Hong Life CalculatorsUnderstanding the astrophotography 500 and NPF rule calculator — concept and principle
When you photograph the night sky from a fixed tripod, Earth's rotation makes stars drift across the sensor. This calculator estimates the longest exposure before stars visibly turn into short trails, using the classic 500 rule and the more modern NPF rule, and it shows the image scale of each pixel.
How it is calculated
- 500 rule: t = 500 ÷ (focal length × crop factor), in seconds.
- NPF rule (simplified): t = (35 × N + 30 × p) ÷ f ÷ cos δ, where N is the f-number, p the pixel pitch in micrometres, f the actual focal length in mm and δ the declination of the target.
- Image scale: 206.265 × p ÷ f arcseconds per pixel.
The principle
The sky turns 360° in one sidereal day, about 15 arcseconds per second of time at the celestial equator. Stars nearer the celestial pole trace smaller circles, so their speed is multiplied by cos δ, which is why the time is divided by cos δ. The 500 rule comes from the film era, when "sharp" meant a small print viewed from a normal distance; it scales only with focal length. The NPF rule, published by Frédéric Michaud of the Société Astronomique de France, adds the aperture (which sets the size of a star's blur spot) and pixel size (how many pixels a trail must cross before you notice it), so it fits high-resolution digital sensors better. Image scale uses 206,265 arcseconds per radian.
Worked example
- Inputs: 24 mm lens, full frame (crop factor 1), f/2.8, pixel pitch 4.3 µm, declination 0°.
- 500 rule: 500 ÷ (24 × 1) = 20.83333333 s.
- NPF: 35 × 2.8 = 98 and 30 × 4.3 = 129; (98 + 129) ÷ 24 = 227 ÷ 24 = 9.458333333 s (cos 0° = 1).
- Image scale: 206.265 × 4.3 ÷ 24 = 36.9558125″ per pixel.
- Check: at about 15″/s, a 9.46 s exposure moves a star about 142″, or roughly 3.8 pixels; the 20.8 s exposure moves it about 8.5 pixels.
| Focal length (mm) | 500 rule (s) |
|---|---|
| 6 | 83.33333333 |
| 12 | 41.66666667 |
| 18 | 27.77777778 |
| 24 | 20.83333333 |
| 30 | 16.66666667 |
| 36 | 13.88888889 |
| 48 | 10.41666667 |
How to read the result
Use the NPF time when you plan to view images at full size or print large; the 500 rule time is acceptable for small web images. If the NPF time is too short for enough signal, raise ISO, open the aperture, use a wider lens, or stack several shorter frames. A star tracker removes the limit entirely.
Common mistakes
- Applying the crop factor to the NPF formula; the pixel pitch already accounts for sensor size, so use the real focal length.
- Assuming the rule is universal for all directions; star motion is fastest near the celestial equator.
- Computing pixel pitch wrongly; divide the sensor width (mm) by the horizontal pixel count and multiply by 1,000.
Frequently asked questions
What declination should I enter for the Milky Way core?
The galactic centre lies near declination −29°, so cos δ is about 0.87 and the exposure can be about 14% longer than on the equator.
Does a smaller f-number lengthen or shorten the NPF time?
A smaller f-number shortens it in this formula, because the sharper star image shows trailing sooner.
Sources: F. Michaud, The NPF rule (Société Astronomique de France, astrophotography commission) · Explanatory Supplement to the Astronomical Almanac, 3rd ed., University Science Books, 2012 (sidereal rotation)