TAHA Engineering Toolsby TAHA Knowledge Lab

Mechanical Engineering

Hydraulic Cylinder Force Calculator

Push and pull force of a hydraulic or pneumatic cylinder from bore, rod and pressure.

Inputs

Hydraulic cylinder cross-section: bore diameter D, rod diameter d, pressure p behind the piston, push force F at the rod end.pDdFPush: F = p × πD² ÷ 4
Pressure p acts on the piston. Extending (push) uses the full bore area of diameter D; retracting (pull) uses the ring area left after subtracting the rod diameter d. Diagram not to scale.

Gauge pressure supplied to the cylinder.

100% = theoretical force. Seal friction typically reduces real force; use the manufacturer’s figure if you have it.

Result

Push force (extend)
78.5398
Pull force (retract)
58.9049
Piston area
78.5398
Annulus area (rod side)
58.9049

At 100 bar, a 100 mm bore cylinder pushes with 78.5398 kN and pulls with 58.9049 kN. Pulling force is lower because the rod takes up part of the piston area.

Educational estimate — check the assumptions below.

About this calculator

A cylinder turns fluid pressure into a straight-line force. The force equals pressure multiplied by the area the pressure acts on. When extending, pressure acts on the full piston. When retracting, the rod covers part of the piston, so only the ring-shaped (annulus) area is used and the force is smaller.

Formula

Fpush = p × πD² ÷ 4    Fpull = p × π(D² − d²) ÷ 4

p = pressure (Pa = N/m²), D = bore, d = rod diameter (m). Multiply by efficiency for an estimate of real force. Handy form: F (kN) = p (bar) × A (cm²) ÷ 100.

Worked example

Bore 100 mm, rod 50 mm, pressure 100 bar (10 MPa):

  • Piston area = π × 100² ÷ 4 = 7854 mm² = 78.54 cm²
  • Push force = 100 × 78.54 ÷ 100 = 78.5 kN (about 8.0 tonne-force)
  • Annulus area = 78.54 − 19.63 = 58.90 cm² → pull force = 58.9 kN

Imperial: 3 in bore at 1000 psi → 7.069 in² × 1000 = 7069 lbf.

Assumptions and limitations

  • Static, theoretical force. Seal friction, back-pressure on the other side of the piston and pressure losses in hoses reduce the real force.
  • Rod buckling, mounting strength and cylinder pressure rating are not checked.

Safety note

Never exceed the pressure rating of the cylinder, hoses, fittings or pump. Stored hydraulic pressure is dangerous: release pressure before any maintenance. Do not use this estimate alone for lifting or pressing equipment design.

References

  • Pascal’s principle: force = pressure × area.