What this calculator does
A pneumatic cylinder converts the pressure of compressed air into a pushing or pulling force, and the force it produces depends only on that pressure and the area of the piston the air is pushing against. This calculator works out both the extend force, generated by air pushing on the full face of the piston, and the retract force, generated by air pushing on the opposite face, which is smaller because the piston rod takes up part of that area.
The relationship is simple in principle, force equals pressure times area, but it is easy to get the units wrong, since pressure is commonly quoted in bar while force calculations need pressure in pascals and area in square metres. This calculator handles that conversion, taking bore and rod diameter in millimetres and supply pressure in bar, and returning force in newtons.
The formula
Extend force is the supply pressure multiplied by the full circular area of the piston bore. Retract force uses a smaller area, the bore area minus the area taken up by the rod, since air on the rod side of the piston cannot push against the section the rod occupies. Leaving the rod diameter at zero gives a simple extend-force-only result using the full bore area for both directions, useful when the rod diameter is not yet known or the retract side is not of interest.
| Term | Meaning |
|---|---|
| Bore diameter | The internal diameter of the cylinder barrel, equal to the diameter of the piston. |
| Rod diameter | The diameter of the piston rod, which reduces the effective piston area on the retract side. |
| Supply pressure | The air pressure delivered to the cylinder, commonly 6 bar in industrial pneumatic systems. |
The inputs explained
| Field | What to enter |
|---|---|
| Bore (piston) diameter (mm) | The internal bore diameter of the cylinder, as stated on its nameplate or datasheet. |
| Rod diameter (0 if unknown) (mm) | The piston rod diameter. Leave at 0 for an extend-force-only calculation using the full bore area. |
| Supply pressure (bar) | The supply air pressure reaching the cylinder, typically read from a regulator or system gauge. |
When to use it
Sizing a cylinder for a known load
Working out the force a candidate bore size produces at the available line pressure checks whether it can move a known load with a reasonable safety margin before it is bought or specified.
Comparing extend and retract force
Because the rod reduces the piston area on one side, the same cylinder pulls with noticeably less force than it pushes, which matters for applications that rely on the retract stroke to do work.
Checking the effect of a pressure regulator setting
Air pressure at the cylinder is often lower than the compressor's output once line losses and a regulator setting are accounted for, so recalculating force at the actual delivered pressure avoids overestimating what the cylinder can do.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does extend force change with bore diameter at 6 bar?
A common range of cylinder bore sizes at a typical 6 bar industrial supply pressure.
| Bore diameter | Extend force |
|---|---|
| 16 mm | 120.6 N |
| 25 mm | 294.5 N |
| 32 mm | 482.5 N |
| 40 mm | 754.0 N |
| 50 mm | 1,178.1 N |
| 63 mm | 1,870.3 N |
| 80 mm | 3,015.9 N |
| 100 mm | 4,712.4 N |
How much does a rod reduce retract force on a 50 mm bore cylinder?
The same 50 mm bore cylinder with a range of rod diameters, showing the drop in retract force.
Questions
Why is retract force lower than extend force?
On the retract stroke, air pushes against the annular area left after subtracting the rod's cross-section from the full bore area. Since that area is smaller than the full bore, the same pressure produces less force pulling in than pushing out.
What happens if I leave the rod diameter at zero?
The calculator treats extend and retract as using the same full bore area, which is a reasonable simplification for the extend stroke or when the rod diameter is not yet known, but it will overstate the true retract force.
Does friction or seal drag reduce the force below this calculation?
Yes. This is the theoretical force from pressure and area alone. Real cylinders lose some of that to seal friction and back-pressure on the exhaust side, so actual delivered force is somewhat lower, particularly at low pressures.
Why convert bar to pascals for this calculation?
Force in newtons requires pressure in pascals (newtons per square metre) multiplied by area in square metres. Bar is a convenient everyday unit for pneumatic pressure but has to be converted to pascals, 1 bar equals 100,000 pascals, before the formula gives a correct force in newtons.
For force from a sudden impact rather than steady pressure, see the impact force calculator.