How this calculation works
A cylinder’s cap end acts over the full bore area. The rod side acts over the bore area minus the rod area. Subtract the opposing pressure force separately for each stroke direction.
Extension = P·Afull − Pback·Aannular; retraction = P·Aannular − Pback·AfullA worked example
A 100 mm bore at 100 bar and zero backpressure produces ideal extension force 78.5398 kN. A 50 mm rod reduces ideal retraction force to 58.9049 kN.
Good to know
Ideal pressure forces and geometry only. Friction, acceleration, buckling, fixtures and hardware ratings are excluded. Both pressures must use the same reference. Negative net force is retained when opposing pressure dominates.
Reference: OpenStax: Pascal’s principle and hydraulics (opens in a new tab) ↗
The rod changes force and displacement
A piston has two different working faces. The cap end sees the full circular bore area. The rod end loses the area occupied by the rod, leaving an annulus. Equal pressure therefore produces less force on the rod side.
For the default 100 mm bore and 50 mm rod, the annular area is three quarters of the full area. At zero opposing pressure, retraction force is three quarters of extension force; the swept volume for the same stroke has the same proportion.
The hydraulic pump power calculator needs pressure rise and flow; cylinder force alone does not specify either the stroke speed or pump input.
Opposing pressure belongs on the other face
Backpressure is a force contribution, not a percentage to subtract from supply pressure indiscriminately. During extension it acts over the annular face; during retraction it acts over the full face. The separate rows show those contributions before subtraction.
The hydraulic pump power calculator uses pressure rise and volume flow. This cylinder page instead evaluates static force and displaced volume, so a large force alone does not establish pump power or stroke speed.
A negative result has a physical interpretation
If the entered opposing pressure force exceeds the driven-side force, the signed net result is negative for that hypothetical direction. Clamping it to zero would hide the force imbalance. Both entered pressures must use a common reference.
The pressure calculator relates one normal force to one area. A real cylinder additionally has seals, moving mass and structural limits. The calculated ideal force does not establish the safe load, pressure rating, buckling resistance or mounting strength of actual equipment.
A few questions, answered
Why is retraction weaker at equal pressure?
The rod occupies part of the piston face, reducing its effective area.
Does stroke length affect static force?
No. It changes the swept volume; static pressure force depends on pressure and effective area.
Does this predict movement speed?
No. Speed would require a compatible delivered flow rate and a motion model.