Momentof Inertia Calculator
Free Momentof inertia Calculator for structural engineering projects. Enter dimensions to get material lists and cost estimates.
Reviewed for accuracy by Abdullah, Technical Content Specialist
Momentof Inertia Calculator
Calculator
Adjust values & calculateEnter your values below. Every result is computed in your browser — no data is sent to any server.
Formula: Rectangle: Ix = bh^3/12 | Circle: I = pi*r^4/4 | Section Modulus: S = I/c
Additional inputs: Outer Width (mm), Outer Height (mm), Wall Thickness (mm).
Worked example — Ix = 1,066,666,667 mm4, Sx = 5,333,333 mm3
Formula
Rectangle: Ix = bh^3/12 | Circle: I = pi*r^4/4 | Section Modulus: S = I/c
The moment of inertia for a rectangle is width times height cubed divided by 12. For a circle it is pi times the radius to the fourth power divided by 4. The section modulus equals the moment of inertia divided by the distance from the neutral axis to the extreme fiber.
Worked Examples
Example 1: Rectangular Beam Section
Problem:Find the moment of inertia for a 200 mm wide by 400 mm deep rectangular beam.
Solution:Ix = b*h^3 / 12 = 200 * 400^3 / 12 = 1,066,666,667 mm4 Iy = h*b^3 / 12 = 400 * 200^3 / 12 = 266,666,667 mm4 Sx = Ix / (h/2) = 1,066,666,667 / 200 = 5,333,333 mm3
Result:Ix = 1,066,666,667 mm4, Sx = 5,333,333 mm3
Example 2: Circular Column Section
Problem:Find the moment of inertia for a circular column with a 300 mm diameter.
Solution:I = pi * r^4 / 4 = pi * 150^4 / 4 = 397,607,813 mm4 S = I / r = 397,607,813 / 150 = 2,650,719 mm3
Result:I = 397,607,813 mm4, S = 2,650,719 mm3
Frequently Asked Questions
What is moment of inertia in structural engineering?
Moment of inertia, also called the second moment of area, is a geometric property of a cross-section that quantifies its resistance to bending. A higher moment of inertia means the section is stiffer and deflects less under load. It is measured in units of length to the fourth power, such as mm4 or in4, and is a fundamental input for beam deflection and stress calculations.
Why are I-beams so efficient for structural use?
I-beams concentrate material in the flanges, which are located far from the neutral axis. Since moment of inertia increases with the square of the distance from the centroid, this arrangement maximizes Ix while minimizing total weight. A rectangular section would need far more material to achieve the same bending stiffness as a properly proportioned I-beam.
What is the section modulus and how does it relate to moment of inertia?
The section modulus S equals the moment of inertia I divided by the distance from the neutral axis to the outermost fiber (c). It directly relates bending moment to maximum bending stress through the formula sigma = M / S. A larger section modulus means lower stress for a given bending moment, making the member more capable of carrying load without yielding.
References
Reviewed for accuracy by Abdullah, Technical Content Specialist · Editorial policy
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