Pneumatic Cylinder Force Calculator

Formula

• F_extend = P × (π/4) × D_bore²
• F_retract = P × (π/4) × (D_bore² − D_rod²)
• P in pascals (bar × 10⁵), diameters in metres

About this calculator

Part of our Fluid Power Calculators collection. Pneumatic and hydraulic cylinder forces and system sizing.

How it works

Extend force uses the full piston area. Retract force uses the annulus area because the rod reduces the effective bore. Enter system pressure and cylinder dimensions to compare push and pull capability on the same actuator.

Enter your values in the inputs above and click CALCULATE. Results appear on the right without a page reload. No login and no server upload.

Worked example

6 bar shop air, 50 mm bore, 20 mm rod diameter.

1. P = 6 bar = 600,000 Pa
2. Bore area = π/4 × 0.05² = 0.001963 m²
3. F_extend = 600,000 × 0.001963 = 1,178 N
4. Annulus area = π/4 × (0.05² − 0.02²) = 0.001650 m² → F_retract = 990 N

Result: Extend 1.18 kN, retract 0.99 kN, retract/extend ratio 0.84.

When to use

• Sizing a pneumatic actuator for push or pull load
• Checking if retract force is enough on a single-rod cylinder
• Comparing bore sizes at a fixed shop pressure

Limitations

• Static force at full pressure; no friction, seal drag, or speed
• Assumes perfect pressure on both sides when calculating retract
• Does not account for rod-end vs blind-end port sizing

FAQ

Why is retract force lower than extend force?

On extend, pressure acts on the full piston area. On retract, the rod occupies part of the bore, so the effective annulus area is smaller.

What pressure should I use?

Typical shop air is 6 to 8 bar (87 to 116 psi). Use the regulated pressure at the cylinder port, not compressor tank pressure.

Can rod diameter equal bore diameter?

Rod must be smaller than bore. If rod approaches bore size, retract force approaches zero.