and safety decisions.
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