Moment of Inertia Calculator
Calculate section properties including area, moment of inertia, section modulus, and radius of gyration for common structural shapes: rectangle, circle, I-beam, T-beam, channel, and triangle.
Engineering Formulas
Rectangle
Circle
I-Beam
T-Beam
Channel (C-Shape)
Triangle (Right Angle)
Worked Example
Rectangular Section 200mm × 300mm
Engineering Notes
Assumptions
Common Mistakes
Frequently Asked Questions
What is moment of inertia?
The moment of inertia (I) is a geometric property of a cross-section that measures its resistance to bending. It depends on the shape and distribution of area about an axis.
What is the difference between Ix and Iy?
Ix is the moment of inertia about the horizontal (x-x) axis, resisting bending about that axis. Iy is about the vertical (y-y) axis. For symmetric sections they may differ significantly.
What is section modulus?
Section modulus (Z = I/y_max) relates bending moment to maximum stress: σ = M/Z. Larger Z means a stronger section for the same material.
Why does centroid location matter?
The centroid is the geometric center. For unsymmetric sections like T-beams, the neutral axis is at the centroid, and the moment of inertia must be computed using the parallel axis theorem.