Star trail and 500 rule calculator
The Earth turns 15 arcseconds a second, so a long exposure smears stars into arcs. How long you can go depends on focal length and pixel size.
micrometres
degrees
Maximum exposure, NPF rule
13.75s
- By the 500 rule
- 25.00 s
- By the stricter 300 rule
- 15.00 s
- Equivalent focal length
- 20.0
- Declination factor Stars near the celestial pole move slowly and tolerate longer exposures.
- 1.0000
- Sky rotation
- 15.0 arcminutes per minute
Show the working
- Focal length = 20
- Crop factor = 1
- Pixel pitch = 5.9
- Aperture = 2.8
- Declination of the target = 0
- Equivalent focal length = 20 * 1 = 20
- By the 500 rule = 20 > 0 ? 500 / 20 : 0 = 25
- By the stricter 300 rule = 20 > 0 ? 300 / 20 : 0 = 15
- Declination factor = cos(rad(0)) = 1
- Maximum exposure, NPF rule = 20 > 0 && 1 > 0 ? (35 * 2.8 + 30 * 5.9) / (20 * 1) : 0 = 13.75
- trail_length = 20 * 15 * 1 = 300
- Sky rotation = 0.25 * 60 = 15
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- 500 rule: seconds = 500 / equivalent focal length
- NPF: seconds = (35 N + 30 p) / (f cos(declination)), with p the pixel pitch in micrometres
The 500 rule dates from film and is far too generous for a modern high-resolution sensor viewed at 100%.
The sky turns 360 degrees in a sidereal day, which is 15.041 arcseconds per second at the celestial equator.