Linear Actuator Force Calculator — Hydraulic & Pneumatic
Enter the supply pressure, bore diameter, and rod diameter of a hydraulic or pneumatic cylinder to get the extension (push) and retraction (pull) forces in kilonewtons and pound-force.
bar
Pressure unit
mm
mm
Force when the cylinder extends — full bore area acts against supply pressure
3.12 kN
- 1
Pressure (N/mm²)
10 bar × 0.1 = 11 bar = 0.1 N/mm²; 1 psi ≈ 0.006895 N/mm². - 2
Bore area
π × (63 ÷ 2)² = 3,117.25 mm² - 3
Extension force (N)
1 × 3,117.25 = 3,117.2 N - 4
Extension force (kN)
3,117.2 ÷ 1000 = 3.12
How does this calculator work?
Extension force = P × π(D/2)² and retraction force = P × π[(D/2)² − (d/2)²]. At 10 bar with a 63 mm bore and 25 mm rod: push ≈ 3.1 kN, pull ≈ 2.6 kN. Real output is 3–10% lower due to seal friction. Convert bar to N/mm² by multiplying by 0.1; convert psi to N/mm² by multiplying by 0.006895.
Formula
How this is calculated
A linear actuator (hydraulic or pneumatic cylinder) converts fluid or gas pressure into linear mechanical force. During extension the full bore area opposes the pressure: F_ext = P × A_bore where A_bore = π(D/2)². During retraction the piston rod displaces part of that area, so only the annular ring between bore and rod sees pressure: F_ret = P × (A_bore − A_rod) = P × π[(D/2)² − (d/2)²]. This makes the pull force always smaller than the push force for any non-zero rod diameter.
Pressure unit conversions: 1 bar = 0.1 N/mm² = 0.1 MPa; 1 psi ≈ 0.006895 N/mm². The product P × A gives force in newtons when pressure is in N/mm² and area in mm² — the calculator converts to kN and lbf. Bore and rod diameters are in millimetres, as standard for ISO cylinders (common bore series: 32, 40, 50, 63, 80, 100, 125, 160, 200 mm).
These are theoretical (ideal) forces. Real cylinders have seal friction (typically 3–10% of theoretical force) and line pressure losses, so actual output is slightly lower. Always apply a safety factor of at least 1.5 when sizing actuators for structural or safety-critical applications. The push/pull ratio equals A_bore / A_annular and shows how much stronger the push stroke is relative to the pull stroke.
Frequently asked questions
During retraction, the piston rod physically occupies part of the bore cross-section on the rod side. Only the annular area (bore area minus rod area) is exposed to pressure — which is smaller than the full bore area. A thicker rod reduces the pull force further, increasing the push/pull ratio.
ISO 6020-2 / ISO 6432 pneumatic cylinders use bore sizes 8, 10, 12, 16, 20, 25, 32, 40, 50, 63, 80, 100 mm with matching rod diameters. Hydraulic cylinders (ISO 6020-1) use a similar metric series with heavier rods. Check your supplier's datasheet for exact bore-to-rod combinations offered for each bore size.
Use the working pressure of your circuit, not the relief valve set pressure. Pneumatic actuators typically operate at 5–10 bar (72–145 psi). Light industrial hydraulic systems run at 100–200 bar (1,450–2,900 psi); heavy machinery up to 350–700 bar. The relief valve may be set 10–20% above working pressure, but the actuator only sees working pressure under normal load.
Also known as
TG we-Calculate Editorial Team. (2026). Linear Actuator Force Calculator — Hydraulic & Pneumatic [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/linear-actuator-force-calculator
TG we-Calculate Editorial Team. "Linear Actuator Force Calculator — Hydraulic & Pneumatic." TG we-Calculate. 2026. https://we-calculate.com/calculator/linear-actuator-force-calculator.
TG we-Calculate Editorial Team, "Linear Actuator Force Calculator — Hydraulic & Pneumatic," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/linear-actuator-force-calculator
@misc{wecalculate_linear_actuator_force_calculator, title = {Linear Actuator Force Calculator — Hydraulic & Pneumatic}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/linear-actuator-force-calculator}}, year = {2026}, note = {TG we-Calculate} }
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