Pneumatic and Hydraulic Cylinder Force and Speed Calculator

Push and pull force, speed, stroke time and flow of a pneumatic or hydraulic cylinder from the bore, rod and pressure.

How it works

The force a cylinder produces is the pressure times the area it acts on. On extension the pressure acts on the full piston area; on retraction it acts on the smaller annulus (piston area minus rod area), so the pull force is lower and the speed for the same flow is higher.

F = p × A × η, Apush = π D² ÷ 4, Apull = π (D² − d²) ÷ 4, v = Q ÷ A

The fluid power p Q is the power the pump or compressor must deliver. The same relations apply to air and oil; for air, the flow Q is the volume at the working pressure, and the air used per stroke is in the Compressed Air Consumption Calculator. Actuator selection and drives are in Motion Control and Actuators.

Worked example

A hydraulic cylinder with a 100 mm bore and 56 mm rod, working at 160 bar with 40 L/min of oil, stroke 500 mm, efficiency 90 %.

  • Areas: piston 78.54 cm²; annulus 53.91 cm².
  • Push force = 160×10⁵ × 0.007854 = 125.7 kN theoretical, 113.1 kN actual (11.5 tonnes-force). Pull force = 86.3 kN theoretical, 77.6 kN actual.
  • Speed: extend = 40 L/min ÷ 78.5 cm² = 84.9 mm/s; retract = 123.7 mm/s.
  • Stroke times: 5.89 s out, 4.04 s back. Oil per stroke: 3.93 L. Fluid power: 160×10⁵ × 40÷60 000 = 10.67 kW.

Things to know

Rod buckling limits the push force of a long, slender cylinder: for strokes more than about ten times the rod diameter, check the buckling load of the rod with the mounting style (see Columns and Buckling).

Pneumatic cylinders lose more to friction and to the pressure drop in the supply: use the pressure at the cylinder, not at the compressor, and an efficiency of 80 to 85 percent for design.

The speed from the flow is the average speed. Air compressibility makes pneumatic cylinders accelerate and slow down unevenly: use flow controls (meter-out) and cushions.

Hydraulic pressure may be limited by the cylinder rating and the relief valve setting. A cylinder with a differential area can also intensify pressure on the rod side when the rod end is blocked: use a relief valve.

Cylinders that decelerate a mass need to dissipate its kinetic energy in the cushion or a shock absorber.

Common questions

Why is the retract force lower than the extend force?

The rod takes up part of the piston area on the rod side, so the pressure acts on a smaller area. A 100 mm bore with a 56 mm rod loses about 31 percent of its area on retraction.

How do I find the cylinder bore for a given force?

Area = F ÷ (p × η), then D = √(4 A ÷ π), rounded up to a standard bore. Leave a margin of 25 percent or more for friction, acceleration and pressure drop.

What pressure is used for pneumatic cylinders?

Typically 6 bar (about 87 psi) gauge; the cylinder force at 6 bar is 0.6 N per mm² of area, or 6 kN per 100 cm².

Sources

  • ISO 6020/6022 (hydraulic cylinders), ISO 15552 (pneumatic cylinders); Festo and Parker cylinder catalogs (force tables).
  • Esposito, A., Fluid Power with Applications, Pearson.

Last reviewed: November 2, 2026