When to use this calculator
Translate moment of inertia to a parallel offset axis. The two axes must be parallel and the reference inertia must pass through the centre of mass.
Explore the force, energy & machines calculators for other questions in this topic. For a related calculation, use the Potential Energy Calculator: Estimate gravitational potential energy relative to a reference height.
PUTTING IT INTO PRACTICE
Parallel Axis Theorem: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Centre-of-mass inertia (kg·m²) | 10 |
| Mass (kg) | 5 |
| Parallel-axis offset (m) | 2 |
| Result | 30 kg·m² |
- Check the input labels and enter the example values above.
- Apply the relationship: Offset-axis inertia = centre-of-mass inertia + mass × offset².
- The result is 30 kg·m², rounded for display.
How to interpret your result
The two axes must be parallel and the reference inertia must pass through the centre of mass.
Distinguish net force from individual forces and specify the direction of displacement. Work can be negative. Force multiplication does not create extra energy because motion distance and losses also matter.
Frequently asked questions
Is mechanical advantage the same as efficiency?
No. Mechanical advantage compares forces; efficiency compares useful output energy or power with the corresponding input.
When is the parallel axis theorem calculator useful?
Translate moment of inertia to a parallel offset axis. The two axes must be parallel and the reference inertia must pass through the centre of mass.
How do I use the parallel axis theorem calculator?
Enter centre-of-mass inertia (kg·m²), mass (kg), parallel-axis offset (m). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Offset-axis inertia = centre-of-mass inertia + mass × offset².
What should I check before using the result?
The two axes must be parallel and the reference inertia must pass through the centre of mass.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see OpenStax: work and energy ↗. This is a topic reference, not an external review or endorsement of this tool.
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