What is the moment of inertia?

The moment of inertia (I) is a measure of an object's resistance to angular acceleration about a given axis. It depends on both the mass of the object and how that mass is distributed relative to the rotation axis. The SI unit is kilogram-meter squared (kg·m²). It is the rotational analog of mass in linear motion.

What is the formula for a solid cylinder?

For a solid cylinder rotating about its central axis: I = ½ × m × R². For a solid cylinder rotating about an axis through its center perpendicular to the length: I = m × (3R² + L²) / 12, where R is the radius and L is the length.

How does a hollow cylinder differ from a solid cylinder?

A hollow cylinder (tube) has mass concentrated farther from the axis, so its moment of inertia is larger. For a thin-walled hollow cylinder: I = m × R². For a thick-walled tube: I = ½ × m × (R_outer² + R_inner²). This is why hollow shafts have a higher inertia-to-weight ratio for the same outer diameter.

Which axis does the thin rod formula use?

This calculator uses the axis through the center of the rod, perpendicular to its length: I = (1/12) × m × L². If you need the end-axis formula (I = (1/3) × m × L²), multiply this result by 4.

What units does this calculator support?

Mass: kilograms (kg), grams (g), pounds (lb), and slugs. Dimensions: meters (m), centimeters (cm), millimeters (mm), and inches (in). Output is shown in kg·m², g·cm², lb·in², and lb·ft².

Moment of Inertia Calculator

Name: Moment of Inertia Calculator
Availability: InStock
Author: Nham Vu

Select a shape, enter mass and dimensions, and get the moment of inertia in kg·m² instantly.

Moment of Inertia

Shape

Mass

Radius (R)

I = ½ × m × R²

Select a shape and enter values on the left.

I = moment of inertia (kg·m²)

Copied!

Summary

Select a shape, enter mass and dimensions, and get the moment of inertia in kg·m² instantly.

How it works

Select the shape of the object from the dropdown (e.g. solid cylinder, sphere).
Enter the mass of the object and select its unit.
Enter the required dimension(s) — radius and/or length — and select units.
The moment of inertia is calculated instantly and shown in kg·m².
Use the unit conversion cards to view the result in other units.
Click "Copy Value" or any conversion card to copy the result to your clipboard.

Use cases

Solve rotational dynamics homework and exam problems.
Calculate the angular inertia of a flywheel or rotating machine part.
Design motors and actuators where rotational inertia matters.
Verify textbook moment of inertia values for standard geometric shapes.
Estimate torque requirements for accelerating rotating systems.
Analyze the rotational behavior of rolling objects on inclines.
Compute inertia for gyroscopes and spinning tops.
Support engineering calculations for robotic arm joints.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu