Enter the gear system’s tangential, radial, and axial forces into the calculator to determine the gear force.

Gear Force Formula

The following equation is used to calculate the Gear Force.

FG = SQRT( Ft^2+Fr^2+Fa^2)
  • Where FG is the total normal force on the gear (N)
  • Ft is the tangential force (N)
  • Fr is the radial force (N)
  • Fa is the axial force (N)

To calculate the gear force, sum the tangential, radial, and axial forces squared, then take the square root of the result.

What is a Gear Force?


A gear force is a force that is transmitted by gears. It can be used to transmit or receive forces between two rotating shafts with the help of gears. Gear forces can be used with belts, chains, and V-belts to transmit torque.

How to Calculate Gear Force?

Example Problem:

The following example outlines the steps and information needed to calculate the Gear Force.

First, determine the tangential force. In this example, the tangential force is measured to be 50N.

Next, determine the radial force. This is measured to be 10 N.

Next, determine the axial force. In this case, the axial force is measured to be 5 N.

Finally, calculate the total gear force using the formula above:

FG = SQRT( Ft^2+Fr^2+Fa^2)

FG = SQRT( 50^2+10^2+5^2)

FG = 51.23 N


What are the practical applications of calculating gear force?

Gear force calculation is crucial in mechanical engineering and design, especially in the automotive, aerospace, and machinery industries. It helps in the design of gear systems that are efficient, safe, and capable of transmitting the desired amount of power or torque between shafts in various machines and vehicles.

How does gear material affect gear force?

The material of the gear affects its strength, durability, and the amount of force it can transmit. Materials like steel can handle higher forces and are more durable, while plastics are suitable for lighter loads and less demanding applications. The choice of material impacts the gear’s performance, lifespan, and suitability for specific tasks.

Can gear force calculation be used for non-circular gears?

Yes, gear force calculation can be adapted for non-circular gears, such as elliptical or cam gears, though the calculation might be more complex. Non-circular gears are used in specialized applications where variable speed or torque is required. The principles of force calculation remain the same, but the shape of the gears introduces additional factors that must be considered.