Circular Shaft Torsion Calculator
Calculate elastic surface shear stress, twist and strain energy for a solid or hollow circular shaft.
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Result
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Calculation steps
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How to calculate
Compute the polar second moment of the circular cross-section and apply linear elastic pure torsion.
J=π(Do⁴−Di⁴)/32; τmax=|T|Do/(2J); twist=TL/(GJ); energy=T²L/(2GJ)
Worked example
A solid20mm shaft, length1m, G=80GPa and torque100N·m has J≈1.57079633×10⁻⁸m⁴, stress≈63.6619772MPa and twist≈4.55945326°.
Assumptions and input details
Uniform isotropic circular shaft, constant torque, small-strain linear elasticity. Length, outer diameter and shear modulus are positive, with0≤inner<outer diameter. Twist follows signed torque; reported maximum stress is a magnitude. No allowable stress, safety factor, yielding, fatigue, stress concentration, keyway, noncircular warping or structural approval is inferred.
References: University of Illinois: circular-shaft torsion
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
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