The 500 rule is broken, and the NPF rule is why

The 500 rule says you divide 500 by your focal length and that is how many seconds you can expose before the stars visibly trail. On a 24mm lens that gives you twenty-one seconds, which is a comfortable number, and it is why the rule has survived.

It is also, on any modern camera, about twice as long as it should be.

What the 500 rule actually assumed

The rule is a piece of film-era shorthand. The Earth rotates once in roughly 24 hours, stars near the celestial equator sweep across the sky at about 15 arcseconds per second of time, and the rule works out how long you can expose before that motion smears a star across enough of the frame to notice.

The word doing all the hidden work there is notice. The 500 rule's threshold was calibrated against what a modest print from a 35mm negative would show. Grain, print size and the resolving limit of the film all set a fairly forgiving bar, and the rule was built to sit just under it.

Now put the same 24mm lens on a 45 megapixel sensor and inspect the file at 100%. You are examining the image at something like six times the enlargement the rule was designed around. A trail that was invisible in a 6x4 print is now an obvious oval.

The rule was not wrong. Its assumptions expired.

What the NPF rule adds

The NPF rule, from Frédéric Michaud of the Société Astronomique du Havre, is the same question asked with the missing variables put back in. In its usual form:

t = (35 × N + 30 × p) / f

where N is the f-number, p is the pixel pitch in micrometres, and f is the focal length in millimetres. The result is seconds.

The two additions are what matter.

Pixel pitch means the rule now knows how finely your sensor samples the image. A star trail that lands entirely inside one pixel is invisible; the same trail across a sensor with half the pixel pitch spans two, and becomes a short line. Higher resolution genuinely does give you less time, and no rule based on focal length alone can express that.

Aperture enters because a real lens does not render a star as a point. Wide open, aberrations spread it. Stopped down, diffraction spreads it. Either way the star already occupies some area before any rotation is added, and a slightly blurred star tolerates slightly more movement before the blur reads as a line. This is why the formula gives a longer exposure at f/4 than at f/1.4, which surprises people until they think about what is being measured.

The two rules, side by side

Same lens, same sky, three cameras:

The 500 rule cannot tell the first two rows apart, because it has no way of knowing the sensor changed. In practice NPF lands at roughly half the 500 rule's answer across most combinations, and that factor of two is precisely the gap between "fine in a small print" and "fine at 100%".

The star trails calculator computes both and shows them together, so you can see the size of the disagreement for your own setup rather than taking the ratio on trust.

Declination, the variable neither rule shows you

Both rules quietly assume you are photographing the celestial equator, which is where stars move fastest.

Apparent motion falls off towards the poles. A star near Polaris barely moves at all over a minute, which is exactly why polar star trail images work. A star on the equator moves the full 15 arcseconds per second. The general correction divides the allowed time by the cosine of the star's declination, so pointing at the pole buys you substantial extra exposure and pointing at the equator buys you none.

For the practical case this matters less than it sounds, because the interesting part of the sky is usually the galactic core, which sits at a southerly declination and moves close to full speed. Treat the rules as the equatorial worst case and you will not be caught out. If you are shooting north in the northern hemisphere, you have more room than the formula gives you.

The other things that decide whether stars look sharp

The exposure limit is only ever one of the constraints, and often not the binding one.

Focus. More astro frames are ruined by focus than by trailing. Infinity marks on lenses are not reliable, focus shifts with temperature over the course of a night, and autofocus has nothing to work with. Focus manually on the brightest star at maximum magnification in live view, then tape the ring, then check again an hour later.

Corner aberration. Fast wide lenses render stars as birds, commas or crosses towards the edges of the frame at maximum aperture. Stopping down one stop from wide open usually improves this dramatically. The NPF rule will give you slightly more time at the narrower aperture, so this trade costs less than it appears — you lose light but gain both exposure time and corner quality.

Stacking. If you are willing to combine frames, the whole calculation changes. Several shorter exposures aligned and averaged will beat one long exposure for noise while keeping the stars perfectly round, and it removes the trailing constraint entirely. The tradeoff is software and time rather than optics.

Atmosphere. On a night with poor seeing, or with any haze, stars are already several arcseconds wide before you start. No exposure rule accounts for this and the only response is to look at the sky.

How to use them

Use NPF as the number you actually set. Use the 500 rule as a sanity check that you have not fat-fingered a decimal point.

If you are shooting for web or moderate prints, and NPF is giving you an uncomfortably short exposure at high ISO, you have room to go past it. Somewhere between the two answers is usually a reasonable compromise, and knowing both tells you exactly how much you are borrowing.

And if you want round stars at 100% on a high resolution body, take NPF seriously, or stack. Those are the two honest options; the third, which is to use the 500 rule and decide afterwards that the trails add motion, is not one.