Star Trail Exposure Calculator
During any exposure the sky keeps turning, so each star draws a short arc on the sensor. This calculator works out exactly how far, in pixels, a star moves during your exposure from first principles: the sky turns 360 degrees in one sidereal day of 86,164 seconds, the motion scales with the cosine of the star's declination, and the resulting angle projects onto the sensor through your focal length and pixel pitch. Use it to confirm an untracked exposure is short enough for pinpoint stars, or long enough for a deliberate trail.
Star trail formula
Sidereal day = 86,164 seconds for 360 degrees
Angle (radians) = (2*pi / 86164) * exposure * cos(declination)
Smear on sensor (mm) = angle * focal length(mm)
Trail length (pixels) = smear(mm) / pixel pitch(mm)
Sky rotation (degrees) = 360 * exposure / 86164
The cosine of declination accounts for stars near the pole moving slower. Pixel pitch in microns is divided by 1,000 to convert to millimetres.
Star motion context
- The sky moves about 15 arcseconds per second of time at the celestial equator.
- Stars near the pole move slower, scaled by the cosine of declination.
- Keep the trail at or below about 1.5 pixels for pinpoint stars.
- Longer focal lengths magnify the motion and trail sooner.
- A star tracker cancels this motion for long untrailed exposures.
Star trail: frequently asked questions
How fast do stars appear to move across the sky?
The sky completes one full turn in a sidereal day of 86,164 seconds, which is 360 degrees, or about 15.04 arcseconds per second of time at the celestial equator. Stars nearer the celestial pole move more slowly, scaled by the cosine of their declination.
How is the pixel smear during an exposure calculated?
The angular motion of a star in radians is (2 pi divided by 86,164) times the exposure seconds, times the cosine of the declination. Multiply that angle by the focal length in millimetres to get the smear on the sensor in millimetres, then divide by the pixel pitch in millimetres to get pixels.
Why does declination matter for star trails?
Stars near the celestial equator trace the largest circles and move fastest across the frame. Stars near the pole barely move; the pole star is almost stationary. The motion scales with the cosine of declination, so a star at 60 degrees declination moves at half the equatorial rate.
How many pixels of trail is acceptable?
For pinpoint stars, keep the smear at or below about 1 to 1.5 pixels. Two or three pixels gives slight visible elongation. For deliberate star trail photos you want the smear to be large, so a long exposure or many stacked frames is the goal instead.
Does this assume an untracked camera?
Yes. The calculator assumes a fixed tripod with no star tracker, so the full sky rotation appears as motion on the sensor. A star tracker cancels this motion, allowing much longer exposures with no trailing, which is why trackers are used for deep-sky work.
Official sources
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.