Shaft Diameter Calculator

How it works

1. 1Enter the transmitted torque and the allowable shear stress for your shaft material.
2. 2The calculator applies d = (16T / πτ)^(1/3) — the classical torsion formula for a solid circular cross-section.
3. 3Read off the minimum required shaft diameter, then apply a safety factor and check for bending before finalising your design.

Use cases

• Sizing a drive shaft for a gearbox or motor coupling during preliminary mechanical design.
• Verifying that an existing shaft cross-section can carry a new torque load without yielding in shear.
• Converting between metric and imperial design specifications when collaborating with international suppliers.

Frequently asked questions

What formula does the calculator use?

It uses the solid-shaft torsion formula d = (16T / πτ)^(1/3), derived from setting the maximum shear stress τ = 16T / (πd³) equal to the allowable value. For example, T = 100 N·m and τ = 40 MPa gives d ≈ 23.4 mm.

Does this account for bending or combined loading?

No — the formula assumes pure torsion only. In practice you must also check bending stress, apply a fatigue stress-concentration factor, and include a design safety factor of at least 1.5–2 before selecting a final shaft size.

What allowable shear stress should I use?

A common rule of thumb is τ ≈ 0.3 × yield strength or 0.18 × ultimate tensile strength for ductile steels under static loading. For AISI 1045 steel (yield ≈ 310 MPa) that is τ ≈ 93 MPa before a safety factor.