Force Equation: F = P x A

Hydraulic cylinder force is determined by Pascal's Law. The force output equals the system pressure multiplied by the effective piston area:

F = P x A

• F = Force output (N, kN, or lbf)
• P = System pressure (bar, psi, or MPa)
• A = Effective piston area (mm2, cm2, or in2)

Push Force (Extension)

When extending, pressure acts on the full bore (cap end) area:

F_push = P x A_bore = P x (pi x D^2 / 4)

Where D is the bore (piston) diameter.

Pull Force (Retraction)

When retracting, pressure acts on the annular (rod end) area - the bore area minus the rod area:

F_pull = P x A_annular = P x pi x (D^2 - d^2) / 4

Where d is the rod diameter. The rod displaces fluid, reducing effective area.

Force Ratio

The ratio of push to pull force depends on the bore-to-rod area ratio:

Force Ratio = F_push / F_pull = D^2 / (D^2 - d^2)

• Typical ratios range from 1.25:1 to 2:1
• Larger rod = higher ratio = greater push advantage
• Speed ratio is inverse: retract is faster by the same factor

Practical Considerations

• Mechanical efficiency: Real cylinders lose 2-8% to seal friction (multiply by 0.92-0.98)
• Dynamic vs static: Moving loads require additional force for acceleration
• Safety factor: Design for 1.5-2x required force minimum
• Rod buckling: Long strokes under push loads may require larger rods