About this tool
The Shaft Torsion Calculator finds the shear stress and angle of twist in a circular drive shaft carrying torque. Work in SI (N·m, mm, GPa) or US units (lbf·in, in, psi), enter the torque directly or let the tool derive it from transmitted power and shaft speed, choose a solid or hollow section, and it returns the maximum surface shear stress, the twist over the shaft length, and the polar moment of inertia. Everything is calculated in your browser.
The polar moment of inertia is J = π·d⁴ / 32 for a solid shaft and J = π·(d_o⁴ − d_i⁴) / 32 for a hollow one. The maximum torsional shear stress at the outer surface is τ = T·r / J, with r the outer radius, and the angle of twist is θ = T·L / (J·G) radians, converted to degrees, where G is the shear modulus of the material (steel ≈ 79.3 GPa, aluminium ≈ 26 GPa, titanium ≈ 44 GPa). When you enter power instead of torque the tool uses T = 9550·kW / rpm for SI or T = 63025·HP / rpm for US units, the standard power-torque relations.
As a worked example, a solid 40 mm steel shaft carrying 500 N·m has J = π × 40⁴ / 32 ≈ 251,327 mm⁴, so the surface shear stress is 500,000 N·mm × 20 mm / 251,327 ≈ 39.8 MPa, and over a 1 m length it twists about 1.44 degrees. A hollow shaft of the same outer diameter removes material near the centre, where it carries little torque, giving nearly the same strength at lower weight — which is why drive shafts are often tubular.