NPF rule calculator

An NPF rule calculator answers a night-sky question the old 500 rule cannot: given your aperture, lens focal length, sensor pixel pitch, and the declination of the field, what is the longest fixed-tripod exposure that still keeps stars sharp? This capability returns the sharper (precise) NPF maximum shutter time in seconds using the full modern formula with accuracy factor one-half, so you leave less trailing on high-resolution sensors than the default NPF or the classic 500 and 600 rules allow. Enter f-number N, native focal length in millimetres, pixel pitch in micrometres, and minimum declination in degrees; the tool echoes the inputs, the cosine of declination, the NPF numerator, both sharper and default shutter times, a readable formula string, and step-by-step substitution you can assert in tests or field notes.

What the NPF rule is and why sharper matters

NPF stands for the three optical and sensor quantities that control how quickly a star trails across pixels during an untracked exposure: N for aperture as an f-number, P for photosite pitch in micrometres, and F for focal length in millimetres. Earth’s rotation makes stars move about fifteen arcseconds of right ascension per second of time; the longer the focal length and the smaller the pixels, the sooner that motion spans more than one pixel and shows as a trail.

The classic 500 rule divides five hundred by focal length and ignores aperture diffraction, pixel size, and sky position, so on modern dense sensors it is almost always too generous. The full NPF formula multiplies an accuracy factor k by a linear combination 16.856 times N plus 0.0997 times f plus 13.713 times p, then divides by f times the cosine of the minimum declination of the frame.

Cosine of declination stretches the allowed time near the poles and shortens it on the celestial equator, which matches how diurnal motion projects onto the sensor. This capability always uses the sharper variant with k equal to one-half—half the default NPF exposure—so the result targets tighter star points for landscape astrophotography and stacked nightscapes. Prefer native millimetre focal length, not crop-factor equivalent length, because the formula already sees true angular scale through pixel pitch.

Aperture enters as f-number, not millimetre hole diameter: wider apertures (smaller N) slightly reduce the recommended time because the point-spread function and the trail model interact in the original calibration.

Practical tips, pixel pitch, and related searches

Compute pixel pitch once per camera body: physical sensor width in millimetres divided by the number of pixels across the long edge, times one thousand, yields pitch in micrometres. Example full-frame bodies often land near five to six micrometres; smaller sensors or higher megapixel counts reduce pitch and therefore shorten the NPF shutter. Use the minimum declination of stars you care about in the frame—not the centre only—if the composition spans a wide strip of sky, because the equatorward edge trails fastest.

Keep optical values inside the published absolute range so the numerator and denominator cannot overflow into a non-finite result. Prefer sending numbers rather than pre-formatted strings when you control the client; string numbers are accepted only when they match a strict finite numeric pattern. This landing targets people searching for an NPF rule calculator, astrophotography shutter speed, or maximum exposure for stars with aperture and pixel pitch; it is not the 500 or 600 rule alone, not a tracker polar-alignment tool, and not a depth-of-field calculator.

Prefer this capability when you already know N, f, p, and δ and only need the sharper max shutter; if you only know crop factor and megapixels without pitch, convert to pitch first.