Enter the resisting tension (N), the coefficient of friction, and the angle (rad) into the calculator to determine the Belt Friction Force. 

Belt Friction Force Formula

The following formula is used to calculate the Belt Friction Force.

BF = RT * e ^ {u*b}
  • Where BF is the Belt Friction Force (N)
  • RT is the resisting tension (N) 
  • u is the coefficient of friction 
  • b is the angle (rad) 

To calculate the belt friction force, multiply the resisting tension by e to the power of the product of the coefficient of friction and the angle.

How to Calculate Belt Friction Force?

The following example problems outline how to calculate the Belt Friction Force.

Example Problem #1

  1. First, determine the resisting tension (N). In this example, the resisting tension (N) is given as 200 .
  2. Next, determine the coefficient of friction. For this problem, the coefficient of friction is given as  .35 .
  3. Next, determine the angle (rad). In this case, the angle (rad) is found to be 1.2.
  4. Finally, calculate the Belt Friction Force using the formula above: 

BF = RT * e ^ (u*b)

Inserting the values from above yields: 

BF = 200 * e ^ (.35*1.2) = 304.392 (N)


What is the significance of the coefficient of friction in calculating belt friction force?

The coefficient of friction is a crucial factor in calculating the belt friction force as it represents the resistance to motion that occurs between the belt and the pulley. A higher coefficient of friction means greater resistance, leading to a higher belt friction force. This parameter is essential for accurately determining the force needed to prevent slippage between the belt and the pulley.

How does the angle (in radians) affect the belt friction force calculation?

The angle, measured in radians, plays a significant role in the calculation of belt friction force. It represents the contact angle between the belt and the pulley. A larger angle increases the contact area, which can enhance the frictional force due to a larger surface area for the friction to act upon. This, in turn, affects the overall belt friction force, making the angle a vital parameter in the calculation.

Can the belt friction force formula be used for any type of belt and pulley system?

Yes, the belt friction force formula can be applied to various types of belt and pulley systems as long as the appropriate values for resisting tension, coefficient of friction, and angle are known. However, it’s important to note that the specific characteristics of the belt material and pulley surface, as well as environmental factors like temperature and humidity, can affect the accuracy of the calculation. Therefore, adjustments or considerations might be necessary for highly specialized or extreme conditions.