Physics

Polar Moment of Inertia Calculator

Find the polar moment of inertia of a round shaft.

Outer diameter

Inner diameter (0 = solid)

Calculated Output

Polar moment of inertia (mm⁴) 251,327.41

Formula: J = π·(D⁴ − d⁴) ÷ 32

Step-by-Step Breakdown

1. Values used:

2. Outer diameter = 40

3. Inner diameter (0 = solid) = 0

5. Polar moment of inertia = 251,327.41mm⁴

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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.