Piston Force Calculator

Piston force is pressure times piston area: F = P x A, where the bore area is A = pi/4 x bore^2. In SI units, pressure in pascals times area in square meters gives force in newtons. Double the pressure or double the area and the force doubles.

Area = pi/4 x 100^2 = 7,853.98 mm^2. Force = 210 bar x area = 164.93 kN, which is 16.82 metric tons-force or 37,078.55 lbf. This is the classic high-pressure hydraulic cylinder size.

On the rod side, the rod itself occupies part of the piston area, so pressure acts only on the annulus (bore area minus rod area). The ratio is 1 minus (rod/bore)^2. Example: 100 mm bore with a 40 mm rod at 7 bar gives 5.50 kN extend but only 4.62 kN retract, a ratio of 84 percent.

Yes, F = P x A applies to both. The difference is the pressure range: hydraulics typically run 100 to 350 bar, while shop-air pneumatics run about 4 to 10 bar. Because force scales linearly with pressure, hydraulics deliver roughly 20 to 50 times more force for the same bore.

Rearrange the formula: d = sqrt(4 x F / (pi x P)), then round UP to the next ISO 3320 standard bore. Example: 100 kN at 210 bar needs exactly 77.87 mm, so the next standard bore is 80 mm, which actually delivers 105.56 kN at that pressure.

ISO 3320 standard metric bores in mm are: 25, 32, 40, 50, 63, 80, 100, 125, 160, 200, 250 and 320. Designing to a standard bore keeps cylinders, seals and mounts interchangeable.

Rod speed is flow divided by bore area: v = Q / A. Example: 20 L/min into a 63 mm bore gives 0.107 m/s, which is 106.9 mm/s. A smaller bore or more pump flow makes the cylinder faster, but the available force drops with the smaller area.

Power = force x speed = F x v, which is identical to pressure x flow (P x Q). Example: 210 bar at 20 L/min is 7.0 kW of hydraulic power, about 9.5 metric hp, before pump and motor losses.

1 kN = 1,000 N = 224.81 lbf. 1 metric ton-force = 9,806.65 N = 2,204.62 lbf. 1 short ton-force = 8,896.44 N = exactly 2,000 lbf. This calculator shows all five force units side by side.

Yes, the results are ideal: they ignore seal and packing friction, which typically costs 5 to 10 percent of theoretical force, plus pressure drops in valves and lines. Size cylinders with a safety factor on the required force, verify against the cylinder datasheet, and never use these numbers as the sole basis for lifting or holding people or critical loads.