NPF Rule vs 500 Rule: How to Calculate the Longest Shutter Speed Without Star Trails

Stars trail because the Earth rotates

Because the Earth rotates, the stars appear to circle the celestial pole (in the northern hemisphere, right next to Polaris). One full turn takes about 23 hours 56 minutes (a sidereal day), so the sky moves about 15.04° per hour. That is only about 0.0042° per second, but the longer the lens and the finer the camera's pixels, the more visible this small movement becomes in a photo.

To record stars as points with the camera fixed in place, the distance each star image moves across the sensor has to stay small enough that you do not notice it. The 500 rule and the NPF rule both estimate how many seconds that allows. Both assume the camera is on a fixed tripod; they do not apply when you track the stars with an equatorial mount or a portable star tracker.

• The longer the focal length (telephoto), the more the motion is magnified and the faster stars trail
• The finer the pixels (higher resolution), the more pixels the same motion crosses
• Stars near the celestial equator (such as Orion) move fastest; the closer to Polaris, the slower
• The wider the aperture, the smaller and sharper the star image, so even slight trailing stands out

The 500 rule: formula and quick-reference table

The 500 rule dates back to the film era and is based on stars looking like points in a small print of roughly 13 × 18 cm to 20 × 25 cm. Resolution does not appear in the formula, so the result is the same however many megapixels your sensor has. For a stricter result, some photographers lower the constant to make a 400 rule or 300 rule.

The table assumes you are aiming at the celestial equator (declination 0°), where stars move fastest. If you follow the 500 rule on a 24 MP full-frame camera, the stars move about 6 pixels across the sensor regardless of focal length. That is why stars that look like points on a phone screen turn into short lines when you zoom to 100% on a computer.

The NPF rule formula

The NPF rule was devised by Frédéric Michaud of the Société Astronomique de France. It is named after the three values it uses: the f-number (N), the pixel pitch (p) and the focal length (f). Unlike the 500 rule, it takes pixel size and aperture into account.

The formula you often see on social media and blogs, (35 × f-number + 30 × pixel pitch) ÷ focal length, is known as the simplified NPF rule. It gives about twice the exposure time of the full formula: stars trail slightly at 100%, but look like points when the image is viewed smaller.

Under the same conditions, stars move about 1.6 pixels with the NPF rule, about 3.4 pixels with the simplified NPF rule and about 6.1 pixels with the 500 rule. As a rule of thumb, 1 to 2 pixels still looks like a round point at 100%, 3 to 4 pixels looks slightly oval at 100%, and anything over 6 pixels is clearly a line.

Why higher-resolution cameras need shorter exposures

Pixel pitch is the sensor width divided by the number of pixels across it. A 24 MP full-frame sensor (36 × 24 mm) is 6,000 pixels wide, giving about 6.0 µm; a 45 MP sensor is about 4.4 µm. The smaller each pixel, the sooner a slightly moving star spills into the next one, so the time you can keep stars as points gets shorter.

The table is for a 14 mm f/2.8 lens aimed at the core of the Milky Way (Sagittarius, declination −29°). The 500 rule gives about 40.8 seconds whatever the resolution, but the trailing rises to about 9.7 pixels on a 61 MP camera. That is why people feel their stars started trailing after they upgraded to a high-resolution body. If you downsize your photos, though, resolution matters less: shrink a 61 MP image to the equivalent of 24 MP and the trailing shrinks by about the same amount.

Where you point the camera (declination) lengthens the exposure

How fast a star moves depends on how far it is from the celestial equator (its declination), in proportion to cos declination. Stars on the celestial equator move fastest, while those around the celestial pole barely move. With the declination correction applied, both the NPF rule and the 500 rule give longer times, as follows.

The table is for a 24 MP full-frame camera at 14 mm f/2.8. A wide-angle frame contains stars at many different declinations, so the stars nearest the equator at the edge of the frame trail first. If in doubt, calculate for declination 0° and you will have a safe time in any direction.

So which rule should you use?

• You check images at 100% on a computer or print them large → the NPF rule
• You view on social media or a phone and would rather have brightness than perfectly round stars → the simplified NPF rule
• You shoot casually with an older camera of around 12 MP or a compact → the 500 rule works fine in practice
• You care more about a bright foreground than slight trailing → use the 500 rule as the upper limit and accept a little trailing

NPF times are shorter than most people expect, so you need a higher ISO to compensate. At 14 mm f/2.8 for 10 seconds under a very dark sky, that means about ISO 6400. How much trailing to accept comes down to a trade-off with noise. For the full set of settings for shooting the Milky Way, see Milky Way camera settings.

1. 1

   Enter your camera details

   In the "Max exposure without trails" tab of the Astrophotography Calculator, enter the sensor size, effective megapixels, and the lens focal length and f-number. For APS-C or Micro Four Thirds, simply enter the focal length printed on the lens and the conversion is done for you.

2. 2

   Choose where you are pointing

   Pick from the Milky Way core, Orion, the Big Dipper and more. The NPF rule, simplified NPF and 500 rule times appear side by side, along with how many pixels the stars trail at each time.

3. 3

   Check the value you can set on the camera

   It shows the nearest 1/3-stop value that does not exceed the calculated time (10 s, 8 s and so on). Set that as your shutter speed and check the suggested ISO as well.

FAQ

Which is correct, the NPF rule or the 500 rule?

Both are guides, built on different assumptions about viewing size. The 500 rule assumes film or a low-resolution camera viewed as a print; the NPF rule assumes a high-resolution digital camera with stars still looking like points at 100%. On a 24 MP full-frame camera at 14 mm f/2.8, stars trail about 6 pixels at the 500 rule's 35 seconds, but stay within about 1.6 pixels at the NPF rule's 9 seconds.

What is the NPF rule formula?

t = (16.856 × f-number + 0.0997 × focal length + 13.713 × pixel pitch in µm) ÷ (focal length × cos declination). The simplified version is (35 × f-number + 30 × pixel pitch) ÷ focal length, which gives about twice the time of the full formula.

What focal length do I use for the 500 rule on APS-C?

Divide by the 35mm-equivalent focal length. Sony, Nikon and Fujifilm APS-C sensors have a crop factor of about 1.53, so a 16 mm lens is about 24.5 mm equivalent and 500 ÷ 24.5 ≈ 20 seconds. Aimed at the Milky Way, that stretches to about 23 seconds.

Why does the NPF time change when I change the aperture?

The wider the aperture, the smaller and sharper the star image, so even slight trailing stands out. At 14 mm, 24 MP, aimed at the Milky Way, you get about 8.7 seconds at f/1.4, 10.6 seconds at f/2.8 and 12.3 seconds at f/4. Stopping down makes the image darker, though, so most people shoot close to wide open.

How do I check whether my stars are trailing?

Play back the image and zoom all the way in on a bright star near the edge of the frame. Round points are fine; if they are narrow ovals or short lines, shorten the exposure. With wide-angle lenses, stars at the edges trail more easily than those in the centre and lens aberrations can also distort them, so check the corners too.