Torsional Shear Stress Calculator
A free, browser-based calculator. Runs entirely in your browser — no sign up, nothing stored.
Enter Values
How to use this calculator
- Enter the applied torque T in newton-metres.
- Enter the solid shaft diameter d in millimetres.
- Read the maximum (surface) torsional shear stress and the polar moment J.
How it works
The Torsional Shear Stress Calculator finds the peak shear stress at the surface of a solid round shaft carrying a torque.
τ = T·r / J, where r = d/2 and the polar second moment J = π·d⁴/32. For a solid round shaft this simplifies to τ = 16T / (π·d³). The stress is largest at the outer surface and zero at the centre.
Worked example
100 N·m on a 20 mm shaft. τ = 16 × 100,000 N·mm ÷ (π × 20³) ≈ 63.7 MPa at the surface.
Frequently asked questions
Does this cover hollow shafts?
No — this is for a solid round shaft. A hollow shaft uses J = π(D⁴ − d⁴)/32 with the stress evaluated at the outer radius.
Can I use these results for final design?
No. These calculators are for first-pass sizing, checking and learning. They assume ideal supports, static loads and elastic behaviour, and they don't apply load factors, member capacity, buckling or connection checks. Always verify against the relevant design code (e.g. AS 4100, AS 1170, Eurocode) and have a qualified engineer sign off structural work.
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Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.