Moment Of Inertia Calculator

moment of inertia formulas and interpretation

Moment of inertia measures resistance to angular acceleration about a chosen axis.

It depends on total mass and how that mass is distributed relative to the axis.

How to use the moment of inertia calculator

Choose a model: Select the physical relationship that matches the known values.
Choose the unknown: Select the quantity you need to calculate.
Enter values and units: Provide every requested measurement using consistent units.
Calculate: Check the formula, converted result, sign, and units.

Formula and variables

Moment of inertia is the mass-weighted squared distance from the rotation axis; standard shapes have closed-form equations.

I = ∫r² dm

I — Moment of inertia: Rotational inertia (kg·m²)
m — Mass: Object mass (kg)
r — Radius: Distance from axis (m)

Solid disk example

A solid disk has mass 8 kg and radius 0.5 m.

Mass: 8 kg
Radius: 0.5 m

I = ½ × 8 × 0.5²
I = 1 kg·m²

Result: Moment of inertia is 1 kg·m².

The disk has 1 kg·m² of rotational inertia about its central axis.

Understanding your results

Interpreting the result

Moving mass farther from the axis increases inertia with the square of distance.

A sign indicates direction only when a consistent rotational sign convention is used.

Assumptions

Rotation is evaluated about a specified axis.
Inputs are converted through coherent SI units.
The selected formula adequately represents the physical system.

Limitations

The calculator does not simulate time-varying inputs.
Vector directions and multiple axes must be resolved separately.
Losses such as friction are not added unless represented in the entered net value.

Common mistakes

Mixing RPM with radians per second.
Using diameter instead of radius.
Entering a zero divisor.
Ignoring the direction represented by a negative value.

Practical use cases

Physics and education

Check rotational kinematics and dynamics exercises.

Machines and mechanisms

Estimate quantities for wheels, shafts, rotors, and rotating equipment.

Frequently asked questions

Why are radians used in rotational formulas?

Radians make angular and linear relationships dimensionally coherent without an extra conversion factor.

Can the result be negative?

Yes. A negative value means the quantity points opposite the direction chosen as positive.

Sources and review

SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
Special Publication 811 — NIST. Accessed 2026-07-11.

Reviewed 2026-07-11.

Moment Of Inertia Calculator