Sidereal Day Calculator
A solar day is one rotation relative to the Sun, while a sidereal day is one rotation relative to the fixed stars. They differ because the body is also orbiting the Sun, so it must rotate a little more than a full turn to bring the Sun back overhead. The two are linked through the orbital period by a simple reciprocal relationship. This calculator finds the sidereal day from the solar day and orbital period, and shows the difference between them. Enter the solar day and orbital period in the same time unit; both are user-editable so it works for any prograde rotating body.
Sidereal day formula
Convert orbital period to hours: P = days * 24
1 / sidereal = 1 / solar + 1 / P (prograde)
sidereal = 1 / (1 / solar + 1 / P)
difference = solar - sidereal
The solar day is longer than the sidereal day for a prograde rotator. The body rotates once relative to the stars in a sidereal day, then a little extra to catch up with the Sun, which it has moved away from along its orbit.
Sidereal time notes
- The defaults model Earth: a 24-hour solar day and a 365.256-day sidereal year.
- Earth's sidereal day is about 23 hours 56 minutes 4 seconds.
- The formula here is for prograde rotation (rotation same direction as orbit).
- Use the same time unit for solar day and orbital period after conversion.
- Telescope tracking mounts are driven at the sidereal rate, not the solar rate.
Sidereal day: frequently asked questions
What is the difference between a solar day and a sidereal day?
A solar day is one rotation relative to the Sun: the time from noon to noon. A sidereal day is one rotation relative to the distant stars. Because a planet also orbits the Sun, it must rotate slightly more than once to bring the Sun back overhead, so the solar day is a little longer than the sidereal day.
How are the two day lengths related?
The relationship is 1 over sidereal day equals 1 over solar day plus 1 over orbital period, for a body that rotates in the same direction it orbits (prograde). This calculator solves for the sidereal day given the solar day and the orbital period.
Why is Earth's sidereal day about 4 minutes shorter?
Earth's solar day is 24 hours, but its sidereal day is about 23 hours 56 minutes 4 seconds, roughly 4 minutes shorter. In one day Earth moves about one degree around its orbit, so it must turn about one extra degree to face the Sun again, adding nearly 4 minutes to the solar day.
Does this work for other planets?
Yes. Enter the body's solar day length and its orbital period in the same time unit and the calculator returns the sidereal day. For retrograde rotators the simple prograde formula does not apply directly, so use it for prograde bodies like Earth and Mars.
Why do astronomers care about the sidereal day?
Telescopes track the stars, not the Sun, so they are driven at the sidereal rate. A star returns to the same position in the sky one sidereal day later, which is why star charts and equatorial mounts are built around sidereal time.
Official sources
- U.S. Naval Observatory: astronomical applications and time.
- NASA NSSDCA: planetary rotation and orbital periods.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.