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Torsion Of A Shaft Calculator

Work out torsion of a shaft instantly with clear inputs, formula shown and shareable results.

About Torsion Of A Shaft Calculator

Torsion of a circular shaft follows tau = Tr/J with J = pi d^4/32, so surface stress is highest and the centre carries almost nothing - which is why hollow shafts are so efficient. 1200 N m on a 50 mm shaft gives 48.9 MPa at the surface and twists a 1.5 m length by about 1.05 degrees.

Formulas

Torsional shear stress

tau = T r / J, J = pi d^4 / 32

Angle of twist

theta = T L / (J G)

Worked example

With the default values below, Torsion Of A Shaft Calculator returns Maximum Shear Stress of 48.892. Change any input above and every figure here is recalculated in your browser.

Inputs used

Applied torqueminimum 0 N m
1,200 N m
Shaft diameterminimum 0 mm
50 mm
Shaft lengthminimum 0 m
1.5 m
Shear modulusminimum 0 GPa
80 GPa

Results

Maximum Shear Stress
48.892 MPa
Polar Second Moment J
6.1359 × 10⁻⁷ m4
Angle Of Twist
2.1010 deg
Same Twist In Radians
3.6669 × 10⁻²

Step by step

  1. 1Values used
  2. 2Torsional shear stress
  3. 3Angle of twist
  4. 4Maximum Shear Stress= 48.892 MPa
  5. 5Polar Second Moment J= 0.0000 m4
  6. 6Angle Of Twist= 2.1010 deg
  7. 7Same Twist In Radians= 0.0367

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why are drive shafts often hollow?

Because the material near the axis is barely stressed. Removing it saves weight with little loss of torsional strength.

How much twist is acceptable?

Machine design practice limits it to about 1 degree per metre of length for power transmission shafts.

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