Calculator Inputs
Formula Used
This calculator is intended for circular shafts under elastic torsion.
θ is the angle of twist, T is torque, L is shaft length, J is the polar moment of inertia, and G is shear modulus.
The solid equation uses one diameter. The hollow equation uses outer diameter D and inner diameter d.
This calculates the maximum shear stress at the outer radius.
Torsional stiffness tells you how much torque is required per radian of rotation.
Strain energy estimates elastic energy stored during twisting.
How to Use This Calculator
- Select a solid or hollow circular shaft.
- Choose whether to calculate J from geometry or enter it directly.
- Enter torque, shaft length, shear modulus, and diameter details.
- Pick units for every field to match your source data.
- Submit the form to display twist, stress, stiffness, strain energy, and the graph.
- Use the export buttons to save results as CSV or PDF.
Example Data Table
| Case | Shaft Type | Torque | Length | Dimensions | G | Angle of Twist | Max Shear Stress |
|---|---|---|---|---|---|---|---|
| Example 1 | Solid Steel | 850 N·m | 1.2 m | 40 mm diameter | 79.3 GPa | 2.9323 deg | 67.6409 MPa |
| Example 2 | Hollow Aluminum | 1400 N·m | 2.5 m | 60 mm OD, 30 mm ID | 26 GPa | 6.4661 deg | 35.2106 MPa |
Frequently Asked Questions
1) What is the angle of twist?
It is the angular rotation of a shaft caused by applied torque. Higher torque and longer shafts increase twist, while larger polar inertia and shear modulus reduce it.
2) Which shafts work with this calculator?
It is designed for circular shafts in elastic torsion. You can model solid circular shafts, hollow circular shafts, or enter a known polar moment directly.
3) Why does shear modulus matter?
Shear modulus measures a material’s resistance to shear deformation. A higher value means the shaft twists less for the same torque, length, and geometry.
4) What is the difference between solid and hollow shafts?
Solid shafts use one diameter. Hollow shafts use outer and inner diameters. Hollow sections can reduce weight while still maintaining useful torsional stiffness.
5) Can I enter the polar moment of inertia directly?
Yes. Choose the direct J mode if you already know the polar moment from a handbook, CAD model, manufacturer sheet, or detailed section analysis.
6) What does the maximum shear stress result mean?
It estimates the highest torsional shear stress at the shaft’s outer surface. Compare it against allowable material stress for design checking.
7) How can I reduce shaft twist?
Reduce length, reduce torque, use a stiffer material, or increase polar inertia by increasing diameter. These changes lower rotation under the same loading.
8) Is this calculator valid beyond elastic behavior?
No. These equations assume linear elastic torsion. For yielding, plastic behavior, stress concentrations, keyways, or noncircular sections, use a more detailed analysis.