500 Rule Calculator (Star Photography Shutter Limit)

Empirical film-era calibration: the sky's 15°/hour rotation, projected through a lens, smears each star by an amount proportional to focal length × time — and 500/f was tuned so the smear stayed inside what a 35mm film scan or small print would hide. It's the same blur-budget logic as depth of field's circle of confusion, frozen at 1990s output sizes. On 24+ MP digital at screen-fit it's usually acceptable; at 100% it never is — hence the 400 rule and NPF below it.

It models the actual blur sources: N (aperture's diffraction and aberration spot), P (pixel pitch — the sensor's own resolution limit) and f. The simplified form t = (35N + 30p)/f gives a 20mm f/2.8 on a 24-MP full frame about 12 s where the 500 rule allows 25 — and at 12 s the stars are genuinely points at 100%. The full NPF also corrects for declination (stars near Polaris move slower — up to 2–3× more time near the celestial pole; this simplified version assumes the worst-case celestial equator).

The untracked triangle is brutally constrained: 12–25 s shutter (this tool), the widest aperture your lens keeps sharp (f/1.8–2.8), and the rest must come from ISO — 3200–6400 is normal, and the noise is the price of stillness. The escape hatches, in increasing commitment: stack 10–20 frames and median-merge the noise away (free, works), buy a faster lens, or buy a star tracker — which removes the time limit entirely and lets ISO 800 f/4 multi-minute exposures embarrass everything else.

Invert the goal: at 15°/hour, a satisfying trail arc wants 30 minutes to 2+ hours of total integration. Modern practice never does it in one exposure (noise, plane streaks, one mistake kills all) — shoot continuous 30-s frames for an hour and stack with lighten-blend; gaps stay invisible because each frame's trail segment connects to the next. Point at Polaris for circles, east/west for diagonal rain, south (northern hemisphere) for gentle arcs. Battery and dew heaters, not math, are the real planning problems.