Untracked exposure
The longest exposure on a fixed tripod before stars stop being points. For Milky Way, star fields and nightscapes.
Read the guide: Shooting the Milky Way without a tracker: the NPF rule versus the 500 rule
Longest exposure, NPF rule
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Your exposure, pixel by pixel
Limit by declination at the frame centre
How to use the untracked exposure calculator
- Pick your camera body, or enter your sensor and pixel size.
- Enter the lens focal length and the aperture you will shoot at.
- Pick the part of the sky you are aiming at. The Milky Way core is the default.
- Use the headline as your longest exposure. Then open the aperture and raise ISO until the brightness line says the frame is bright enough.
Questions
What is the NPF rule?
A formula by Frédéric Michaud for the longest exposure before stars visibly trail on a fixed tripod. Unlike the 500 rule it accounts for pixel size, aperture and declination, so it holds up on modern high-resolution sensors.
NPF rule or 500 rule?
The NPF rule. The 500 rule dates from film and ignores pixel size, so on a 24 MP full-frame camera at 24 mm it allows about 21 s and stars trail about 6 pixels. The NPF rule gives about 10 s at f/1.8 and 11 s at f/2.8 for the same setup.
Does ISO affect star trails?
No. Stars move the same distance at any ISO. ISO only sets how bright the frame is, which is why you raise it to make up for the short exposure.
Why can I expose longer near Polaris?
Stars near the celestial pole move in small circles and barely shift across the sensor, while stars on the celestial equator move fastest. The limit grows as 1 / cos(declination).
How do I get longer exposures without trails?
Use a star tracker, which turns the camera with the sky so exposures of one to several minutes stay sharp. Or stack many short frames, which lowers noise without trailing.
Method
The NPF rule
Frédéric Michaud of the Société Astronomique du Havre published the NPF rule in 2010. It sets the exposure where star trailing stays hidden inside the blur that the lens aperture and the pixel size already cause:
t = k x (16.856 N + 0.0997 f + 13.713 p) / (f x cos(dec)) N aperture (f-number) f focal length, mm p pixel size, µm dec declination of the stars k 2 for the standard result, 1 for pixel-sharp stars at 100%
The headline uses k = 2, the value PhotoPills calls "Default" and most apps show. "Pixel-sharp" is k = 1, PhotoPills' "Accurate", exactly half as long. The widely quoted shortcut, (35 N + 30 p) / f, lands close to k = 2 on the celestial equator: doubling 16.856 and 13.713 gives 33.7 and 27.4.
Checked against published results: for a Sony A7R III at 19 mm f/2.8, PhotoPills' "Accurate" gives 5.88 s and this formula 5.84 s. The simplified rule for 24 mm f/2 with 4.3 µm pixels gives 8.3 s in Galactic Hunter's example and 8.29 s here.
ISO and brightness
ISO does not change how far a star moves, so it plays no part in the trailing limit. It sets how bright the frame is. Brightness scales with time x ISO / N², so halving the time costs one stop, and doubling the ISO wins it back. The brightness line compares your settings with a common dark-sky Milky Way starting point of 20 s at f/2.8 and ISO 3200. Under a brighter sky, the same settings give a brighter background, so you can use less.
Exact trail length
The trail itself is plain geometry. A star moves at the sidereal rate times the cosine of its declination, and the image scale converts arcseconds to pixels:
image scale = 206.265 x p / f arcsec per pixel trail (px) = 15.041 x cos(dec) x t / image scale
The 500 rule
500 / (f x crop factor) came from film, where grain was far coarser than modern pixels. On a 24 MP full-frame body at 24 mm it allows 20.8 s, which trails about 6 pixels on the equator. It is shown for comparison only.
Limits
- Stars near the celestial pole barely move and stars on the equator move fastest. By default the tool uses the declination at the frame centre, like other calculators. A wide lens covers a big range of declinations, though, and corner stars toward the equator move faster. "Worst corner" mode uses the declination at the centre moved toward the equator by the angle from the centre to a corner (atan of half the sensor diagonal over the focal length), the worst case for any camera rotation. Aim a 14 mm full-frame lens at 74° and the frame reaches down to about 17°.
- The rule ignores lens aberrations. Coma and astigmatism in the corners of fast wide lenses often smear stars more than trailing does. Stopping down a third to a full stop helps and changes N in the formula.
- Pixel size from sensor width and pixel count. Presets use the published effective resolution of each body.