Enter the gauge pressure (air pressure), and the full bore piston diameter into the calculator to determine the cylinder force.

Cylinder Force Calculator

Enter any 2 values to calculate the missing variable

Cylinder Force Formula

The following formula is used to calculate the theoretical (ideal) force exerted by a pneumatic or hydraulic cylinder on the full-bore (extension/push) side.

F = P \cdot \pi \cdot \frac{d^2}{4}
  • Where F is the force exerted by the cylinder (N in SI, or lbf if using psi and inches)
  • P is the pressure difference across the piston (Pa = N/m² in SI, or psi in US customary units)
  • d is the full bore (piston) diameter (m in SI, or in in US customary units)

Note: For a single-rod cylinder, the retract (pull) force is lower because the effective area is the bore area minus the rod area:

F_\text{retract} = P \cdot \pi \cdot \frac{(d_\text{bore}^2 - d_\text{rod}^2)}{4}

To calculate the cylinder force, multiply the cylinder pressure by the cross-sectional area. Actual force can be slightly lower due to seal friction and other losses.

Cylinder Force Definition

What is a pneumatic cylinder? A pneumatic cylinder is a device that converts pressure delivered by air into an output force. That output force is considered the cylinder force.

Example Problem

How to calculate a cylinder force?

  1. First, determine the gauge pressure.

    For this example, the air pressure supplied to the cylinder is 125 psi (pounds per square inch)

  2. Next, determine the piston diameter.

    The inner bore diameter in this example is 5 inches.

  3. Finally, calculate the cylinder force.

    Using the formula, the cylinder force is calculated to be: 125*3.14159*(5^2)/4 = 2454.37 lbf.

FAQ

Does cylinder force change with size? At the same pressure, as the diameter of a cylinder increases, the force generated increases with the square of the diameter increase. This means that going from a 1-inch diameter cylinder to a 2-inch diameter cylinder increases the force by 4 times.

Does cylinder force change with air pressure change? For a fixed piston area, the force generated by a cylinder is linearly proportional to the (gauge) air pressure. In general, ΔF = ΔP × A, where A is the piston area. For example, a 5-inch bore has an area of about 19.63 in², so increasing pressure by 1 psi increases force by about 19.63 lbf.

cylinder force calculator
cylinder force formula