Shaft Diameter Calculator

Inputs

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Torque carried by the shaft.
N·m
Optional bending moment at the critical shaft section. Leave 0 for pure torsion.
N·m
Material allowable shear stress before applying the safety factor. If already derated, set safety factor to 1.
MPa
Design stress is allowable shear stress divided by this factor.

Results

Default result
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Required diameter (d)
23.35 mm
Pass

Round up to the next available stock diameter, then recheck stress and deflection.

Theoretical minimum solid round diameter. Round up to a stock size.

Also computed

Equivalent torque (T_e) 100 N·m

sqrt(T^2 + M^2) for the maximum-shear combined-load formula.

Max shear at diameter (tau_max) Pass 40 MPa

Equals the design shear stress at the solved diameter.

Design shear stress (tau_d) 40 MPa

allowable shear / safety factor.

Torsional shear (tau_t) 40 MPa

Bending stress (sigma_b) 0 MPa

Polar moment J (J) 2.919 cm⁴

J = pi d^4 / 32 for a solid round shaft.

Method notes 3 notes
  • Pure torsion uses tau = 16T/(pi d^3). With bending included, the maximum-shear check is tau_max = sqrt((sigma_b/2)^2 + tau_t^2).
  • The combined-load rearrangement is d = [16*sqrt(T^2 + M^2)/(pi*tau_d)]^(1/3), with T and M in N*mm and tau_d = tau_allow / safety factor.
  • This is a static solid-shaft screen. It does not include fatigue, stress concentrations at keyways/shoulders, shaft deflection, critical speed, material yield in bending, or bearing reactions.

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