Calculate shaft torsion, shear stress, angle of twist, power, and strain from torque, speed, diameter, length, and shear modulus.

Uniform circular shaft, linear elastic pure torsion and small strain. Verify the material shear modulus and allowable stress separately; this is not a shaft safety rating.

Use the value for your material grade and conditions.

Optional shaft power

Shaft Torque Formula

The following formula is used to calculate the Shaft Torque.

Tshaft = ss ร— J / r
  • Where Tshaft is the Shaft Torque (N-m)
  • ss is the shear stress (N/m^2) 
  • J is the polar moment of inertia (m^4) 
  • r is the radius (m) 

To calculate shaft torque, multiply the shear stress by the polar moment of inertia, then divide by the radius.

How to Calculate Shaft Torque?

The following example problems outline how to calculate Shaft Torque.

Example Problem #1

  1. First, determine the shear stress (N/m^2). In this example, the shear stress (N/m^2) is determined to be 500.
  2. Next, determine the polar moment of inertia (m^4). For this problem, the polar moment of inertia (m^4) is measured to be 30.
  3. Next, determine the radius (m). In this case, the radius (m) is found to be 4.
  4. Finally, calculate the Shaft Torque using the formula above: 

Tshaft = ss * J/r

Inserting the values from above and solving yields: 

Tshaft = 500 * 30/4 = 3,750 (N-m)

Example Problem #2

Using the same method as above, determine the variables required by the formula. For this example problem, these are:

shear stress (N/m^2) = 750

polar moment of inertia (m^4) = 10

radius (m) = 50

Entering these given values into the calculator or the formula above yields: 

Tshaft = 750 * 10/50 = 150 (N-m)