Shaft Size Calculator

Enter the transmitted power, shaft speed, and allowable shear stress to find the minimum safe shaft diameter using the torsion design formula.

Quick Facts

Torsion (shear stress) formula
τ = 16T / (πd³)
Maximum shear stress on the outer surface of a solid round shaft carrying torque T.
Diameter from torque
d = (16T / (π·τ_allow))^(1/3)
The torsion formula solved for diameter using your allowable design stress.
Torque from power
T = 60P / (2πN)
P is power in watts and N is speed in rpm; result is torque in N·m.
Keyway allowance
+5-10% diameter
A keyway removes material and concentrates stress, so designers often add 5-10% to the calculated diameter.

Your Results

Calculated
Design Torque
-
T = 60P / (2πN), in newton-meters
Minimum Diameter (mm)
-
d = (16T / (π·τ_allow))^(1/3)
Minimum Diameter (in)
-
Same result converted to inches
Practical Diameter (mm)
-
+10% keyway margin, rounded up to the next mm

Ready

Enter power, shaft speed, and allowable shear stress, then press Calculate.

Shaft Diameter Formula and Method

A power-transmission shaft — the rotating rod inside a motor, gearbox, pump, or conveyor drive — is sized so it can carry its twisting load without exceeding a safe shear stress. This calculator finds the minimum diameter for a solid, circular steel shaft subjected to pure torsion: it converts your transmitted power and rotational speed into a design torque, then solves the torsion formula for the diameter that keeps the shaft's shear stress at or below your chosen allowable value.

Deriving the diameter formula

Power transmitted by a rotating shaft is P = T·ω, where ω is the angular speed in radians per second. Since ω = 2πN/60 for a speed N in revolutions per minute, the torque is T = 60P / (2πN) — commonly written T = 9549·P(kW)/N(rpm) in newton-meters. For a solid circular shaft, mechanics of materials gives the maximum shear stress at the outer surface as τ = T·c/J, where c = d/2 is the outer radius and J = πd⁴/32 is the polar moment of inertia. Substituting gives the classic torsion formula τ = 16T / (πd³). Setting τ equal to the allowable shear stress τallow and solving for d yields d = (16T / (π·τallow))^(1/3), the minimum diameter that keeps the shaft below that stress.

Choosing an allowable shear stress

The allowable stress you enter should already include a safety margin, not just the raw material strength. General-purpose carbon steel shafting is commonly designed to 40-60 MPa (about 5,800-8,700 psi); higher-strength alloy steels or lower safety factors can justify larger values, while shock loads, fatigue, or keyways call for lower ones. Formal codes such as ASME B106.1M set the allowable stress as the smaller of a fraction of the yield strength and a fraction of the ultimate tensile strength, then reduce it further (commonly by 25%) where a keyway is present.

Limits of a torsion-only calculation

This calculator sizes a shaft for torque alone. Most real shafts also carry bending moments from gears, pulleys, belts, or their own weight, and combined bending-torsion loading requires a different equation (for example, the ASME code method or the distortion-energy/maximum-shear-stress approaches in references like Shigley's Mechanical Engineering Design). Treat the diameter here as a torsion-only lower bound: verify bending stresses separately, add the keyway allowance shown in the practical diameter result, and round up to a stocked shaft size before finalizing a design.

Frequently Asked Questions

What formula does this shaft size calculator use?
It first finds the transmitted torque from power and rotational speed, T = 60P / (2πN), then solves the torsion (shear stress) formula for a solid round shaft, τ = 16T / (πd³), for diameter: d = (16T / (π · τ_allow))^(1/3).
What allowable shear stress should I use for a steel shaft?
For general-purpose carbon steel shafting, 40-60 MPa (about 5,800-8,700 psi) is a common design range once a safety factor is already built in. Alloy steels and higher safety factors can justify different values, and codes such as ASME B106.1M give a formal method for setting the allowable stress from a material's yield and ultimate strength.
Does this calculator account for bending loads or keyways?
No. This is a torsion-only sizing calculation for shafts loaded mainly by twisting (power transmission). It does not include bending moments, shock loading, or fatigue. If a keyway is cut into the shaft, add roughly 5-10% to the calculated diameter to offset the stress concentration, and for shafts with significant bending use a combined-loading method such as the ASME code equation or the distortion-energy theory in Shigley's Mechanical Engineering Design.
Why does the calculator show a rounded-up "practical diameter"?
The torsion formula gives a bare theoretical minimum. Real shafts need extra material for keyways, fillets, and available stock sizes, so the practical diameter adds about a 10% margin and rounds up to the next whole millimeter as a safer starting point for detailed design.

Related calculators