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Moment of Inertia Shape Calculator — result sheet
Calculate mass moment of inertia for common uniform rods, disks, hoops, and rectangular plates about a stated central or end axis.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Rod center ML²/12; rod end ML²/3; disk MR²/2; hoop MR²; rectangular plate M(a²+b²)/12.
The shape selector makes the axis convention explicit because the same mass and length can have different rotational inertia about different axes.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Shape and axis — 5 choices
- Mass — minimum 1.0E-6; maximum 1000000000
- Length or radius — minimum 1.0E-6; maximum 1000000
- Second rectangle side — minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Shape and axis | disk |
| Mass | 10 |
| Length or radius | 0.5 |
| Second rectangle side | 0.3 |
For the solid disk, moment of inertia = 1.25 mass·length².
Assumptions and limits
- The body is uniform and the selected textbook axis matches the selected shape.
- Mass and dimensions use compatible units, so inertia has mass·length² units.
- This is a rigid-body model and does not certify a mechanical design or rotating assembly.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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