Shaft Size Calculator — Minimum Diameter for Torsion
Find the minimum diameter of a solid circular shaft to safely transmit a known torque or a power-speed combination. Enter the allowable material shear stress and a safety factor, and get the theoretical minimum plus the nearest standard ISO/ANSI shaft size.
Input mode
kW
rpm
MPa
×
Theoretical minimum for torsion only — no bending or fatigue included
Shaft
- 1
Design shear stress
τ_design = 40 ÷ 1.5 = 26.6667Allowable shear stress divided by the safety factor. - 2
Torque from power
T = 5 × 1000 × 60 ÷ (2π × 1,450) = 32.9286 - 3
Min shaft diameter
d = ∛(16 × 32,928.6 ÷ (π × 26.6667)) = 18.46T converted to N·mm (×1000). Formula: d = ∛(16T / πτ).
How does this calculator work?
Minimum shaft diameter = ∛(16T / πτ_design). Convert power to torque via T = P×60/(2π×n), divide the material's allowable shear stress by your safety factor to get τ_design, then solve for d. Round up to the next standard size. This covers torsion only — add bending/fatigue analysis for real designs.
Formula
How this is calculated
A rotating shaft transmits torque T, which creates a shear stress τ = 16T / (π d³) on the outer surface of a solid circular cross-section (derived from τ = T·r / J with J = πd⁴/32). Rearranging gives the minimum diameter: d = ∛(16T / (πτ)). The design shear stress is the material's allowable shear stress divided by the safety factor — for carbon steel shafts this is typically 40–60 MPa before applying the factor.
If only power and rotational speed are known (the usual motor nameplate data), torque is derived first: T = P × 60 / (2π × n), where P is in watts and n is in rpm. This calculator uses kilowatts for convenience.
Important limitations: this formula covers pure torsion only. Real shafts also experience bending from transverse loads (gears, pulleys, belts), axial loads, and fatigue due to rotating-bending stress reversals — all of which increase the required diameter. The ASME design code for shafts under combined loading replaces the simple torsion formula with a combined stress criterion. Always verify critical shafts with a full fatigue analysis per the applicable design standard.
Frequently asked questions
A common starting point is 40–60 MPa for carbon steel (e.g. AISI 1045) under steady torsion, or 55–80 MPa for alloy/stainless steel. These values already reflect some conservatism; apply an additional safety factor for shock, reversing loads or uncertainty in material properties.
A safety factor of 1.5 is typical for steady, well-characterised loads in a controlled environment. Use 2–3 for shock or impact loads, machinery with vibration, or when material properties are uncertain. For safety-critical applications follow the relevant design standard (e.g. ASME B106, ISO 281).
No. Keyways reduce the effective cross-section and introduce stress concentrations, so the nominal diameter found here should be increased by about 5–15% when a keyway is present, or the shaft should be re-analysed with a stress concentration factor applied.
Also known as
TG we-Calculate Editorial Team. (2026). Shaft Size Calculator — Minimum Diameter for Torsion [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/shaft-size-calculator
TG we-Calculate Editorial Team. "Shaft Size Calculator — Minimum Diameter for Torsion." TG we-Calculate. 2026. https://we-calculate.com/calculator/shaft-size-calculator.
TG we-Calculate Editorial Team, "Shaft Size Calculator — Minimum Diameter for Torsion," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/shaft-size-calculator
@misc{wecalculate_shaft_size_calculator, title = {Shaft Size Calculator — Minimum Diameter for Torsion}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/shaft-size-calculator}}, year = {2026}, note = {TG we-Calculate} }
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