Hydraulic Cylinder Force Calculator
Enter the bore, rod and pressure and get the cylinder's push and pull force in pounds, tons and kilonewtons, or the pressure needed for a force.
The result updates as you type.
Theoretical force
Push 17,671 lbf · pull 13,254 lbf
8.84 / 6.63 short tons · 78.6 / 59 kN · 8.02 / 6.01 tonnes-force
| Piston area (push) | 7.069 in² (4,560 mm²) |
| Annulus area (pull, piston minus rod) | 5.301 in² (3,420 mm²) |
What this page cannot tell you
Real output after friction, seal drag and pressure losses, which is lower; whether the cylinder, rod, pins or mounting are rated for this force; or buckling of a long rod in compression. Never exceed the cylinder's rated pressure.
Pressure needed for a push force
Uses the bore and number of cylinders above.
How to calculate hydraulic cylinder force
- Enter the bore. Inside diameter of the barrel (piston diameter).
- Enter the rod. Rod diameter, for the pull (retract) force.
- Enter the pressure. Working pressure in psi or bar.
- Read push and pull. In lbf, short tons, kN and tonnes-force.
10 situations where a cylinder force calculator helps
Log splitters
Tons of splitting force from bore and pump pressure.
Choosing a cylinder
Find the bore that gives the force you need at your pressure.
Retract vs extend
Pull force is lower because the rod takes up piston area.
Tractor loader and 3-point work
Estimate lift cylinder force.
Press builds
Shop presses rated in tons.
Dump trailers
Force available to lift a bed.
Metric cylinders
Enter mm and bar; get kN and tonnes.
Two cylinders in parallel
Multiply force by the number working together.
Pressure needed
Work backwards from a force to the pressure.
Teaching hydraulics
A worked example of force = pressure × area.
How the force is worked out
Pressure is force per unit area (OpenStax College Physics 2e §11.3), so force = pressure × area. Extending, the fluid pushes on the whole piston: area = π × bore² ÷ 4. Retracting, the rod takes up part of the piston, leaving the annulus: area = π × (bore² − rod²) ÷ 4. With psi and square inches the result is pounds-force.
Conversions: 1 bar = 14.5038 psi; 1 lbf = 4.44822 N; a short ton-force is 2,000 lbf and a tonne-force 9,806.65 N.
Limits: this is theoretical force. Seal friction, pressure losses and the relief valve setting reduce real output, and a cylinder, rod, pins and mountings each have their own ratings. A long rod under compression can buckle well below this force. Never exceed the cylinder's rated pressure. Everything runs in your browser.
Sources
Frequently asked questions
How do I calculate hydraulic cylinder force?
Force (lbf) = pressure (psi) × piston area (in²). A 3 in bore at 2,500 psi pushes about 17,671 lbf (8.8 tons).
Why is the pull force lower?
On retract the rod occupies part of the piston area, so less area sees pressure.
How many tons is my log splitter?
Bore area × pump pressure ÷ 2,000. A 4 in bore at 3,000 psi is about 18.8 tons.
How do I convert bar to psi?
Multiply by 14.5038.
What pressure do I need for a given force?
Force ÷ piston area; use the second calculator on the page.
Is the real force the same?
It's lower — friction and losses take some, and relief valves limit pressure.
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