Shaft Diameter from Power and Speed Calculator (Torsion, Solid and Hollow)
The smallest solid shaft that carries a given power at a given speed without exceeding the allowable shear stress, and the hollow shaft that does the same job lighter.
Results
Minimum diameter of a solid shaft
23.0
mm
Torque transmitted
95.5
N·m
Outer diameter of the hollow shaft
23.5
mm
Inner diameter of the hollow shaft
11.7
mm
Weight of the hollow shaft compared with the solid one
78.3
%
What this tool does
Power and speed give the torque, T = 9549 × kW ÷ rpm, and torsion fixes the diameter: d = ∛(16T ÷ πτ). The cube root is forgiving — doubling the torque raises the diameter by only 26 %. A hollow shaft with a bore half the outside diameter is about 2 % wider than the solid one but around 22 % lighter, because the material near the axis does little. This is a torsion-only check: bending, keyways, shock loads and fatigue usually call for a lower allowable stress or a larger service factor.
Formula
T = 9549 × P(kW) ÷ n(rpm) · d = ∛(16 T ÷ (π τ)) · hollow: D = ∛(16 T ÷ (π τ (1 − k⁴)))
Variables
| Symbol | Meaning | Unit |
|---|---|---|
pw | Power transmitted | kW |
rp | Shaft speed | rpm |
ta | Allowable shear stress | MPa |
ks | Service factor (shocks, starts) | — |
kb | Bore ratio of a hollow shaft (inner ÷ outer diameter, 0 = solid) | — |
DS | Minimum diameter of a solid shaft | mm |
T | Torque transmitted | N·m |
DH | Outer diameter of the hollow shaft | mm |
DI | Inner diameter of the hollow shaft | mm |
WT | Weight of the hollow shaft compared with the solid one | % |
Worked example
- Power transmitted15 kW
- Shaft speed1500 rpm
- Allowable shear stress40 MPa
- Service factor (shocks, starts)1
- Bore ratio of a hollow shaft (inner ÷ outer diameter, 0 = solid)0.5
- Minimum diameter of a solid shaft23.0 mm
- Torque transmitted95.5 N·m
- Outer diameter of the hollow shaft23.5 mm
- Inner diameter of the hollow shaft11.7 mm
- Weight of the hollow shaft compared with the solid one78.3 %
Limitations
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.