Shaft Torsion Calculator (Shear Stress, Twist and Power)
Shear stress, angle of twist and torsional stiffness for a solid or hollow shaft carrying a torque, entered either directly in N m or as power at a running speed. The results include the polar second moment of area, the torsional section modulus, the twist per metre used to check machine shaft alignment limits, and the factor of safety against shear yield.
How to use this calculator
- Enter the shaft outside diameter and the bore diameter, leaving the bore at 0 for a solid shaft.
- Choose how the load is given: enter the torque directly, or enter the power and the running speed and let the calculator convert.
- Enter the length over which the twist is measured, the shear modulus of the material, and its yield strength.
- Read the maximum shear stress, the angle of twist, the twist per metre, the factor of safety, and the equivalent solid shaft diameter for the same torsional stiffness.
Frequently asked questions
How do I calculate the shear stress in a shaft?
The general form is tau = T x c / J with c the outer radius and J the polar second moment of area. For a solid shaft that reduces to tau = 16 T / (pi d^3). For a hollow shaft it becomes tau = 16 T d / (pi x (d^4 - di^4)), which is why boring the centre out raises the stress at the outer fibre even though the shaft is lighter.
What is an acceptable angle of twist?
Machine shafts are usually held below 1 degree per metre so that gears, bearings and keyways stay aligned. Precision drives and instrument shafts often work to 0.25 degree per metre. A long line shaft is usually checked against a total twist limit instead, commonly 1 degree over a length of 20 diameters.
How do I convert power and speed into torque?
T = 9550 x P / n with P in kilowatts, n in rpm and T in newton metres. The exact constant is 60000 / 2 pi = 9549.3, so 15 kW at 1500 rpm is 95.5 N m. Going the other way, P = T x 2 pi x n / 60000.
Is a hollow shaft stronger than a solid one?
For the same outside diameter, yes. Torsional stiffness depends on J, which grows with the fourth power of the radius, so the material near the outside does almost all the work and the core contributes little. Boring a solid shaft out to 0.707 times its diameter halves the weight and costs a quarter of the stiffness, which is why driveshafts and machine spindles are usually hollow.