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Circular Shaft Torsional Constant Calculator — result sheet
Calculate the polar torsional constant, elastic torsional stiffness, twist, and surface shear stress for a solid circular shaft.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For a solid circular shaft J = πd⁴/32; torsional stiffness k = GJ/L; twist θ = TL/(GJ); surface shear stress τ = 16T/(πd³).
The page keeps the geometric polar constant J separate from material stiffness G and span length. That makes the strong diameter dependence visible while keeping the result an elastic, uniform solid-shaft estimate rather than a structural approval.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Solid shaft diameter — mm; minimum 1.0E-6; maximum 1000000
- Shaft length — m; minimum 1.0E-6; maximum 1000000
- Shear modulus — GPa; minimum 1.0E-6; maximum 1000000
- Applied torque — N·m; minimum 0; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Solid shaft diameter | 20 |
| Shaft length | 1 |
| Shear modulus | 80 |
| Applied torque | 100 |
J ≈ 1.5708×10⁻⁸ m⁴; stiffness ≈ 1,256.64 N·m/rad; twist ≈ 0.07958 rad and surface shear stress ≈ 6.366 MPa.
Assumptions and limits
- The shaft is solid, circular, prismatic, and loaded by a torque about its axis.
- Diameter is converted from millimetres to metres and shear modulus from gigapascals to pascals.
- The material is linearly elastic and the twist remains within small-deformation torsion assumptions.
- The torque is nonnegative and the reported stress is a magnitude at the outer surface.
- Stress concentrations, keyways, hollow sections, warping, yielding, fatigue, buckling, and connections are not modeled.
- The result does not select a material allowable, safety factor, or acceptable angular twist.
- Use an appropriately reviewed mechanical design for a real shaft, coupling, or rotating machine.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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