Practical tools for measured work
Rotational moment of inertia calculator
Calculate mass inertia for defined shapes and axes, including valid parallel-axis offsets.
Calculate the layout, check the diagram, then print the result for the shop or jobsite.
How it works
Central-axis mass inertia: ring mr², disk mr²/2, solid sphere 2mr²/5, thin spherical shell 2mr²/3, thin rod mL²/12, rectangular plate m(L²+W²)/12. A rod about its end uses mL²/3. For supported central-axis shapes, a parallel offset d adds md².
Current-input example
The result above uses these exact values. This snapshot is included when the page is printed so the output can be checked against the original measurements.
- Shape and rotation axis
- Solid disk about central normal
- Mass
- 2 kg
- Radius
- 3 m
- Parallel axis offset from centre
- 0 m
Primary result: Mass moment of inertia: 9 kg·m².
Before using the result
- Check the selected mode, units and input values before using the result.
- Read the assumptions and rounding rules; compare the worked example with your intended calculation.
- A numerical result does not supply missing context or change the stated limitations.
Limitations
This is rotational mass inertia in kg·m², not structural second moment of area in length⁴. Shapes have uniform mass distribution and the specified axis. Point-mass radius and rod-end modes already define their axis and do not accept an extra offset.
Frequently asked questions
Which physical model does this result assume?
Use only the configuration named in the selected mode. Enter consistent SI units and check the stated direction, axis and equilibrium assumptions. These educational ideal models do not certify equipment, structures or lifting arrangements.
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