A hydraulic cylinder force calculator for push and pull
A hydraulic cylinder turns fluid pressure into force, and the force is simply the pressure times the area it acts on. This hydraulic cylinder force calculator works out the push force on the full bore side and the smaller pull force on the rod side from the bore diameter, rod diameter and working pressure, in metric or imperial units.
It also finds the speed from the pump flow, the time for a stroke and the oil volume used, and it can work backwards from the force you need to the pressure that delivers it. A small table shows how the force changes at a quarter, half, three quarters and the full pressure.
The numbers are the theoretical output at the pressure you enter, with an efficiency field for seal friction. Real systems also have back-pressure, acceleration loads and side loads, so check the cylinder rating, rod buckling and relief valve settings, and have load-bearing designs reviewed by a qualified engineer.
How to use the Hydraulic Cylinder Force Calculator
- Choose whether to find the force from a pressure or the pressure for a target force.
- Enter the bore diameter and rod diameter, picking mm, cm or inches.
- Enter the pressure (or the target force), the pump flow and the stroke.
- Set the efficiency if you want realistic rather than theoretical force.
- Read the push and pull forces, the speeds and the oil volume.
Hydraulic Cylinder Force Calculator features
Push and pull
Full-bore and annulus areas give the two forces.
Speed and time
Extend and retract speed and stroke time from the pump flow.
Either direction
Force from pressure, or pressure for a force.
Units
mm, cm, in; bar, MPa, psi, kPa; kN, N, lbf, tonne-force; L/min or gpm.
Hydraulic cylinder formulas
The bore area is A = π D² ÷ 4 and the rod-side annulus area is A = π (D² − d²) ÷ 4. The force is F = P × A × η, the speed is v = Q ÷ A and the oil volume of a stroke is the area times the stroke length. Because the annulus is smaller, the cylinder pulls with less force than it pushes, and retracts faster for the same flow.
Example: a cylinder with a 100 mm bore and 56 mm rod at 160 bar. The bore area is 78.54 cm², so the push force is 160 × 10⁵ Pa × 78.54 × 10⁻⁴ m² = 125.7 kN, about 12.8 tonnes-force. The annulus is 53.9 cm², giving a pull force of 86.3 kN. With 20 L/min the cylinder extends at 42 mm/s and retracts at 62 mm/s.
Things to check in the real system
- The system pressure sets the force, not the pump size: a relief valve limits it, so confirm its setting against the cylinder’s rated pressure.
- Seal friction typically takes a few per cent; use the efficiency field. Back-pressure from the opposite side reduces the net force further.
- Long, slender rods can buckle in compression. Check the rod against the column buckling limit for your mounting style.
- Differential (regenerative) circuits, where oil from the rod side joins the pump flow, change the effective area and are not modelled here.
Hydraulic Cylinder Force Calculator FAQ
How do I calculate hydraulic cylinder force?
Multiply the pressure by the piston area: F = P × π D² ÷ 4. At 160 bar a 100 mm bore gives about 125.7 kN.
Why is the pull force lower than the push force?
On the retract stroke the pressure acts on the annulus, the bore area minus the rod area, which is smaller.
How do I find the speed of a hydraulic cylinder?
Divide the pump flow by the area: v = Q ÷ A. 20 L/min into a 78.5 cm² bore gives about 42 mm/s.
How many tonnes is that force?
Divide the force in newtons by 9,806.65 for tonnes-force. 125.7 kN is about 12.8 tonnes-force.
What bore do I need for a given force?
Switch to the pressure mode, enter the force, and try bores until the pressure is below your system pressure, or use A = F ÷ P to get the area and the bore from it.
Does it include the efficiency of the cylinder?
Only through the efficiency field. The default of 100% is the theoretical output.