Polar Moment of Inertia Calculator

Find the polar moment of inertia of a round shaft.

Outer diameter

Inner diameter (0 = solid)

Polar moment of inertia (mm⁴) 251,327.41

Formula: J = π·(D⁴ − d⁴) ÷ 32

Step-by-step with your numbers:

1. Values used:

2. Outer diameter = 40

3. Inner diameter (0 = solid) = 0

5. Polar moment of inertia = 251,327.41mm⁴

Did we solve your problem today?

The polar moment of inertia measures a circular cross-section's resistance to twisting.

The math behind it

J = π·(D⁴ − d⁴) ÷ 32. Set the inner diameter to 0 for a solid shaft.

Solid 40 mm shaft → J ≈ 251,327 mm⁴.

Why is a hollow shaft efficient?

Most torsional strength comes from material far from the axis, so the core adds little.