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Shaft Angle of Twist Calculator — result sheet
Calculate elastic shaft twist from torque, shaft length, shear modulus, and polar second moment of area.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Angle of twist θ = TL/(GJ) in radians.
The elastic torsion model relates twist to applied torque and length, and inversely to stiffness and polar geometry.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Applied torque — N·m; minimum 0; maximum 1000000000
- Shaft length — m; minimum 1.0E-6; maximum 1000000
- Shear modulus — Pa; minimum 1.0E-6; maximum 1000000000000
- Polar second moment — m⁴; minimum 1.0E-24; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Applied torque | 100 |
| Shaft length | 1 |
| Shear modulus | 80000000000 |
| Polar second moment | 1.0E-8 |
Twist = 0.125 rad ≈ 7.162°.
Assumptions and limits
- Inputs use SI units and stiffness and polar moment are positive.
- The shaft is prismatic, elastic, and under uniform torsion.
- Yield, warping, stress concentration, fatigue, buckling, and design approval are not modeled.
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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