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Moment Of Inertia Calculator

Enter your values below to get the result first, then scroll for the full explanation and guidance.

Step 1 • Add values

Use the calculator

Enter your values below to generate an instant result. You can update the inputs at any time to compare different scenarios.

Example: a uniform 10 kg disk of radius 0.5 m has mass moment of inertia 1.25 kg m squared about its central perpendicular axis.

Results refresh instantly as values change.

Mass moment of inertia

1.25 kg m²Uniform solid disk, central perpendicular axis

Mass moment of inertia: 1.25 kg m² (Uniform solid disk, central perpendicular axis)

For a uniformly distributed solid disk rotating around the perpendicular axis through its centre, I = (1/2) m r².

Disk and axis

For a uniformly distributed solid disk rotating around the perpendicular axis through its centre, I = (1/2) m r².

Result snapshot

A quick visual read of the values behind this result.

Mass10 kg
Radius0.5 m

Recommended next checks

  • →Check that the object is a uniform solid disk and the rotation axis passes through its centre.
  • →Use a different formula for a ring, rod, sphere or displaced axis.
Mass
10 kg
Radius
0.5 m

Try different values to compare results.

Enter the mass and radius of a uniform solid disk to calculate its rotational mass moment of inertia about the perpendicular axis through its centre.

Fast to use

Built for comparison

Clear result output

Table of Contents

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About Moment Of Inertia Calculator

Moment Of Inertia Calculator helps you work through the main numbers for this topic quickly with a simple input flow and an instant result.

Use the calculator result as a practical starting point, then review the explanation and assumptions on the page if you want more context.

Uniform disk about its centre

For this specific shape and axis, I = (1/2) m r squared. A 10 kg disk of radius 0.5 m has I = 0.5 x 10 x 0.5 squared = 1.25 kg m squared. Changing the axis or mass distribution requires a different expression.

Formula explained

Calculation flow

This calculator is structured for fast UK-focused estimates with clear inputs, repeatable logic, and instant results.

Formula

Input values -> calculation engine -> instant result

How the result is built

1Enter the values requested in the form.
2The calculator applies the configured formula logic.
3The result updates instantly with a breakdown.
4Use the output to compare scenarios quickly.

Example

Example: a uniform 10 kg disk of radius 0.5 m has mass moment of inertia 1.25 kg m squared about its central perpendicular axis.

Assumptions

  • Uniform solid disk with mass in kilograms and radius in metres.
  • Axis is perpendicular to the disk through its centre; not a second moment of area or a different body/axis.
  • Nonzero mass and radius required.

Source basis

  • UK-focused calculator flow
  • Structured input validation
  • Instant result breakdowns

FAQ

Common questions

No. The expression applies only to a uniform solid disk around its central perpendicular axis.

Trust and notes

Assumptions and important notes

This calculator is designed to give a fast estimate using the method shown on the page. Results are most useful when your inputs are accurate and the tool matches your situation.

Use the result as guidance rather than a final diagnosis or professional decision. If the result could affect health, legal, financial, or compliance decisions, verify it with a qualified source where appropriate.

  • Uniform solid disk with mass in kilograms and radius in metres.
  • Axis is perpendicular to the disk through its centre; not a second moment of area or a different body/axis.
  • Nonzero mass and radius required.

Method

UK calculator guidance

Last reviewed

April 17, 2026