When to use this calculator
Kepler’s third law links orbital size to period. The same simple AU-year form cannot be applied unchanged around stars of different mass.
Explore the orbits & escape calculators for other questions in this topic. For a related calculation, use the Orbit Semi Major Axis Calculator: Find an ellipse’s semi-major axis from periapsis and apoapsis distances.
PUTTING IT INTO PRACTICE
Kepler Orbital Period: 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 |
|---|---|
| Semi-major axis (AU) | 4 |
| Result | 8 years |
- Check the input labels and enter the example values above.
- Apply the relationship: Period in years ≈ √(semi-major axis in AU³).
- The result is 8 years, rounded for display.
How to interpret your result
Assumes a central mass of one solar mass and negligible orbiting mass; uses the astronomical-unit/year approximation.
Use radius from the centre of the attracting body, not altitude above its surface. Choose the gravitational parameter of the correct primary. Drag, rotation and other bodies are excluded from these simple models.
Frequently asked questions
Can I use altitude directly as orbital radius?
No. Add the central body’s radius to altitude when a formula requires distance from its centre.
When is the kepler orbital period calculator useful?
Kepler’s third law links orbital size to period. The same simple AU-year form cannot be applied unchanged around stars of different mass.
How do I use the kepler orbital period calculator?
Enter semi-major axis (au). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Period in years ≈ √(semi-major axis in AU³).
What should I check before using the result?
Assumes a central mass of one solar mass and negligible orbiting mass; uses the astronomical-unit/year approximation.
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 NASA: orbits and Kepler’s laws ↗. This is a topic reference, not an external review or endorsement of this tool.
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