Calculate belt wrap angle for open or crossed belts from pulley diameters and center distance, with results for both pulleys in degrees and radians.

Belt Wrap Angle Calculator

Enter both pulley diameters and the center distance to get the wrap angle.

Open belt
Crossed belt

Related Calculators

Belt Wrap Angle Formula

The following formula is used to calculate the belt wrap angle (angle of contact) on the smaller pulley for an open (uncrossed) belt drive, given the pulley diameters and center distance.

\theta = 2\arccos\left(\frac{D_2 - D_1}{2C}\right)

Variables:

  • θ is the wrap angle (angle of contact) on the smaller pulley (in radians if you use the formula as written; convert to degrees if needed)
  • D₁ is the diameter of the smaller pulley
  • D₂ is the diameter of the larger pulley
  • C is the center distance between the pulleys

To calculate the smaller-pulley wrap angle, compute the ratio (D₂ − D₁)/(2C) and take the arccosine. Multiply by 2 to obtain θ (in radians). Convert to degrees by multiplying by 180/π if necessary. For an open belt drive, the wrap angle on the larger pulley is θlarge = 2π − θ (or 360° − θ).

What is a Belt Wrap Angle?

The belt wrap angle refers to the angle subtended by the belt on the surface of a pulley. It is a crucial parameter in belt drive systems as it affects the amount of frictional force between the belt and the pulley, which in turn influences the power transmission capability of the system. A larger wrap angle generally means better grip and less slippage, leading to more efficient power transmission. The wrap angle is determined by the diameters of the pulleys and the center distance between them.

How to Calculate Belt Wrap Angle?

The following steps outline how to calculate the Belt Wrap Angle.

  1. First, measure the diameter of the smaller pulley (D₁).
  2. Next, measure the diameter of the larger pulley (D₂).
  3. Next, measure the center distance between the pulleys (C).
  4. Finally, calculate the smaller-pulley wrap angle using the formula θ = 2 * arccos((D₂ - D₁) / (2 * C)) (this gives θ in radians; convert to degrees if needed).
  5. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Diameter of Smaller Pulley (D₁) = 10 cm

Diameter of Larger Pulley (D₂) = 20 cm

Center Distance (C) = 30 cm