What this calculator does
Stars move. The earth turns a degree every four minutes, and at some exposure length that motion stops being a point of light and becomes a short line. The 500 rule is the old field approximation for where that happens: divide 500 by the effective focal length and you have your seconds.
It is a rule of thumb rather than physics, and it was calibrated for film and for prints viewed at arm's length. On a modern sensor examined at full magnification it is generous, which is why photographers now often use 300 or even 200 in its place. All four divisors are here so you can see the difference rather than argue about it.
The formula
The rule is seconds = divisor ÷ (focal length × crop factor), using the effective focal length because a crop sensor magnifies the apparent motion. The declination allowance is real physics rather than a rule of thumb: a star's apparent speed is proportional to the cosine of its declination, so targets near the celestial pole move more slowly and tolerate longer exposures by a factor of 1 ÷ cos(declination).
| Term | Meaning |
|---|---|
| Divisor | 500 is the classic figure. 300 and 200 are the modern stricter versions for high resolution sensors. |
| Crop factor | Multiplies the effective focal length, so a crop sensor shortens the allowed exposure. |
| Declination | How far the target sits from the celestial equator. The pole is 90 degrees and barely moves. |
| Integration | Total exposure across many frames, stacked afterwards to reduce noise. |
The inputs explained
| Field | What to enter |
|---|---|
| Focal length (mm) | The focal length marked on the lens, before any crop factor. |
| Crop factor | 1 for full frame, about 1.5 or 1.6 for APS-C, 2 for micro four thirds. |
| Divisor | The divisor. Start at 500 for a quick look and drop to 300 if you intend to examine the frame closely. |
| Declination of the target (°) | Declination of what you are pointing at, in degrees. Leave at zero for the celestial equator, which is the strictest case and a safe default. |
| Total integration wanted (min) | Total integration you want across all frames, used to work out how many exposures that takes. |
When to use it
Setting up a wide field shot
A 24mm lens on full frame gives 20.8 seconds under the 500 rule. Round down to the 20 seconds your camera actually offers and you have a usable starting point for a single frame of the Milky Way.
Working out how many frames to stack
Thirty minutes of integration at 20.8 seconds a frame is 87 exposures. That is the number that decides whether your battery and your patience will last, and it is easy to underestimate.
Shooting near the pole
Point at a target 60 degrees from the equator and the allowance doubles, so the same lens tolerates 41.7 seconds. This is why circumpolar shots can use much longer exposures than anything near the equator.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How long can each lens expose?
Only the focal length changes.
| Focal length | Longest exposure before trailing | Under the stricter 300 rule | Frames for your total integration |
|---|---|---|---|
| 14mm | 35.7 s | 21.4 s | 51 |
| 20mm | 25.0 s | 15.0 s | 72 |
| 24mm | 20.8 s | 12.5 s | 87 |
| 35mm | 14.3 s | 8.6 s | 126 |
| 50mm | 10.0 s | 6.0 s | 180 |
| 85mm | 5.9 s | 3.5 s | 306 |
What does declination buy you?
The same lens pointed at targets further from the celestial equator.
| Declination | Longest exposure before trailing | Declination allowance | Frames for your total integration |
|---|---|---|---|
| 0° | 20.8 s | 1.00× | 87 |
| 30° | 24.1 s | 1.15× | 75 |
| 45° | 29.5 s | 1.41× | 62 |
| 60° | 41.7 s | 2.00× | 44 |
| 75° | 80.5 s | 3.86× | 23 |
| 85° | 239.0 s | 11.47× | 8 |
Questions
Is the 500 rule accurate?
It is a rule of thumb, not a calculation. It was calibrated for film and modest print sizes, and on a high resolution sensor viewed at 100 per cent it allows visible trailing. Use 300 if you intend to pixel peep, or a proper NPF calculation if you want to account for pixel pitch and aperture.
Why does a crop sensor shorten the exposure?
Because it magnifies the image, so the same star motion covers more pixels. Multiplying the focal length by the crop factor handles it, and an APS-C body at 24mm behaves like 36mm on full frame.
What is the declination allowance?
Stars near the celestial pole trace smaller circles and move more slowly across the frame. Their apparent speed scales with the cosine of declination, so the tolerable exposure scales with one over it. This part is physics rather than a rule of thumb.
Does a star tracker change this?
Entirely. A tracker follows the sky, so exposures are limited by the tracker's accuracy and by light pollution rather than by the earth's rotation. This page describes untracked shooting only.
Why round the exposure down?
Because cameras offer a fixed set of shutter speeds and none of them is 20.8 seconds. Rounding down to 20 keeps you inside the rule, where rounding up to 25 does not.
For the depth of field on a wide lens wide open, see depth of field. For daylight exposures long enough to need filters there is ND filter exposure, and for how a crop sensor changes the framing, crop factor.