Shaft Diameter Calculator (Torsion, from Power & Speed)
By Santaji GadepatilinUpdated November 3, 2026
A rotating shaft must carry its torque without the torsional shear stress at its surface exceeding a safe limit. This shaft diameter calculator converts power and speed into torque and then sizes a solid circular shaft from the torsion formula τ = 16T ÷ (πd³), using an allowable shear stress that already includes your safety margin.
How to use the shaft diameter calculator
Enter the power to be transmitted, the shaft speed in rpm and the allowable shear stress for the shaft material. The calculator returns the torque and the minimum solid-shaft diameter; round up to the next standard size. To check an existing shaft, enter its diameter and clear the allowable stress to see the actual stress.
Shaft diameter formula (torsion)
T = P ÷ (2πN ÷ 60) · τ = 16 T ÷ (π d³) · d = ∛(16 T ÷ (π τ))
Example
A 15 kW motor running at 1,450 rpm, steel shaft with τallow = 40 MPa:
- T = 15,000 ÷ (2π × 1450 ÷ 60) = 98.79 N·m
- d = ∛(16 × 98.79 ÷ (π × 40 × 10⁶)) = 23.3 mm → choose a 25 mm shaft
Minimum shaft diameter at τ = 40 MPa
| Power | Torque at 1450 rpm | d at 1450 rpm | d at 960 rpm | d at 2900 rpm |
|---|---|---|---|---|
| 0.75 kW | 4.9 N·m | 8.6 mm | 9.8 mm | 6.8 mm |
| 2.2 kW | 14.5 N·m | 12.3 mm | 14.1 mm | 9.7 mm |
| 5.5 kW | 36.2 N·m | 16.6 mm | 19.1 mm | 13.2 mm |
| 11 kW | 72.4 N·m | 21.0 mm | 24.1 mm | 16.6 mm |
| 15 kW | 98.8 N·m | 23.3 mm | 26.7 mm | 18.5 mm |
| 30 kW | 197.6 N·m | 29.3 mm | 33.6 mm | 23.3 mm |
| 55 kW | 362.2 N·m | 35.9 mm | 41.1 mm | 28.5 mm |
| 90 kW | 592.7 N·m | 42.3 mm | 48.5 mm | 33.5 mm |
| 160 kW | 1053.7 N·m | 51.2 mm | 58.7 mm | 40.6 mm |
Notes
- Keyways, shoulders and grooves concentrate stress; fatigue design for these features needs stress-concentration factors.
- Long shafts may be governed by twist rather than strength — a common limit is 0.25° per metre for machinery shafts.
- Check that a motor’s shaft size matches its output torque using the torque, power & speed calculator.
Frequently asked questions
How do you calculate shaft diameter from torque?
For a solid round shaft, d = ∛(16T ÷ (π τ)), where T is the torque and τ the allowable shear stress. Torque comes from power and speed, T = P ÷ (2πN/60).
What allowable shear stress should I use?
The ASME shaft code suggests the lower of 18% of ultimate strength or 30% of yield, reduced by 25% for keyways. For commercial mild-steel shafting this gives about 40 MPa.
Does this account for bending?
No. Shafts carrying pulleys, gears or overhung loads also bend. Then combine them with the equivalent torque √(M² + T²) in place of T, and apply shock factors for the load type.
How does speed affect shaft size?
At the same power, torque is inversely proportional to speed, and diameter grows with the cube root of torque. Halving the speed increases the diameter by about 26%.