# Shaft Size Calculator

URL: https://speedycalculator.com/calculators/physics/shaft-size/
Last updated: 2026-10-30

> The shaft size calculator finds the minimum diameter of a solid or hollow shaft transmitting a given power at a given speed, based on allowable shear stress (twisting), bending, combined loading or torsional rigidity.

## Inputs

- Design basis
- Power P (kW, W, hp)
- Speed (rpm)
- Bending moment M (N·m, lbf·ft, kgf·m, N·mm)
- Allowable shear stress τ (MPa, psi, ksi)
- Allowable bending stress σ (MPa, psi, ksi)
- Shear modulus G (GPa, MPa, Pa, psi, Mpsi)
- Allowable twist (°, rad, arcmin, arcsec, mrad)
- Length for that twist (m, cm, mm, km, in, ft, yd, mi)
- Hollow shaft ratio k = d_i/d_o (0 = solid)

## Results

- Transmitted torque
- Solid shaft diameter
- Hollow shaft outer diameter
- Hollow shaft inner diameter
- Weight saving of the hollow shaft

## 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
```

## Explanation

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

FieldWhat to enterDesign basisChoose one: Twisting moment only, Bending moment only, Combined twisting and bending, Torsional rigidityPower PUnits: kW, W, hpSpeed (rpm)A numberBending moment MUnits: N·m, lbf·ft, kgf·m, N·mmAllowable shear stress τUnits: MPa, psi, ksiAllowable bending stress σUnits: MPa, psi, ksiShear modulus GUnits: GPa, MPa, Pa, psi, MpsiAllowable twistUnits: °, rad, arcmin, arcsec, mradLength for that twistUnits: 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)7.521.178311.2524.24311526.682918.7528.743322.530.54443033.6184

## 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.

## FAQ

**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.


## Sources

- [Shigley's Mechanical Engineering Design (Budynas & Nisbett) – reference text](https://www.mheducation.com/highered/product/shigley-s-mechanical-engineering-design-budynas/M9780073398204.html)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)