500 Rule & NPF Calculator
Pick your sensor, megapixels, focal length, aperture and the declination of the sky you’re framing: get the longest exposure for pinpoint stars with the NPF rule, compare it with the 500 rule and see how many pixels the star would travel with each.
Your camera, lens and sky
The declination of the stars in your frame closest to the celestial equator. With a wide-angle lens the equator is almost always in shot: leave it at 0°.
NPF vs the 500 rule
| Rule | Exposure | On camera | Trail | Trailing (k) |
|---|---|---|---|---|
| Full NPF (k = 1) | ||||
| Simplified NPF | ||||
“On camera” is the next standard shutter speed down (in third stops), so you never go over. Trail: how far the star moves across the sensor during the exposure. Trailing (k): trail ÷ star radius in the NPF model; 1 = pinpoint, 2 = barely noticeable, 3 = noticeable.
How the 500 rule and the NPF rule are calculated
The 500 rule only looks at the equivalent focal length:
Frédéric Michaud’s NPF rule adds the aperture N, the pixel pitch p (in µm) and the declination δ. This is the full form, with the focal length f in mm:
It comes from a physical model: a star is not a point on the sensor but a spot whose diameter adds up atmospheric turbulence (3″ of seeing), lens diffraction (4.47·λ·N, with λ = 550 nm) and the sensor’s demosaicing (2 pixels). Meanwhile the Earth’s rotation (one turn every 86,164 s relative to the stars) shifts it by f·cos δ ÷ 13,713 mm per second. At k = 1 the star moves by its radius and stays round; at k = 2, by one diameter (barely noticeable); at k = 3, by three radii.
The simplified NPF rule, (35·N + 30·p) ÷ f, is the one most calculators use: it amounts to k = 2 with the star on the celestial equator and no turbulence. The calculator’s table shows all three side by side and, for each, how many pixels the star travels and which k that equals.
Worked example: the 500 rule vs NPF with a 20 mm lens
A 20 mm lens at f/2.8 on a 24 MP full-frame camera (6.0 µm pixels), aimed at a patch of sky that includes the celestial equator (δ = 0°):
- 500 rule: 500 ÷ 20 = 25 s. The star travels 6.1 pixels: trailing of k = 3.8.
- Simplified NPF: (35 × 2.8 + 30 × 6) ÷ 20 = 13.9 s (13 s on camera).
- Full NPF at k = 1: (16.9 × 2.8 + 13.7 × 6 + 0.1 × 20) ÷ 20 = 6.6 s (6 s on camera). The star is 3.2 pixels across and moves 1.6: its radius.
With the same lens on a 61 MP full-frame camera (3.76 µm pixels), the 500 rule still says 25 s, but now the star travels 9.7 pixels. Full NPF at k = 1 drops to 5.0 s.
500 rule or NPF rule: which to use
The 500 rule was born with film, which resolves far less than a modern sensor, and it ignores both megapixels and aperture. With today’s 3–6 µm pixels it leaves visible trails at 100 % view, more so the higher the camera’s resolution. Use NPF: k = 1 if you will enlarge or crop; k = 2 (or the simplified rule) for the web, social media and moderate prints, as Michaud suggests. His model assumes a lens with moderate aberrations and 3″ seeing: treat the result as a starting point and check your first frame zoomed in.
Methodology & sources
Every result is computed in your browser with the formula shown above — nothing is sent to a server. The numeric model is based on this data and these references:
- Frédéric Michaud (Société Astronomique du Havre) — “La Règle NPF”: full (with k and declination) and simplified formulas (in French)
- Frédéric Michaud — “Les coulisses de la règle NPF”: the star-image model (3″ seeing, λ = 550 nm, 4.47·λ·N diffraction, 2 pixels of demosaicing), the 86,164 s sidereal day and where the 500 rule comes from (in French)
- Crop factor from the sensor diagonal (43.27 mm on full frame): APS-C Sony/Nikon/Fuji 1.53×, Canon 1.61×, Micro Four Thirds 2×, the same as our crop factor calculator.
- Pixel pitch from megapixels: the pixels are assumed to cover the whole sensor at the listed size (p = width ÷ horizontal pixels). If you know your camera’s exact figure, enter it directly.
- Trail: star at the centre of the frame, with a sidereal day of 86,164.09 s. “On camera” rounds down to the next standard shutter speed; Michaud suggests the nearest one, we never go over the limit.
Formula reviewed and verified against real-world cases.