NPF Rule Exposure Calculator

Every star in the sky is moving, or rather you are, at about 15 arcseconds per second at the celestial equator. On a fixed tripod that motion eventually records as a short line instead of a point, and the question is how long you have before it becomes visible. The NPF rule answers it properly, accounting for pixel size and lens aperture, where the older and far more widely repeated 500 rule does not.

What is the NPF rule and where does it come from?

The NPF rule estimates the longest exposure before star trailing becomes visible on a fixed tripod. The name comes from its three inputs: N for the aperture number, P for pixel pitch, and F for focal length.

Seconds = (35 × N + 30 × pixel pitch) ÷ (focal length × cos declination)

Aperture appears because a faster lens produces a smaller star image, and a smaller star image smears into a visible line sooner. Pixel pitch appears because trailing is only visible once a star crosses more than about one pixel, so a sensor with large pixels tolerates more motion. Focal length appears because it magnifies the motion. Declination appears because stars near the celestial pole trace much smaller circles than stars on the equator.

Worked through for a common case: a 24 mm f/2.8 lens on a full frame sensor with 5.9 micron pixels, pointed at the celestial equator. That is 35 times 2.8, which is 98, plus 30 times 5.9, which is 177. The sum, 275, divided by 24 gives about 11.5 seconds. Point at 40 degrees declination instead and the cosine of 40 is 0.766, so the allowance rises to about 15 seconds.

Why does the 500 rule give the wrong answer?

The 500 rule is simply 500 divided by the focal length, and its virtue is that you can do it in your head. It was written in the film era, where grain was coarse enough to hide a little trailing and nobody examined a negative at 100 percent on a monitor. It contains no term for pixel size and no term for aperture, which are the two things that decide whether trailing is visible on a digital sensor.

The gap is not small, and it widens as sensors gain resolution. Halving the pixel pitch roughly halves the tolerable exposure, and modern high resolution bodies have very small pixels.

Read the bottom two rows and the case for a tracker makes itself. At 200 mm you have under two seconds, and at 600 mm you have well under one. No amount of ISO recovers the light you did not collect, so untracked astrophotography stops working somewhere around 100 mm, and everything longer than that needs the sky to be followed rather than frozen.

How much does pointing direction change the answer?

A great deal, and it is free. The sky rotates about the celestial pole, so a star at the pole barely moves while a star on the celestial equator moves at the full 15 arcseconds per second. The NPF rule handles this by dividing by the cosine of declination.

This is why untracked star trail compositions are almost always shot toward the pole, and why a beginner shooting the Milky Way core low in the south has the hardest possible case: low declination, plus atmosphere near the horizon, plus usually the worst light pollution.

What do you do when the exposure is too short?

Four levers, in the order they cost you the least.

1. Open the aperture. Going from f/4 to f/2.8 doubles the light and shortens the NPF allowance only slightly, because the aperture term is small compared with the pixel term. This is the cheapest win available and most people leave it on the table.
2. Shorten the focal length. Exposure allowance scales inversely with focal length, so 14 mm buys nearly twice what 24 mm does. Wide field Milky Way work exists partly because the physics pushes you there.
3. Stack more frames. Signal to noise improves with the square root of the frame count, so 100 frames of 10 seconds is meaningfully cleaner than 25 frames of 10 seconds. It does not recover detail lost to trailing, only noise.
4. Track the sky. A star tracker turns 15 seconds into two to four minutes, which is roughly a sixteen fold increase in light per frame and lets you drop the ISO by two stops. A compact star tracker is the single highest impact purchase in untracked astrophotography, and a full GoTo tracking mount adds the ability to autoguide and to carry a small telescope rather than only a lens.

Note what is not on that list: raising the ISO. ISO does not collect more light, it amplifies what was already collected, and past the point where read noise is swamped it buys almost nothing. Most modern sensors reach that point somewhere between ISO 800 and ISO 3200, and pushing beyond it mostly costs dynamic range in the star cores.

How does this change once a telescope is involved?

It stops being the governing limit and starts being a footnote. A telescope at 600 mm on a fixed mount allows under a second, which is useless for anything except the Moon and the brighter planets, and those are shot as video and stacked rather than as single exposures. Once you mount a camera behind a telescope, the questions become mount tracking accuracy, polar alignment and guiding, which the equatorial mount setup guide covers.

The exception is the bright end. The Moon is bright enough that a planetary camera can run at hundreds of frames per second and stack the sharpest few percent, which sidesteps both trailing and atmospheric seeing at once. That technique, lucky imaging, is the reason amateur planetary photographs improved so dramatically once video capture became cheap. The lunar photography guide works through it.

Related tools and guides

• Field of view calculator, sensor coverage and image scale
• Focal ratio calculator, why f number sets exposure length
• Mount payload calculator, before you buy a tracker
• Exposure time by focal length chart
• Best star trackers
• How to start astrophotography