Free · Material properties

Circular Shaft Twist from Torque & Torsional Rigidity

Calculate elastic twist of a uniform circular shaft using torque, length, polar second moment of area and shear modulus, including reverse inputs.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

With torque 100 N·m, length 1 m, polar area moment 1,000,000 mm⁴ and shear modulus 1 GPa, the twist is 0.1 rad, approximately 5.72958°.

θ = TL / (GJ)

Worked example

Enter these known values and leave the other values blank.

Signed torque T
100 N·m
Uniform shaft length L
1 m
Polar second moment of area J
1000000 mm⁴
Shear modulus G
1 GPa
Signed angle of twist θ
5.73 deg

Assumptions and limitations

  • The shaft is straight and circular, with constant torque, section and shear modulus over the entered length, in the linear elastic torsion model.
  • Length, polar area moment and shear modulus are positive. Torque and twist may be signed and may be zero.
  • J is a geometric area moment in length to the fourth power, not a mass moment of inertia.
  • The formula returns radians in coherent SI units; the angle selector converts that result to degrees or multiples of π radians.
  • Noncircular sections, varying torque, warping and plastic deformation require a different model.

Common questions

How does length affect twist?

Under the same torque, material and section, doubling length doubles the angle of twist.

Is a zero torque allowed?

Yes. With positive length and rigidity, zero torque produces zero twist. Some inverse calculations are then underdetermined.

References

Pound-force inches use the exact international pound and inch with standard gravity. Pound-force feet use the exact international pound and foot with standard gravity. Kilogram-force centimeters use standard gravity and exactly one centimeter. Pounds-force per square inch use the exact international pound and inch with standard gravity, replacing the rounded captured factor.

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