engineering

Torsion Calculator

Calculate shear stress and angle of twist for solid and hollow circular shafts under torsion

Torsion Calculator

Calculate shear stress and angle of twist for circular shafts under torque.

Steel ≈ 80 GPa · Aluminum ≈ 26 GPa

Results

Max Shear Stress τ_max

20.3718 MPa

= 2.0372e+7 Pa

Angle of Twist θ

0.5836°

= 0.010186 rad

Polar Moment J

6.1359e-7 m⁴

Formulas

J = πd⁴/32 = π×5.000e-2⁴/32
J = 6.1359e-7 m⁴
τ_max = Tr/J = 500 × 0.0250 / 6.1359e-7
τ_max = 20.3718 MPa
θ = TL/(GJ) = 500 × 1 / (80 GPa × 6.1359e-7)
θ = 0.010186 rad = 0.5836°

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Torsion Calculator. Most fields include unit selectors so you can work in your preferred unit system.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors.

3

Read the results

The Torsion Calculator instantly computes the output and displays results with units. All calculations happen in your browser — no loading time and no data sent to a server.

Formula Reference

Shear Stress in Shaft

τ = T·r / J

Variables: T = applied torque, r = radial distance from center, J = polar moment of inertia

Angle of Twist

φ = T·L / (G·J)

Variables: L = shaft length, G = shear modulus

When to Use This Calculator

  • •Use the Torsion Calculator when solving homework or exam problems that require quick numerical verification of your hand calculations.
  • •Use it during the design phase to rapidly iterate on parameters before running detailed finite element simulations.
  • •Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility.
  • •Use it to generate reference data for a technical report or presentation without manual computation.

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