Torsional Shear Stress Calculator
Computes shaft torsional shear stress from applied torque, diameter and polar moment of area.
Enter Values
Minimum 0
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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Cite this tool
Zerdly. (2026). Torsional Shear Stress Calculator. Retrieved from https://www.zerdly.com/tools/torsional-shear-stress-calculator/
Tip: Enter any known values to calculate the remaining results.
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