Physics and Engineering
Moment of Inertia Calculator
Moment of Inertia Calculator calculate mass moment of inertia for common ideal shapes about a named central, end, or symmetry axis.
Physics and Engineering
Moment of Inertia Calculator
Calculate mass moment of inertia for common ideal shapes about a named central, end, or symmetry axis.
Formula
Shape equations include mr^2, 1/2 mr^2, 1/12 mL^2, 1/3 mL^2, 2/5 mr^2, 2/3 mr^2, and 1/12 m(a^2+b^2).
About the Moment of Inertia Calculator
Calculate mass moment of inertia for common ideal shapes about a named central, end, or symmetry axis.
How the Moment of Inertia Calculator Works
The selected ideal-shape equation uses only its relevant dimensions and reports the coefficient multiplying mass and squared length alongside the SI result.
Formula
Shape equations include mr^2, 1/2 mr^2, 1/12 mL^2, 1/3 mL^2, 2/5 mr^2, 2/3 mr^2, and 1/12 m(a^2+b^2).
The calculation runs in your browser. Values are validated for required ranges, compatible units, and method-specific restrictions before results are displayed.
Required Inputs
- Ideal shape and axis (required).
- Mass (required) - enter in kg.
- Radius (optional) - enter in m.
- Length (optional) - enter in m.
- Rectangle width (optional) - enter in m.
Results Reported
The result panel reports the final answer and the intermediate quantities needed to check the calculation:
- Mass moment of inertia (kg m2)
- Equation used
- Dimension-squared coefficient
- Radius of gyration (m)
Moment of Inertia Calculator Example
Select Example Data in the calculator to load this reproducible input set:
| Input | Example value |
|---|---|
| Ideal shape and axis | solid_disk |
| Mass | 10 kg |
| Radius | 0.5 m |
| Length | 2 m |
| Rectangle width | 1 m |
How to Use the Calculator
- Confirm that the calculator title and formula match the quantity you need.
- Enter every required value using the unit shown with its field.
- Select Example Data to inspect a valid input set, or enter your own values and select Calculate.
- Review all reported values and the displayed formula before using the answer.
- Use Copy Result or Download CSV when you need a reusable record.
Accuracy and Limitations
The axis must match the menu description and dimensions must be meters. Compound bodies, holes, offset axes, density variation, and products of inertia require component analysis.
Keep units consistent, use measurements that represent the actual situation, retain full precision during the calculation, and round only the final answer. Professional decisions may require current official rules, field measurements, laboratory methods, or specialist review.
Frequently Asked Questions
What does the Moment of Inertia Calculator calculate?
Calculate mass moment of inertia for common ideal shapes about a named central, end, or symmetry axis.
Which formula does the Moment of Inertia Calculator use?
Shape equations include mr^2, 1/2 mr^2, 1/12 mL^2, 1/3 mL^2, 2/5 mr^2, 2/3 mr^2, and 1/12 m(a^2+b^2). The selected ideal-shape equation uses only its relevant dimensions and reports the coefficient multiplying mass and squared length alongside the SI result.
What should I check before using the Moment of Inertia Calculator result?
The axis must match the menu description and dimensions must be meters. Compound bodies, holes, offset axes, density variation, and products of inertia require component analysis.