Enter the torque applied, length of the shaft, polar moment of inertia, and shear modulus into the calculator to determine the angle of twist.

Angle of Twist Formula

The following formula can be used to calculate the angle of twist of a solid shaft.

a = ( T * L )/( J * G)
  • Where a is the angle of twist (radians)
  • T is the torque applied (N*m)
  • L is the length (m)
  • J is the polar moment of inertia
  • G is the shear modulus (N/m^2)

To calculate and angle of twist, divide the product of the torque and length by the product of the polar moment of inertia and shear modulus.

Angle of Twist Definition

An angle of twist is defined as the measure of the amount of twist in radians an object undergoes when subjected to a torque.

Angle of Twist Example

How to calculate an angle of twist?

  1. First, determine the torque applied.

    Measure the total torque.

  2. Next, determine the length.

    Measure the length of the rod.

  3. Next, determine the polar moment of inertia.

    Calculate the moment of inertia of the rod.

  4. Next, determine the shear modulus.

    Calculate the shear modulus of the rod.

  5. Finally, calculate the angle of twist.

    Calculate the angle of twist using the equation above.


What is angle of twist?

An angle of twist the measure of the amount of twist an object, typically a rod, undergoes when a torque is applied in to the ends of the rod.

What is the polar moment of inertia?

The polar moment of inertia is the measure of the object’s resistance to twisting.