# Pneumatic Cylinder Force Calculator

*“Pneumatic System: Principles and Maintenance“*Tata McGraw-Hill Education (1995)

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, with its small diameter, it 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:

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

The reciprocating motion is composed of 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, and, 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.

**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.

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:

**F _{t} = P × A_{u}**

where:

**F**– theoretical force. It's theoretical as it doesn't consider friction and spring forces;_{t}**P**– the pressure inside the cylinder, and**A**– useful area in contact with the gas._{u}

### Single-acting pneumatic air cylinder calculation.

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

**F _{effec} = F_{t} - F_{f} - F_{s} = P × A_{u} - F_{f} - F_{s}**

where:

**F**– 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._{f}**F**– Spring force, which depends on Hooke's law. We can neglect it in the presence of high pressures._{s}

In single-acting cylinders, **A _{u} = (π/4) × D²**. Therefore, the final form of the formula is:

**F _{effec} = P × (π/4) × D² - F_{f} - F_{s}**.

### 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:

**F _{effec} = F_{t} - F_{f}**

The useful area used to calculate the theoretical force equals **A _{u} = π × D² / 4** for the outward stroke and

**A**for the return stroke, where

_{u}= π × (D² - d²) / 4**d**is the

**rod diameter**. The final form of the formula is thereore:

for the outward stroke, and^{out}F_{effec}= P × (π/4) × D² - F_{f}for the return stroke.^{return}F_{effec}= P × (π/4) × (D² - d²) - F_{f}

## 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:

- Select
**"Single-acting"**in the cylinder type option. - Input
**400000 Pa**in the "Cylinder pressure (P)" box. - Input
**50 mm**in the "piston diameter (D)" box. - 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.

## FAQ

### 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:**

- Use the cylinder diameter (d) to calculate the cylinder area, which is
**A = π × d² / 4**. - Determine the pressure
**P**inside the cylinder. **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**.