Piston Force Calculator — Hydraulic & Pneumatic Cylinders
Calculate the push (extend) and pull (retract) force of a hydraulic or pneumatic cylinder. Enter the operating pressure, bore diameter and rod diameter to get force in kN and lbf instantly.
Pressure unit
Diameter unit
Force on full bore area — cylinder pushing out
- 1
Pressure (Pa)
100 bar × 100 000 = 10,000,000 - 2
Full bore area (m²)
π × (0.08 ÷ 2)² = 0.00502655 - 3
Extend force (N)
10,000,000 × 0.00502655 = 50,265.5 - 4
Extend force (kN)
50,265.5 ÷ 1 000 = 50.27
How does this calculator work?
Piston force: F_extend = P × π/4 × Bore²; F_retract = P × π/4 × (Bore² − Rod²). Enter pressure (bar, psi, kPa or MPa) and bore/rod diameters (mm, cm, in or m). Outputs extend and retract force in kN and lbf, piston areas and the extend/retract ratio.
Formula
How this is calculated
A linear actuator (hydraulic or pneumatic cylinder) produces force by applying fluid pressure over the piston face area: F = P × A. During extension, pressure acts on the full bore area A_full = π/4 × Bore². During retraction, the rod occupies part of the piston face, so the effective area is the annular ring: A_annular = π/4 × (Bore² − Rod²). The extend force is therefore always larger than the retract force for the same pressure.
All inputs are converted to SI units internally (Pa and m²) so the result in Newtons is exact. The output is then converted to kN and lbf for convenience. The extend/retract ratio (= A_full / A_annular) is a fixed geometric property of the cylinder — equal pressure always produces that ratio between the two forces.
This calculator treats the cylinder as ideal — it ignores friction (seal drag), back-pressure on the return port, pressure losses in hoses and fittings, and compressibility (for pneumatics at high pressure). Practical force is typically 85–95% of the theoretical value after accounting for cylinder efficiency.
Frequently asked questions
During extension, pressure pushes against the full bore area. During retraction, the rod takes up part of the piston face, leaving only the annular area for pressure to act on. For the same supply pressure, force = pressure × area, so the smaller annular area produces less retract force.
Hydraulic systems typically operate at 70–700 bar (1 000–10 000 psi). Pneumatic systems usually work at 4–10 bar (60–145 psi). Both use the same force formula — just enter the gauge pressure and the calculator handles the unit conversion.
Rearrange the formula: required bore = √(4 F / π P). Pick the nearest available standard bore size and verify the computed force exceeds your requirement with a safety margin of at least 1.25–1.5×. Remember to check retract force separately if your application needs pulling force.
Also known as
TG we-Calculate Editorial Team. (2026). Piston Force Calculator — Hydraulic & Pneumatic Cylinders [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/piston-force-calculator
TG we-Calculate Editorial Team. "Piston Force Calculator — Hydraulic & Pneumatic Cylinders." TG we-Calculate. 2026. https://we-calculate.com/calculator/piston-force-calculator.
TG we-Calculate Editorial Team, "Piston Force Calculator — Hydraulic & Pneumatic Cylinders," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/piston-force-calculator
@misc{wecalculate_piston_force_calculator, title = {Piston Force Calculator — Hydraulic & Pneumatic Cylinders}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/piston-force-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?