Orbital Period Calculator (Kepler Third Law)
Fill in the values and the answer updates as you type.
How the Orbital Period Calculator (Kepler Third Law) works
Kepler third law for a small body orbiting a star: period² = semi-major axis³ ÷ star mass, with the period in years, the axis in astronomical units (AU), and the mass in solar masses. Average speed = orbit circumference ÷ period, treating the orbit as a circle. An orbit at 5.2 AU matches Jupiter. Example: with Semi-major axis of the orbit 5.2 AU and Mass of the central star 1 solar masses, the result is Orbital period (years) = 11.86; Orbital period (days) = 4,331.07; Average orbital speed (km/s) = 13.06.
Inputs and results
The Orbital Period Calculator (Kepler Third Law) takes 2 inputs and gives 3 results.
What you enter
- Semi-major axis of the orbit (AU) — starts at 5.2.
- Mass of the central star (solar masses) — starts at 1.
What you get
- Orbital period (years)
- Orbital period (days)
- Average orbital speed (km/s)
Example: Orbital Period Calculator (Kepler Third Law) with the starting values
With semi-major axis of the orbit 5.2 AU and mass of the central star 1 solar masses, the calculator returns:
| Orbital period (years) | 11.86 |
|---|---|
| Orbital period (days) | 4,331.07 |
| Average orbital speed (km/s) | 13.06 |
Change any value above and the results update straight away.
Orbital Period Calculator (Kepler Third Law) FAQ
How do I use the Orbital Period Calculator (Kepler Third Law)?
Enter semi-major axis of the orbit and mass of the central star in the fields, then read orbital period (years), orbital period (days) and average orbital speed (km/s) in the result panel. The answer updates as you type, and you can press Calculate or Enter to refresh it. Use “Copy link” to share your exact numbers with someone else.
What does the Orbital Period Calculator (Kepler Third Law) calculate?
How long a planet takes to orbit a star from its orbit size. It returns orbital period (years), orbital period (days) and average orbital speed (km/s) from the 2 values you provide.
What values does the Orbital Period Calculator (Kepler Third Law) start with?
It opens with semi-major axis of the orbit 5.2 AU and mass of the central star 1 solar masses so you can see a working result straight away. Replace them with your own numbers, or press Reset to return to these starting values.
Is the Orbital Period Calculator (Kepler Third Law) free and private?
Yes. It is free, needs no account, and runs in your browser, so nothing you type is sent to or stored on our servers. See the Privacy Policy for details.
Can I rely on the Orbital Period Calculator (Kepler Third Law) for important decisions?
Treat the result as a well-rounded estimate. Real situations often have details a general calculator cannot know, so confirm important decisions with a qualified professional. See the Disclaimer for more.