NPF rule: longest untracked exposure.

What the NPF rule says

The rule gives the longest exposure before a star’s motion is noticeable, from three things: the lens aperture N (as an f-number), the sensor’s pixel pitch p in micrometres, and the focal length f in millimetres. Light Stalking states it as exposure in seconds ≈ (35 × N + 30 × p) ÷ f. Pixel pitch is the sensor width in millimetres divided by the pixels across it, times 1000. Unlike the 500 rule it knows how fine the pixels are, so a high-resolution sensor gets a shorter time than a low-resolution one behind the same lens.

Use the real focal length

Pixel pitch already carries the sensor’s size, so enter the focal length printed on the lens. Entering a 35 mm equivalent would count the crop factor twice. The one place a crop factor matters is the 500 rule, which was written for full frame; the optional field divides 500 by the equivalent focal length for that comparison only.

What the trail length shows

The sky turns once in a sidereal day, which Wikipedia gives as about 86,164.09 seconds, so a star on the celestial equator moves 1,296,000 ÷ 86,164.09 = 15.04 arcseconds per second. Wikipedia’s plate scale page gives the image scale as 206,265 × pixel size ÷ focal length, in arcseconds per pixel. Divide one by the other and you have the trail in pixels for any exposure. That arithmetic is this page’s, not part of the published rule. It shows that NPF is not a zero-trail guarantee: at its own time it allows a few pixels of smear.

Declination

Stars near the celestial pole move across the frame more slowly than stars on the equator, by the cosine of the declination. If you enter a declination, the page divides the NPF time by that cosine and reports the trail at the longer time. The Light Stalking article itself is unclear on the direction of its declination setting and advises leaving it at zero if you are unsure, so treat the stretched time as geometry, not as part of the published formula. Use the declination of the stars farthest from the pole in your frame.

Worked example

Light Stalking works a Nikon D750 with a 24 mm f/2.8 lens: sensor 35.9 × 24.0 mm, 6016 × 4016 pixels, so pixel pitch is 35.9 ÷ 6016 × 1000 = 5.97 µm. NPF = (35 × 2.8 + 30 × 5.97) ÷ 24 = (98 + 179.1) ÷ 24 = 11.5 seconds, which the article rounds to 12. The 500 rule gives 500 ÷ 24 = 20.8 seconds, which the article says can show trails in large prints. The image scale is 206,265 × 0.00597 ÷ 24 = 51.3 arcseconds per pixel, so 11.5 seconds gives a trail of 15.04 × 11.54 = 173.6 arcseconds, or 3.4 pixels, and 20.8 seconds gives 6.1 pixels.

Limits

The NPF rule is a rule of thumb for untracked, fixed-tripod shots. It says nothing about lens sharpness, wind, or how big you print. If you are tracking, the limit is set by your polar alignment instead, and the polar alignment calculator linked here handles that case.