Calculate hydraulic or pneumatic cylinder force, required pressure, or bore for extend and retract strokes with real unit conversions and efficiency losses.
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Cylinder Force Formula
The cylinder force calculator uses the piston area and the applied pressure to find hydraulic or pneumatic cylinder force. The model converts inputs to pascals, meters and newtons. The formulas below describe ideal extension at 100% efficiency and zero opposing gauge pressure. For the chosen efficiency η, use F = P × A × η; for retraction use A = π(D² − d²)/4, where d is rod diameter.
- F = cylinder force, in pounds-force when using base units
- P = pressure, in psi when using base units
- D = bore piston diameter, in inches when using base units
- pi = 3.14159
If you enter pressure and bore diameter, the calculator finds the cylinder force. If you enter force and bore diameter, it finds the required pressure. If you enter force and pressure, it finds the required bore diameter. Unit selections are converted internally before the formula is applied, then the result is converted back to the unit you selected.
Common Pressure and Force Unit Conversions
These conversions are useful when checking inputs or comparing a result to equipment specifications.
| Unit | Equivalent | Used for |
|---|---|---|
| 1 bar | 14.5038 psi | Hydraulic and pneumatic pressure ratings |
| 1 kPa | 0.145038 psi | Metric pressure inputs |
| 1 atm | 14.6959 psi | Atmospheric pressure comparison |
| 1 lbf | 4.44822 N | Force output conversion |
| 1 kN | 224.809 lbf | Larger cylinder force ratings |
Ideal Extend Force at 100 psi and 100% Efficiency
| Bore Diameter | Piston Area | Force at 100 psi |
|---|---|---|
| 1 in | 0.785 in² | 78.5 lbf |
| 2 in | 3.142 in² | 314.2 lbf |
| 3 in | 7.069 in² | 706.9 lbf |
| 4 in | 12.566 in² | 1,256.6 lbf |
Example Calculations
Example 1: Find cylinder force
You have a cylinder with a pressure of 100 psi and a bore diameter of 2 inches. Select Extend and 100% efficiency for this ideal example.
The cylinder force is about 314.16 lbf.
Example 2: Find required bore diameter
You need 1,000 lbf of force at 250 psi. Select Extend and 100% efficiency for this ideal example.
The required bore diameter is about 2.26 inches.
FAQ
Does this calculate extend force or retract force?
The calculator supports both strokes. Extend uses the full bore area. Retract subtracts the rod area; the rod must be smaller than the bore. The model assumes zero opposing gauge pressure.
Why does force increase so quickly when diameter increases?
Force depends on piston area, and piston area depends on diameter squared. Doubling the bore diameter gives four times the piston area, so the cylinder can produce four times the force at the same pressure.
Should friction and efficiency be included?
The chosen efficiency scales ideal pressure-area force. The default 90% is an adjustable assumption, not a measured efficiency. Back pressure, dynamic loads, pressure drop, rod buckling and side loading require separate checks against the cylinder manufacturer’s ratings.
