9.1: How to Calculate the Force Output of an Hydraulic Cylinder in Extention (Pushing)

The output force of a hydraulic cylinder depends on two factors:

1. The pressure supplied by the hydraulic system
2. The area over which that pressure is applied

When a cylinder is extending, fluid pressure acts across the full piston area on the cap end of the cylinder. The force produced is the product of pressure and this piston area.

To calculate theoretical force output:

Force (lbs)=Pressure (psi) × Piston Area (in²)

Where the piston area is calculated by:

A = 0.7854 × D²

This formula assumes no losses due to friction or leakage. In practice, the actual force may be slightly lower due to these factors, but this gives a reliable baseline for sizing components and understanding system capabilities.

Example: Calculating the Extension Force of a Cylinder Given its Size and Pressure

To determine the force output of a hydraulic cylinder when it's extending, use the following formula:

P × A = F

Where:

• F = Force in pounds (lbs)
• P = Pressure in pounds per square inch (psi)
• A = Area of the piston in square inches (in²)

Since hydraulic cylinders use round pistons, we calculate piston area using the formula for the area of a circle:

A = 0.7854 × D²

Where D is the bore diameter of the cylinder.

Example Calculation

Let’s say the cylinder has a bore diameter of 2.0 inches and is subjected to 1000 psi of hydraulic pressure.

A=0.7854 × D²

A= 0.7854 × (2.0)²

A = 0.7854 × 4 = 3.1416 in.²

F = P × A

F=1000 × 3.1416=3,142 lbs

Result:
The cylinder can theoretically exert 3,142 pounds of force while extending at 1000 psi.

Additional Practice Problem

Determine the minimum pressure required to lift a known load given:

• Load to lift = 5,000 lbs
• Cylinder Bore = 3.0 in
• Rod Diameter = 1.0 in

We’re lifting, so this is an extension force problem. First, calculate piston area:

A = 0.7854 × (3.0)² = 0.7854 × 9 = 7.069 in²

Now solve for pressure:

P = F / A = 5000 x 7.069 ≈ 707 psi

Answer

A pressure of approximately 707 psi is required to lift a 5,000 lb load using a 3-inch bore cylinder.

A big lesson to learn here is that larger bore cylinders reduce the pressure required to move a load.

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