Calculate cylinder force, pressure, or bore diameter from any two values with PSI, bar, kPa, atm, inches, mm, cm, or meters, with selectable units.
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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 base calculation uses psi, inches, and pounds-force.
F = P * pi * (D/2)^2
P = F / (pi * (D/2)^2)
D = 2 * sqrt(F / (pi * P))
- 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 |
Typical Cylinder Force Values at 100 psi
| 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.
F = 100 * pi * (2/2)^2
F = 314.1593 lbf
The cylinder force is about 314.16 lbf.
Example 2: Find required bore diameter
You need 1,000 lbf of force at 250 psi.
D = 2 * sqrt(1000 / (pi * 250))
D = 2.2568 in
The required bore diameter is about 2.26 inches.
FAQ
Does this calculate extend force or retract force?
This formula calculates force from the full piston bore area. That is typically the extend force for a single-rod cylinder. Retract force is lower because the rod takes up part of the piston area. To calculate retract force, you would subtract the rod area from the piston area before multiplying by 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 calculator gives theoretical force based on pressure and piston area. Real cylinders may produce less usable force because of seal friction, mechanical losses, pressure drop, or side loading. For sizing real equipment, use a safety factor and check the cylinder manufacturer’s ratings.
