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Mass Moment of Inertia for Common Shapes — result sheet
Calculate the mass moment of inertia about a stated idealized axis for a point mass, rod, hoop, disk, sphere, or cylinder.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: I = MR² (point/hoop), ½MR² (disk/cylinder), ML²/12 (rod center), ML²/3 (rod end), or 2MR²/5 (solid sphere); Kᵣ = ½Iω².
Mass moment of inertia measures how strongly an idealized mass distribution resists angular acceleration about a selected axis. The same mass can have different inertia when its shape or axis changes, so the axis is part of the calculator's contract.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Idealized shape and axis — 7 choices
- Mass — kg; minimum 1.0E-6; maximum 1000000000
- Radius — m; minimum 1.0E-6; maximum 1000000
- Rod or cylinder length — m; minimum 1.0E-6; maximum 1000000
- Angular speed — rad/s; minimum 0; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Idealized shape and axis | solid-disk |
| Mass | 2 |
| Radius | 0.3 |
| Rod or cylinder length | 1 |
| Angular speed | 10 |
I = 0.09 kg·m² and Kᵣ = 4.5 J
Assumptions and limits
- Each selected body is uniform, rigid, and aligned with the named idealized axis.
- The radius and length are geometric inputs in meters and the mass is in kilograms.
- The rotational-energy output is a classical estimate and does not include friction, deformation, or translational motion.
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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