500 rule and NPF rule calculator for untracked star photos
On a tripod, stars drift across the sensor. The 500 rule divides 500 by the focal length (times the crop factor); the NPF rule by Frédéric Michaud also uses the f-number, the pixel pitch and the declination, and on modern high-resolution sensors gives much shorter limits. The calculator shows both and the resulting trail length in pixels.
Two rules for the same question
On a fixed tripod the Earth’s rotation carries the stars across the frame. The sky turns once per sidereal day of 86,164 s (IERS), which is 15.041″ per second at the celestial equator. The question is how long the shutter can stay open before that drift shows.
The 500 rule divides a constant by the focal length, adjusted for crop factor:
t (s) = 500 ÷ (focal length × crop factor)
It is a film-era rule of thumb, and we found no original publication. In his derivation article, Michaud traces it to Dick Hutchinson, who used a 600 ÷ focal length rule for aurora photography in the 1990s, and cites a 1997 photographic sky atlas that recommends 500 for stars above 50° declination (we have not seen the atlas). Michaud himself proposes a stricter “4 − crop” variant, which works out to about 300 for full frame and 375–400 for APS-C and Micro Four Thirds; the calculator offers 400 and 300 as alternatives to 500.
The NPF rule was developed by Frédéric Michaud of the Société Astronomique du Havre (SAH), who publishes two forms:
simplified: t = (35 N + 30 p) ÷ f
complete: t = k × (16.9 N + 0.10 f + 13.7 p) ÷ (f × cos δ)
with N the f-number, p the pixel pitch in µm, f the focal length in mm, δ the lowest declination in the frame, and k a tolerance from 1 (perfectly point-like stars) to 3 (slightly elongated). Michaud’s derivation article builds the complete form from the size of a star image (diffraction, 3″ of seeing and the blur of colour demosaicing) and the speed of the star across the sensor, and explains that the simplified form corresponds to k = 2 on the celestial equator without turbulence. The author asks that any use of the rule credit him and the SAH; the formula on this page is his.
Worked examples
All at the celestial equator (δ = 0), with pixel pitch from the camera makers’ specifications (the Sony value is derived from sensor width ÷ pixels, because Sony does not publish it):
| Camera and lens | 500 rule | NPF simplified | NPF complete, k = 1 / 2 / 3 |
|---|---|---|---|
| Canon EOS R6 Mark II (6.00 µm), 24 mm f/2.8 | 20.8 s | 11.6 s | 5.5 / 11.0 / 16.5 s |
| Canon EOS R7 (3.2 µm, crop 1.62), 16 mm f/2.8 | 19.3 s | 12.1 s | 5.8 / 11.6 / 17.4 s |
| Sony Alpha 7 IV (5.12 µm derived), 20 mm f/1.8 | 24.9 s | 10.8 s | 5.1 / 10.3 / 15.4 s |
The trail column in the calculator turns each time into pixels: 15.041″/s × t × cos δ ÷ image scale. For the R6 Mark II example, the 500-rule exposure smears a star over about 6 pixels, and the simplified NPF exposure over about 3.4.
Declination
Stars away from the celestial equator move more slowly, in proportion to cos δ. The complete NPF rule divides by cos δ, so towards the Galactic Centre (Sgr A* is at declination −29.0° in SIMBAD) the R6 Mark II example grows from 11.0 s to 12.6 s with k = 2. Near the poles the allowed time grows without limit; the calculator caps the declination at 89° to keep the numbers finite. If your frame spans a range of declinations, use the one closest to the equator, because those stars trail first.
Choosing k
The k setting is a judgement about how round the stars must be. k = 1 is strict and suits images that will be viewed at full resolution or cropped; k = 2 matches the simplified rule; k = 3 accepts slightly oval stars. Michaud’s page notes the rule is meant for nightscape photography with camera lenses, not for telescopes or planetary imaging.
For the history of both rules and a fuller comparison, see the NPF vs 500 rule guide. Sensor data for common camera bodies is in the DSLR and mirrorless table.
Questions
- What is the NPF rule?
- A rule for the longest untracked exposure developed by Frédéric Michaud of the Société Astronomique du Havre. Its simplified form is t = (35 × N + 30 × p) ÷ f, with N the f-number, p the pixel pitch in µm and f the focal length in mm.
- Why is the NPF rule shorter than the 500 rule?
- The 500 rule comes from film photography and ignores pixel size. Modern sensors have pixels of a few micrometres, so a trail that was invisible on film covers several pixels. With a 24 mm f/2.8 lens on a full-frame camera with 6 µm pixels, the 500 rule allows 20.8 s, which trails about 6 pixels; the simplified NPF rule allows 11.6 s.
- Does declination matter?
- Yes. Stars near the celestial pole move more slowly across the sky than stars on the celestial equator, in proportion to the cosine of the declination. The complete NPF rule divides by cos δ; the 500 rule ignores it.
Sources
- La règle NPF Frédéric Michaud, Société Astronomique du Havre. Simplified and complete formulas; k from 1 (point-like) to 3 (slightly elongated); the author asks that implementations credit him and the SAH. Accessed October 12, 2026.
- Les coulisses de la règle NPF Frédéric Michaud, Société Astronomique du Havre. Derivation; the simplified form corresponds to k = 2, δ = 0 and no turbulence; history of the 500 rule. Accessed October 12, 2026.
- Shooting the Aurora Borealis Dick Hutchinson (eaglestation.com). Film-era 600 ÷ focal length rule; no original publication of the 500 rule was found. Accessed October 12, 2026.
- Sgr A* in SIMBAD CDS, Strasbourg. Accessed October 12, 2026.
- Useful constants: Earth's rotation IERS / Observatoire de Paris. Sidereal day 86164.09 s, so the sky turns 15.041″ per second. Accessed October 12, 2026.