Momentof Inertia Calculator
Free Momentof inertia Calculator for structural engineering projects. Enter dimensions to get material lists and cost estimates.
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\nIy = h*b^3 / 12 = 400 * 200^3 / 12 = 266,666,667 mm4\nSx = 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\nS = 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.
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.
How accurate are the results from Momentof Inertia Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.
Can I use Momentof Inertia Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.
Does Momentof Inertia Calculator work offline?
Once the page is loaded, the calculation logic runs entirely in your browser. If you have already opened the page, most calculators will continue to work even if your internet connection is lost, since no server requests are needed for computation.