Moment of Inertia Calculator
Compare idealized inertia values for a solid cylinder and a solid sphere with the same mass and radius. The tool shows the method and key assumptions so you can inspect how the input values lead to the estimate.
How to use this calculator
- Enter mass (kg) using the unit and definition shown beside the input.
- Enter radius (m) using the unit and definition shown beside the input.
- Check that all values refer to the same time period and scenario.
- Review the outputs alongside the assumptions before using them in a decision.
Formula and assumptions
Solid cylinder about its central longitudinal axis: I=½mr²; solid sphere about a diameter: I=⅖mr².
- These formulas apply to uniform solid shapes about the stated axes. Hollow shapes, composite assemblies and different axes require different formulas.
- The estimate is calculated from values you enter. It does not connect to external accounts, obtain live prices, or validate local regulations or engineering specifications.
Worked examples
Worked example
For mass 8 kg and radius 0.25 m, I-cylinder=0.25 kg·m² and I-sphere=0.20 kg·m².
Enter mass and radius using SI units.
Choose the physical shape and axis that match the object when using the result.
Understanding the result
These formulas apply to uniform solid shapes about the stated axes. Hollow shapes, composite assemblies and different axes require different formulas.
Change one input at a time to see how sensitive the output is to that assumption.
Important notes
These formulas apply to uniform solid shapes about the stated axes. Hollow shapes, composite assemblies and different axes require different formulas.
Frequently asked questions
What formula does the Moment of Inertia Calculator use?
Solid cylinder about its central longitudinal axis: I=½mr²; solid sphere about a diameter: I=⅖mr².
What should I verify before relying on the result?
These formulas apply to uniform solid shapes about the stated axes. Hollow shapes, composite assemblies and different axes require different formulas.
Can I compare different scenarios?
Yes. Change one assumption at a time, keep units and definitions consistent, and save the inputs used for each comparison.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.