Shaft Torsion Calculator
Torsional shear stress and angle of twist for a solid circular shaft.
INPUTS
N·m
mm
m
GPa
RESULTS
Polar moment J = πd⁴/32
61.36 ×10⁴ mm⁴
Max shear stress τ = 16T/πd³
20.37 MPa
Angle of twist φ = TL/GJ
0.875 °
Twist in radians
0.01528 rad
How it works
In a circular shaft, torsional shear stress grows linearly from zero at the centre to a maximum at the surface: τ = T·r/J. Since the core carries almost nothing, hollow shafts deliver nearly the same strength at a fraction of the weight — the reason drive shafts and bike frames are tubes.
Worked example
T = 500 N·m on a 50 mm steel shaft (G = 80 GPa), 1.5 m long: τmax = 16·500000/(π·50³) = 20.4 MPa at the surface; twist φ = TL/GJ = 0.87° over the length.
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