Physics

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Angle of Twist Calculator.

Calculate torsional twist for a solid circular shaft.

On-device calculationNo signup
01

Set your values

Results update as you type.

angleRadians: 0.079577

angleRadians

0.000000
angleDegrees: 4.559453

angleDegrees

0.000000
polarMoment: 0

polarMoment

0.000000

Use Cases

Mechanical design of drive shafts

Engineers use this calculator to ensure that a solid shaft will not twist excessively under applied torque, which is critical for power transmission systems.

Example: Check a 2 m long steel shaft (diameter 0.05 m) under 500 N·m torque with G = 79 GPa.

Educational demonstrations in physics

Students can quickly compute twist angles to understand torsional deformation and verify theoretical results in mechanics of materials courses.

Example: Calculate twist for a brass shaft with given dimensions and compare with lab measurements.

Frequently Asked Questions

What is the angle of twist in a shaft?
The angle of twist is the angular deformation of a shaft when subjected to torque. It depends on the applied torque, shaft length, diameter, and material shear modulus. This calculator computes it for a solid circular shaft.
What units are used in this calculator?
Torque is in Newton-meters (N·m), shaft length in meters (m), shaft diameter in meters (m), and shear modulus in Pascals (Pa). The result is given in radians.
Can this calculator be used for hollow shafts?
No, this calculator is specifically for solid circular shafts. For hollow shafts, the polar moment of inertia differs, and a different formula is required.

Tips & Common Mistakes

Tips

  • Ensure all inputs are in the correct units: torque in N·m, length in m, diameter in m, and shear modulus in Pa. Convert if necessary.
  • Use consistent units to avoid errors. For example, if shear modulus is given in GPa, convert to Pa (1 GPa = 1e9 Pa) before entering.
  • The result is in radians. To convert to degrees, multiply by 180/π (approximately 57.2958).
  • For a given material, a larger diameter significantly reduces the twist angle because the polar moment of inertia scales with the fourth power of diameter.

Common Mistakes to Avoid

  • Using diameter instead of radius in the formula. The calculator expects diameter, so do not halve it manually.
  • Forgetting to convert shear modulus from GPa to Pa. Entering 79 instead of 79e9 will give a wildly incorrect result.
  • Mixing units, such as entering length in millimeters while other inputs are in meters, leading to errors of orders of magnitude.

Last updated: August 13, 2026