Shafts carry torque from motors to machines. Too thin and they twist, bend or break; too thick and they waste weight and money. These classic design formulas give the minimum safe diameter.
How to use the Shaft Size Calculator
- Design basis
- Power P
- Speed (rpm)
- Bending moment M
- Allowable shear stress τ
- Allowable bending stress σ
- Shear modulus G
- Allowable twist
- Length for that twist
- Hollow shaft ratio k = d_i/d_o (0 = solid)
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the design basis and enter the power, speed and allowable values. For a hollow shaft, enter the ratio of inner to outer diameter.
Inputs explained
| Field | What to enter |
|---|---|
| Design basis | Choose one: Twisting moment only, Bending moment only, Combined twisting and bending, Torsional rigidity |
| Power P | Units: kW, W, hp |
| Speed (rpm) | A number |
| Bending moment M | Units: N·m, lbf·ft, kgf·m, N·mm |
| Allowable shear stress τ | Units: MPa, psi, ksi |
| Allowable bending stress σ | Units: MPa, psi, ksi |
| Shear modulus G | Units: GPa, MPa, Pa, psi, Mpsi |
| Allowable twist | Units: °, rad, arcmin, arcsec, mrad |
| Length for that twist | Units: m, cm, mm, km, in, ft … |
| Hollow shaft ratio k = d_i/d_o (0 = solid) | A number |
What each result means
- Transmitted torque = [Power P]÷(2×pi×[Speed (rpm)]÷60)
- Hollow shaft inner diameter = [Hollow shaft ratio k = d_i÷d_o (0 = solid)]×[Hollow shaft outer diameter]
- Weight saving of the hollow shaft = (1 – ([Hollow shaft outer diameter]^2 – [Hollow shaft inner diameter]^2)÷[Solid shaft diameter]^2)×100
Example values
How the main result changes when Power P changes and everything else stays at the example values above:
| Power P (kW) | Solid shaft diameter (mm) |
|---|---|
| 7.5 | 21.1783 |
| 11.25 | 24.2431 |
| 15 | 26.6829 |
| 18.75 | 28.7433 |
| 22.5 | 30.5444 |
| 30 | 33.6184 |
Formula
T = P/ω · Twisting: d = (16T/(πτ))^{1/3} · Bending: d = (32M/(πσ))^{1/3} · Combined: T_e = √(M² + T²)
Rigidity: d = (32TL/(πGθ))^{1/4} · Hollow: d_o = d/(1 − k⁴)^{1/3}, k = d_i/d_o
Worked example
Inputs — Design basis: Twisting moment only; Power P: 15 kW; Speed (rpm): 960; Allowable shear stress τ: 40 MPa; Hollow shaft ratio k = d_i/d_o (0 = solid): 0.5.
Results — Transmitted torque = 149.20776 N·m; Solid shaft diameter = 26.6829 mm; Hollow shaft outer diameter = 27.2632 mm; Hollow shaft inner diameter = 13.6316 mm; Weight saving of the hollow shaft = 21.703 %.
Key terms
- Equivalent torque
- √(M² + T²), combining bending and torsion.
Frequently asked questions
What allowable shear stress should I use?
Often 40–55 MPa for commercial steel shafts with keyways.
Why consider rigidity?
Long shafts may twist too much even if strong enough (limit ~1° per 20 diameters).
Why are hollow shafts lighter for the same strength?
Material near the centre carries little torque.
Does this include keyways and fatigue?
No – apply appropriate factors for real designs.