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Hydraulic Cylinder Force Calculator: Formulas and Example

Calculate theoretical hydraulic cylinder extension and retraction force from pressure, bore and rod diameter.

Use basic pressure-and-area formulas to estimate theoretical cylinder force. Actual system performance also depends on losses, friction, side load, geometry and safety factors.

Extension Force Formula

Extension force = Pressure × Full piston area. For a circular piston, area = π × bore² ÷ 4.

In SI units, force in newtons can be calculated from pressure in pascals and area in square metres. A convenient engineering conversion is: force (kN) ≈ pressure (bar) × piston area (cm²) ÷ 100.

Retraction Force Formula

Retraction force = Pressure × Annular area. Annular area equals full piston area minus rod area, so retraction force is normally lower than extension force at the same pressure.

Worked Example

For an 80 mm bore at 160 bar, the piston area is approximately 50.27 cm². The theoretical extension force is about 80.4 kN before allowing for efficiency, geometry and safety factors.

Inputs Required for Final Sizing

  • Required force in both directions
  • System working and peak pressure
  • Bore, rod diameter and stroke
  • Mounting geometry and load angle
  • Speed, flow, duty cycle and environment

Do not select a cylinder from theoretical force alone. Confirm structural capacity, buckling risk, mounting loads, cushioning and system limits.


Need a project-specific review? Use the RFQ form to share the application, dimensions, pressure, quantity and drawing.