A power-transmitting shaft is sized by the twist it carries. First the power and speed are turned into torque — the same power at a lower speed means more torque, which is why slow, heavy machines have fat shafts. Then the shaft diameter is set so the torsional shear stress stays below an allowable value. Because stress depends on diameter cubed, the diameter only grows as the cube root of torque, so shafts are forgiving of load increases but unforgiving of being undersized at a keyway.
Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: classic torsion theory / ASME shaft practice.
The shaft equations
Keep units consistent: with torque in N·mm and stress in MPa (N/mm²), the diameter comes out in millimetres. The service factor Kt scales the mean torque up to a design torque before sizing, covering starting shock and uneven loads. Choosing the next standard shaft size up then leaves a little extra margin, which the calculator reports as the actual stress at that diameter.
Worked example — a 15 kW gearbox input shaft
Scenario: 15 kW at 1500 rpm, keyed steel shaft (τ_allow = 40 MPa), steady duty (Kt = 1).
The minimum is 23 mm, so the next standard size of 25 mm is selected. At 25 mm the actual shear stress drops to about 31 MPa, leaving comfortable margin below the 40 MPa allowable. If the drive were shock-loaded, applying a service factor of 1.5 would push the design torque to 143 N·m and the minimum diameter to ~26 mm, bumping the choice to a 28 mm shaft.
Frequently Asked Questions
T = 9550·P/N (kW, rpm → N·m), then d = (16T/(π·τ_allow))^(1/3). Diameter grows as the cube root of torque.
~40 MPa for keyed commercial steel shafting, ~55 MPa without a keyway (classic ASME practice). Alloy steels allow more.
τ = 16T/(π·d³) for a solid shaft, from τ = T·r/J with J = π·d⁴/32. Assumes pure torsion.
Peak torque exceeds the average during starts and jams. Multiply mean torque by ~1.25–3.0 before sizing to avoid fatigue at keyways.
Hollow shafts save weight by removing low-stress core material, at higher cost and slightly larger OD. This tool sizes a solid shaft.