Moment Of Inertia Calculator
Calculate the moment of inertia for common shapes (rectangle, circle, triangle) about their centroidal axes. Useful for physics and engineering applications.
Published by:
isCalculator Editorial Team
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How to use this tool?
This calculator computes the area moment of inertia (I) for common cross-sectional shapes. Use it for beam bending or structural analysis.
Step-by-Step Instructions
- Select a shape from the dropdown: Rectangle, Circle, or Triangle.
- Enter dimensions in consistent units (e.g., all in inches or all in mm):
- Rectangle: Base (width) and Height.
- Circle: Radius only (Height field is hidden).
- Triangle: Base and Height.
- Click "Calculate Moment of Inertia".
- View the result (in units4) and the formula with step-by-step calculation.
Important Notes
- All inputs must be positive numbers. The calculator validates this automatically.
- Use any unit system (metric or imperial) as long as you are consistent — the output will be in the same units raised to the fourth power.
- The result is the centroidal moment of inertia (about the horizontal axis through the centroid).
Previous Results
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Frequently Asked Questions
Moment of inertia is a measure of an object's resistance to rotational acceleration about an axis. It depends on the mass distribution relative to the axis.
This calculator supports rectangles, circles, and triangles, calculating the moment of inertia about their centroidal axes.
You can use any consistent units (e.g., meters, inches). The result will be in units^4 (e.g., m^4, in^4).