Physics

Angle of Twist Calculator

Find how much a shaft twists under torque.

Torque (N·m)

Length

Shear modulus (GPa)

Polar moment of inertia (mm⁴)

Calculated Output

Angle of twist (rad) 0.0051

Angle of twist (°) 0.2901

Formula: φ = T·L ÷ (G·J)

Step-by-Step Breakdown

1. Values used:

2. Torque = 200 N·m

3. Length = 500

4. Shear modulus = 79 GPa

5. Polar moment of inertia = 250,000 mm⁴

7. Torque / Length = 0.4

8. Angle of twist = (Torque x Length) / Shear modulus = 0.4 / 79 = 0.0051rad

9. Angle of twist = 0.2901°

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The math behind it

φ = T·L ÷ (G·J), in radians. Longer or thinner shafts twist more.

200 N·m, 500 mm, G 79 GPa, J 250,000 mm⁴ → about 0.0051 rad (0.29°).

How to limit twist?

Use a larger-diameter or shorter shaft, or a stiffer material.