Sidereal Day Calculator
A sidereal day is one rotation of a planet relative to the distant stars, which is slightly shorter than the solar day because the planet also advances along its orbit each day. This calculator takes the body's mean solar day and its orbital period in the same time unit, then returns the sidereal day length, the difference from the solar day and the extra rotation angle the planet must turn each solar day to bring the Sun back overhead. The relation is exact for prograde rotation: just the reciprocal sum of solar day and orbital period.
Sidereal day formula
1 / sidereal day = 1 / solar day + 1 / orbital period
sidereal day = solar day * orbital period / (solar day + orbital period)
extra rotation per solar day (deg) = 360 * solar day / orbital period
Each solar day the planet advances along its orbit, so it must rotate a bit more than 360 degrees to face the Sun again. Adding the orbital rate to the rotation rate gives the sidereal rotation rate, whose reciprocal is the sidereal day. The extra rotation angle is the fraction of an orbit completed in one solar day, times 360 degrees.
Sidereal day context
- For a prograde rotator the sidereal day is shorter than the solar day.
- Earth's sidereal day is about 23 hours 56 minutes against its 24-hour mean solar day.
- The difference equals the time to turn the extra orbital angle each day.
- Enter both the solar day and orbital period in the same time unit.
- This tool assumes prograde rotation; retrograde rotators reverse the sign.
Sidereal day: frequently asked questions
What is the difference between a solar day and a sidereal day?
A solar day is the time for the Sun to return to the same position in the sky; a sidereal day is the time for the planet to rotate once relative to the distant stars. They differ because the planet also moves along its orbit each day, so it must rotate a little extra to bring the Sun back overhead.
How is the sidereal day calculated?
For a prograde rotator, the reciprocal of the sidereal day equals the reciprocal of the solar day plus the reciprocal of the orbital period. Rearranged, the sidereal day equals the solar day times the orbital period divided by the sum of the two. This calculator applies that exact relation.
Why is the sidereal day shorter than the solar day on Earth?
Because Earth orbits prograde (the same direction it spins), it must turn slightly more than 360 degrees each solar day to face the Sun again. So one full rotation against the stars, the sidereal day, takes a bit less time: about 23 hours 56 minutes against the 24-hour mean solar day.
What inputs do I enter?
Enter the mean solar day length and the orbital period in the same time unit, such as hours or days. The calculator returns the sidereal day in that unit and the extra rotation angle per solar day in degrees. Both inputs describe the specific body you are studying.
Does this work for any planet?
Yes, for a prograde rotator. Enter that body's mean solar day and its orbital period and the formula gives its sidereal day. Retrograde rotators (where the spin opposes the orbit) follow a sign-reversed version; this tool assumes prograde rotation.
Official sources
- NASA: NSSDCA Earth Fact Sheet (rotation periods).
- U.S. Naval Observatory: Sidereal Time Explanation.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.