Calculator Inputs
Formula Used
Polar moment of inertia for a hollow circular tube:
J = (π / 32) × (Do4 − Di4)
Torsional rigidity:
GJ = G × J
Torsional stiffness:
k = GJ / L
Angle of twist:
θ = T × L / (G × J)
Maximum shear stress:
τmax = T × ro / J
How to Use This Calculator
- Enter the outer diameter of the tube.
- Choose whether you want to enter inner diameter or wall thickness.
- Enter tube length and applied torque.
- Select a material preset or type a custom shear modulus.
- Choose your preferred units for dimensions, torque, and modulus.
- Press the calculate button to see stiffness, twist, stress, and the graph.
- Use the CSV or PDF buttons to export your calculated report.
Example Data Table
| Example | Outer Dia. (mm) | Inner Dia. (mm) | Length (m) | G (GPa) | Torque (N·m) | Stiffness (N·m/rad) | Twist (deg) | Max Stress (MPa) |
|---|---|---|---|---|---|---|---|---|
| Steel Lab Tube | 50.00 | 40.00 | 1.20 | 79.30 | 600.00 | 23,939.67 | 1.4360 | 41.4062 |
| Aluminum Utility Tube | 80.00 | 72.00 | 1.80 | 26.00 | 350.00 | 19,975.28 | 1.0039 | 10.1236 |
| Titanium Precision Tube | 35.00 | 29.00 | 0.90 | 44.00 | 250.00 | 3,807.78 | 3.7618 | 56.1716 |
Frequently Asked Questions
1) What does torsional stiffness mean?
Torsional stiffness tells you how much torque is required to twist a tube by a certain angle. A larger value means the tube resists twisting more strongly and feels more rigid in service.
2) Why does the calculator use the polar moment J?
The polar moment of inertia describes how the tube cross section distributes material around its center. Larger J values make circular tubes much better at resisting torsion under the same material and length conditions.
3) Can I enter wall thickness instead of inner diameter?
Yes. Choose the wall thickness mode and the calculator will derive the inner diameter automatically. This is useful when tube catalogs list outside diameter and wall thickness instead of inside diameter.
4) Which shear modulus should I use?
Use the shear modulus that matches your material and heat treatment. Material handbooks or supplier data sheets usually provide it. The preset values are typical engineering estimates and work well for preliminary design.
5) What units can this calculator handle?
It accepts common diameter units, length units, torque units, and modulus units. All values are converted internally to SI before calculation, then displayed in a practical engineering format for easy interpretation.
6) When should I avoid using this model?
Avoid it when plastic deformation, stress concentrations, keyways, noncircular sections, composite layups, restrained warping, or dynamic vibration dominate the problem. In those cases, a more detailed structural model is better.
7) Why do longer tubes twist more?
Twist angle is directly proportional to length in the torsion equation. If all other inputs remain the same, doubling the tube length doubles the angular twist and reduces stiffness.
8) What does maximum shear stress tell me?
Maximum shear stress estimates the highest torsional stress at the outer surface. Compare it with your material’s allowable shear stress or yield criterion to judge whether the tube remains safely within elastic limits.