Moment of inertia of a circular section

Q: What is the moment of inertia of a circle?

About any centroidal axis Ix = Iy = πR⁴/4, or πd⁴/64 in terms of the diameter.

Q: Why does the editor give a slightly different number?

The interactive calculator represents a circle as a polygon: the more sides, the closer it gets to πR⁴/4. The link below opens the section with 64 sides.

For a circle both axial moments are equal and the polar moment is twice as large — the value used when checking shafts in torsion.

Circular section with the radius R marked

Input data

Units

Enter positive numbers in every field

Open this section in the editor

Formulas

A = π R^{2}

I_{x} = I_{y} = \frac{π R^{4}}{4}

I_{p} = \frac{π R^{4}}{2}

About this calculator

A circular section is equally stiff in every direction, which suits parts loaded from changing directions: shafts, rods, columns. The polar moment Ip = Ix + Iy = πR⁴/2 governs the resistance to torsion.

Frequently asked questions

What is the moment of inertia of a circle?

Why does the editor give a slightly different number?

Moment of inertia of a rectangular section
Moment of inertia of a rectangular section with a hole
Moment of inertia of an annular section (tube)
Moment of inertia of a right triangle
Moment of inertia of a triangle from three points

Formulas

About this calculator

Frequently asked questions

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