Physics

Torsional Stiffness Calculator

Find the torsional stiffness of a shaft.

Shear modulus (GPa)

Polar moment of inertia (mm⁴)

Length

Calculated Output

Torsional stiffness (N·m/rad) 39,500

Formula: k = G·J ÷ L

Step-by-Step Breakdown

1. Values used:

2. Shear modulus = 79 GPa

3. Polar moment of inertia = 250,000 mm⁴

4. Length = 500

6. Shear modulus x Polar moment of inertia = 79 x 250,000 = 19,750,000

7. Torsional stiffness = (Shear modulus x Polar moment of inertia) / Length = 19,750,000 / 500 = 39,500N·m/rad

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The math behind it

k = G·J ÷ L, where J is the polar moment of inertia and L the shaft length.

G 79 GPa, J 250,000 mm⁴, L 500 mm → about 39,500 N·m/rad.

How to make a stiffer shaft?

Increase diameter (J ∝ d⁴) or shorten the length.