Moment of Inertia Calculator

Select a cross-section shape and enter dimensions to calculate moment of inertia, section modulus, and radius of gyration.

Cross-Section Shape

Width b (mm)

Height h (mm)

Moment of Inertia (Ixx)

mm⁴

Section Modulus (Sx)

—

Radius of Gyration (r)

—

Cross-Sectional Area

—

Ixx (cm⁴)

—

Moment of Inertia Formulas

Rectangle: I = bh³/12

Circle: I = πd⁴/64

Triangle: I = bh³/36

Section Modulus: S = I / c

Radius of Gyration: r = √(I / A)

Beam analysis.

Material stress.

Beam deflection.

Gear design.

Weld loads.

Area shapes.