Pneumatic Cylinder Force Calculator
Enter your cylinder bore diameter, rod diameter, supply pressure and an optional friction allowance to get the theoretical and effective force for both the extend and retract strokes. Switch between metric (bar, mm, N) and imperial (psi, inches, lbf) units - all results update instantly. The show-your-work panel walks through every formula step so you can verify the math before ordering.
Formula
Worked example
An 80 mm bore cylinder with a 22 mm rod at 6 bar (0.6 MPa), no back pressure, 10% friction: bore area = pi x 80^2 / 4 = 5027 mm^2; theoretical extend force = 0.6 N/mm^2 x 5027 mm^2 = 3016 N; effective extend force = 3016 x 0.90 = 2714 N. Annular area = pi x (80^2 - 22^2) / 4 = 4647 mm^2; theoretical retract = 0.6 x 4647 = 2788 N; effective retract = 2788 x 0.90 = 2509 N.
How pneumatic cylinder force is calculated
The force a pneumatic cylinder produces equals the gauge pressure of the compressed air multiplied by the effective piston area. For the extend stroke that area is the full bore cross-section: Abore = π × D² / 4. For the retract stroke of a double-acting cylinder the piston rod passes through the piston, so the effective area is smaller: Aannular = π × (D² − d²) / 4, where d is the rod diameter. This is why a cylinder is always stronger pushing out than pulling back.
When back pressure exists on the exhaust side (for example when using meter-out flow control), the opposing force must be subtracted. Adding a friction allowance of 5-15% of the theoretical force gives the effective, usable force - this accounts for piston and rod seal drag, which increases as seals wear.
Single-acting vs double-acting cylinders
A double-acting cylinder uses air pressure for both the extend and retract strokes, with each end of the cylinder vented to exhaust alternately. The retract force is lower than the extend force by a factor equal to the area ratio (Aannular / Abore). A rod that is 25% of the bore diameter causes about a 6% force reduction on retract; a rod that is 50% of the bore causes about a 25% reduction.
A single-acting (spring-return) cylinder uses air only for the extend stroke. The return stroke is driven by a pre-compressed spring inside the cylinder, so the effective extend force is reduced by the spring pre-load. The calculator deducts the spring force automatically when single-acting mode is selected. These cylinders are simpler and fail safe (they return to the retracted position if air pressure is lost) but they produce less extend force for a given bore size.
Choosing the right bore size
Start from the required effective force (load plus a safety factor of 1.25-2.0), the supply pressure available, and an assumed friction loss of 10%. Rearrange the formula to get the minimum bore: D = 2 × √(Frequired / (π × P × (1 - friction%))). Then select the next standard ISO 15552 bore size above that calculated minimum. The reference table on this page lists theoretical forces for all standard bore sizes at 6 bar.
- Allow extra margin if the supply line is long (pressure drop in the hose reduces available pressure).
- If the retract force is critical, choose a smaller rod diameter to maximise the annular area.
- For high-cycle applications, budget 10-15% friction; for new, well-lubricated cylinders 5% is typical.
Unit conversion and practical tips
This calculator works in either metric or imperial units. In metric, pressure is entered in bar (1 bar = 100 kPa = 14.504 psi) and dimensions in millimetres; forces are reported in Newtons (1 kN = 1000 N = 224.8 lbf). In imperial mode, pressure is in psi and dimensions in inches; forces are in pound-force (lbf).
Quick rule of thumb in metric: multiply the bore area in cm² by the pressure in bar to get force in daN (decanewtons, roughly equal to kgf). For example, a 100 mm bore has an area of about 78.5 cm², giving 78.5 × 6 = 471 daN at 6 bar before friction.
Typical bore diameter and force at 6 bar (metric)
| Bore (mm) | Bore area (mm²) | Force at 6 bar (N) | Force at 6 bar (kgf) |
|---|---|---|---|
| 20 | 314 | 1885 | 192 |
| 25 | 491 | 2945 | 300 |
| 32 | 804 | 4825 | 492 |
| 40 | 1257 | 7540 | 769 |
| 50 | 1963 | 11781 | 1201 |
| 63 | 3117 | 18703 | 1907 |
| 80 | 5027 | 30159 | 3075 |
| 100 | 7854 | 47124 | 4805 |
| 125 | 12272 | 73631 | 7507 |
| 160 | 20106 | 120637 | 12301 |
| 200 | 31416 | 188496 | 19222 |
| 250 | 49087 | 294524 | 30034 |
Theoretical extend force at 6 bar gauge pressure with no friction loss. Standard ISO 15552 bore sizes.
Frequently asked questions
Why is the retract force less than the extend force?
In a double-acting cylinder the piston rod occupies part of the bore on the rod side. That reduces the area the air can push against during the retract stroke. The force difference depends on the rod-to-bore diameter ratio: a rod that is half the bore diameter reduces the retract-side area by about 25%.
What friction percentage should I use?
For new cylinders with good lubrication, 5% is a reasonable starting point. For standard industrial duty in typical conditions, 10% is commonly used. For high-temperature, high-cycle, or poorly lubricated applications, 15% or more may be appropriate. Never design to the 0% theoretical value: real seals always create drag.
How do I convert bar to psi?
1 bar = 14.504 psi. Standard compressed air systems operate at 5-10 bar, which is roughly 73-145 psi. The calculator handles the conversion automatically when you switch units.
What is back pressure and when does it matter?
Back pressure is the pressure that builds on the exhaust side of the cylinder when flow is restricted, for example by a meter-out flow control valve. If the exhaust is venting freely to atmosphere, back pressure is essentially zero. In throttled circuits it can reach 0.5-2 bar and meaningfully reduces effective force, so this calculator lets you include it.
Does this formula work for hydraulic cylinders too?
Yes, the force formula is identical: F = P x A. Hydraulic systems use much higher pressures (100-350 bar vs 5-10 bar for pneumatics), so hydraulic cylinders produce far more force from a smaller bore. Switch the pressure input to bar and enter your hydraulic supply pressure to get the result.
What safety factor should I apply to the calculated force?
A safety factor of 1.25 to 2.0 is standard depending on the application. Use the lower end (1.25) for well-characterised, steady loads. Use 1.5-2.0 for dynamic loads, start-up surges, or systems where a cylinder failure could cause injury or equipment damage. The effective force this calculator returns already includes your friction allowance, so apply the safety factor on top of that figure when sizing the cylinder.
How do I calculate the force needed to move a known load?
Add the load force plus any gravity component (mass in kg x 9.81 for vertical applications) plus an estimate for friction in the mechanism. Multiply that total by your safety factor (1.25-2.0). That is the minimum effective force the cylinder must deliver, and you can enter it in reverse to find the bore size you need.