Star Trail Calculator
Star trail photographs record the apparent motion of stars as the Earth turns. The length of each arc depends only on how long the shutter stays open, because the sky rotates at a fixed rate of one full turn per sidereal day. This calculator converts an exposure time into the arc angle traced around the celestial pole, and works the reverse problem too: how long an exposure you need for a target arc. Enter your exposure in minutes to see the degrees of arc, the fraction of a full circle, and the underlying rotation rate.
Star trail formula
Sidereal day = 86,164.0905 seconds
Exposure seconds = exposure minutes * 60
Arc degrees = exposure seconds / sidereal day * 360
Fraction = arc degrees / 360 * 100
Rotation rate = 360 / sidereal day * 3600 (degrees per hour)
Time for target = target arc / 360 * sidereal day / 60 (minutes)
The sidereal day is a measured astronomical constant published by the U.S. Naval Observatory. Every other step is exact geometry, so the arc angle follows directly from the exposure time.
Star trail photography notes
- The sky rotates about 15.041 degrees per hour, one full turn per sidereal day.
- The arc angle is identical for every star; only the on-image length changes with declination.
- Stars near the celestial pole, such as Polaris in the north, trace short tight arcs.
- Stars on the celestial equator sweep the longest streaks across the frame.
- Long total trails are usually built by stacking many shorter exposures rather than one long one.
Star trails: frequently asked questions
How long is a star trail for a given exposure?
Stars appear to circle the celestial pole once per sidereal day, which is 23.9344696 hours, equivalent to 86,164.0905 seconds. The arc angle is the exposure time divided by the sidereal day, multiplied by 360 degrees. So a 60-minute exposure traces about 15.04 degrees of arc.
Why use the sidereal day, not 24 hours?
The 24-hour solar day is measured relative to the Sun. Stars track relative to the fixed celestial sphere, which the Earth completes in one sidereal day of about 23 hours 56 minutes. Using the sidereal day gives the true rate of apparent star motion: about 15.041 degrees per hour.
Does declination affect the arc angle?
The angular arc swept in this calculator (degrees around the celestial pole) is the same for all stars regardless of declination. However, the physical length of the trail on your image depends on declination: stars near the pole trace short arcs, while stars on the celestial equator trace the longest streaks.
How do I get a full circle trail?
A complete 360-degree circle requires one full sidereal day of exposure, about 23 hours 56 minutes, which is only achievable near the poles in continuous darkness. In practice photographers stack many shorter frames to build long trails without a single ultra-long exposure.
What is the rotation rate in degrees per minute?
360 degrees divided by 86,164.0905 seconds is about 0.004178 degrees per second, or roughly 0.2507 degrees per minute, or about 15.041 degrees per hour. This calculator applies that exact rate to any exposure time you enter.
Official sources
- U.S. Naval Observatory: Sidereal Time and the sidereal day.
- NASA: How long is a day on Earth (solar vs sidereal).
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.