Stars move. At the celestial equator they cross the sky at about fifteen degrees an hour, and if the exposure is long enough that movement smears a point of light into a short line. The 500 rule is the usual rough guard against it.
seconds = 500 ÷ (focal length × crop factor)
A 24mm lens on a full-frame body gives 20.8 seconds, and since a camera dial works in whole seconds the practical setting is 20. The 500 rule calculator reports both, because the difference between the theoretical figure and the setting you can actually select is the part a rule of thumb usually leaves out.
The crop factor is doing real work
Put that same 24mm lens on an APS-C body with a 1.5 crop factor and the figure becomes 13.9 seconds, or 13 on the dial. Nothing about the lens changed. What changed is that the sensor is capturing a narrower slice of the sky across the same number of pixels, so the same angular movement of a star travels further across the frame.
That is why the rule is written against the full-frame equivalent focal length, 36mm in this case, rather than the number printed on the barrel. Go the other way and a 14mm ultra-wide on full frame buys 35.7 seconds, which is most of why ultra-wides dominate landscape astrophotography.
Why 500 is generous
The rule was calibrated in an era of lower pixel density, and it allows a trail of a few pixels on a film-era frame. On a modern high-resolution sensor viewed at 100 per cent, that trail is visible. The stricter 300 rule is the common correction: at the same 36mm equivalent it gives 8.3 seconds rather than 13.9.
Which divisor is right depends on how closely the image will be examined, and that is a judgement rather than a calculation, so the divisor is a field on the page rather than a fixed number. There is also a declination allowance: stars near the celestial pole trace much smaller circles and trail far more slowly than stars at the equator, so a shot aimed at Polaris tolerates a longer exposure than the rule suggests.
Shorter exposures mean more of them
A shorter frame is not a loss if you intend to stack. Thirty minutes of total integration at 20.8 seconds is 87 frames; at 8.3 seconds it is 216. Stacking recovers the signal that a single short exposure gives up, and the calculator reports the frame count because that is what decides whether the session is practical.
The same arithmetic of intervals and counts turns up in time-lapse planning, and for daylight long exposures the ND filter calculator handles the opposite problem of making an exposure longer on purpose. If you are shooting video rather than stills, shutter angle is the equivalent constraint on how long each frame may be open.