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Pneumatic Cylinder Force Calculator

Created by Luis Hoyos
Reviewed by Steven Wooding
Based on research by
S. R. Majumdar Pneumatic System: Principles and Maintenance; McGraw-Hill Education; 1995
Last updated: Apr 19, 2024

The force calculation in a pneumatic cylinder is an essential part of its design and selection.

Pneumatic cylinders are one of the most relevant elements of a pneumatic system. They contain a rod, which is the most stressed component as its small diameter supports the force exerted by the whole cylinder. Therefore, calculating the pneumatic cylinder force output is mandatory to avoid mechanical failure.

Keep reading to learn more about:

  • What is a pneumatic cylinder?
  • How a pneumatic cylinder works.
  • How to calculate the force of a pneumatic cylinder.

🔎 The design of the rod deals with axial stress and buckling. Once you have calculated the forces applied, you can look at our stress calculator for the axial stress analysis.

What is a pneumatic cylinder, and how does it work?

A pneumatic cylinder is a device that exerts a force and a reciprocating motion. Its three main components are:

  1. Cylinder — a hollow piece that encloses the other two components.
  2. Piston — the component directly subjected to the gas pressure by forming a seal.
  3. Rod — the part attached to the piston that exerts the force over an external resistance.

The reciprocating motion comprises two strokes: 1. outward stroke, or output stroke, in which the cylinder gets fully extended, and 2. return stroke, or inward stroke, when the cylinder returns to the initial position.

They're similar to hydraulic cylinders, but there are some differences:

  • Instead of a liquid, the pressurized fluid is a gas.
  • The available pressures and forces are lower for a gas.
  • They're quieter, cleaner, and require less space.

Compressed gas instead of a liquid makes them more suitable for small spaces that don't allow large amounts of fluid storage or require transportation.

The gas used is usually air, so these devices are sometimes called pneumatic air cylinders or air cylinders.

How does a pneumatic cylinder work?

The gas is pressurized and brought to the cylinder by a compressor and a pipe system (composed mainly of air conditioning and control devices). This pressure exerts a force on the piston; consequently, the piston applies a force of the same magnitude to the rod.

The two main types of pneumatic cylinders:

  • Single-acting cylinders: the gas gets in and out of the cylinder only through one port. A spring usually achieves the return stroke, although any external force can do it.
Gif animation of a single-acting cylinder
Animation of a single-acting pneumatic cylinder. Attribution: User: RainerB., Public domain, via Wikimedia Commons.
  • Double-acting cylinders: in these cylinders, we don't use a spring but pressurized gas to achieve the return stroke. They're used to exert force in two directions.
Gif animation of a double-acting cylinder.
Animation of a double-acting pneumatic cylinder. Attribution: I, RainerB., CC BY-SA 3.0, via Wikimedia Commons.

Now, let's see how to calculate forces in pneumatic cylinders.

How to calculate pneumatic cylinder force?

The force calculation of an air cylinder depends on the pressure inside the cylinder, the piston diameter, the friction force generated by the seal components, and the spring force (in the case of single-acting devices).

The more basic formula to calculate the force of an air cylinder is:

Ft = P × Au

, where:

  • Ft – theoretical force. It's theoretical as it doesn't consider friction and spring forces;
  • P – the pressure inside the cylinder, and
  • Au – useful area in contact with the gas.

Single-acting pneumatic air cylinder calculation.

The effective force exerted decreases due to friction and the spring:

Feffec = Ft - Ff - Fs = P × Au - Ff - Fs

, where:

  • Ff – Friction force, which depends on the operating pressure, piston speed, and materials. A common practice is to consider it equal to 3-20% of the effective force for 4-8 bar pressure ranges.
  • Fs – Spring force, which depends on Hooke's law. We can neglect it in the presence of high pressures, but if you think it's significant, you can obtain it with the Hooke's law calculator.

In single-acting cylinders, Au = (π/4) × D². Therefore, the final form of the formula is:

Feffec = P × (π/4) × D² - Ff - Fs.

Double-acting pneumatic air cylinder calculation.

In this type of cylinder, the spring force disappears, while the friction force behaves similarly to single-acting cylinders:

Feffec = Ft - Ff

The useful area used to calculate the theoretical force equals Au = π × D² / 4 for the outward stroke and Au = π × (D² - d²) / 4 for the return stroke, where d is the rod diameter. The final form of the formula is, therefore:

  • outFeffec = P × (π/4) × D² - Ff for the outward stroke, and
  • returnFeffec = P × (π/4) × (D² - d²) - Ff for the return stroke.

How to use this air cylinder force calculator

Suppose you want to calculate the force of a pneumatic cylinder (single-acting) with a piston of 50 mm diameter and pressure inside its cylinder of 400,000 Pa. Follow these steps:

  1. Select "Single-acting" in the cylinder type option.
  2. Input 400000 Pa in the "Cylinder pressure (P)" box.
  3. Type in 50 mm in the "piston diameter (D)" box.
  4. That's it. The calculated output force of your pneumatic cylinder should be 785.4 Newtons.

Now suppose you wanted to calculate the force of a double-acting cylinder with the same characteristics and a 5 mm rod diameter. In that case, additionally, you should select "double-acting" as the cylinder type and type 5 mm in the "Rod diameter (d)" box. The outward stroke force should be the same, and the return stroke force should be 777.5 N.

🙋 The calculator's advanced mode allows you to consider the friction force as a percentage loss.


What is a stroke in a pneumatic cylinder?

The pneumatic cylinder stroke is the phase during which the piston travels from the minimum extended length to the maximum extended length position or vice versa. Stroke length is the distance covered during this movement.

How do I calculate hydraulic cylinder force?

Follow these steps to calculate hydraulic cylinder force:

  1. Use the cylinder diameter (d) to calculate the cylinder area, which is A = π × d² / 4.
  2. Determine the pressure P inside the cylinder.
  3. Multiply the pressure by the area. In that way, you calculate the hydraulic cylinder force, F = P × A.

What is the bore in a pneumatic cylinder?

The bore in a pneumatic cylinder is the round space where the pressurized fluid lies and exerts force. "Bore diameter" refers to the diameter of this hole, but it's usually called just "bore."

How much force can a pneumatic cylinder lift?

How much force a pneumatic cylinder can lift mainly depends on its pressure, diameter, and efficiency. We can find pneumatic cylinders operating at forces that go from 2 N up to 45,000 N.

Luis Hoyos
Cylinder type
Picture of a single acting cylinder
Cylinder pressure (P)
Piston diameter (D)
Piston area (Aᵤ)
Cylinder force
Outward stroke force (F₁)
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