NPF rule calculator

Name your lens, your aperture, your sensor and where you are pointing, and this calculator returns the longest exposure that still leaves stars as points — the NPF rule worked out properly, next to the 500 rule you were probably using, so you can see the difference. Free, no account, nothing stored.

What it does, and why it is here

The rule most people arrive with is 500 divided by the focal length. It has one virtue — you can do it in your head, in the dark — and one problem: it was calibrated for the grain of pushed 35 mm film, and film grain is coarse. A modern sensor resolves far finer detail than that grain ever did, so the trail that used to hide inside a grain clump now covers several pixels and shows plainly at 100%. Across ordinary setups the 500 rule runs three to six times too generous.

The NPF rule, published in 2017 by Frédéric Michaud of the Société Astronomique du Havre, fixes that by using the three things that actually decide the answer — N for the aperture number, P for the pixel pitch, F for the focal length:

t = (16.856 × N + 0.0997 × f + 13.713 × p) ÷ (f × cos δ)

Which is exactly why it needs a calculator. It asks for your pixel pitch in microns, a number nobody has to hand and no camera prints anywhere, and for the declination of what you are framing, which changes the answer by a factor of eleven between Orion and Polaris. This page derives the first from your sensor and its resolution, takes the second from a named target or a number, and gives you the one figure to dial in.

What you fill in

• What you point at — a named target fills the declination in for you; choose typed below to keep your own number.
• Declination, in degrees — 0 is the celestial equator, where stars move fastest and the exposure is shortest; near the pole they barely move. Left at 0 you get the answer that is always safe.
• Focal length, in mm — as marked on the lens, not the 35 mm equivalent. The tool works out the equivalent itself and shows it back to you.
• Aperture, as an f-number — it belongs in the formula because a lens stopped down draws a slightly larger diffraction disc, and a fatter star tolerates a little more movement before the movement shows.
• Sensor format and resolution in megapixels — the pair that gives the pixel pitch. This is the half of the problem the 500 rule cannot see: two cameras with the same sensor and the same lens do not trail at the same exposure if one packs twice the pixels.

What you get back

• Set your camera to — the answer, rounded down to something you can dial. A limit of 9.3 seconds becomes 8, not 10: the figure is a ceiling, and the next step up is the one that trails.
• Three answers side by side — NPF accurate, NPF in its simple quoted form, and the 500 rule. The first is the one to use; the other two are there so you can see how far the rule you were using was off.
• Pixel pitch in microns and frame width in pixels — derived, so you never have to look them up, and reusable everywhere else this comes up.
• Equivalent focal length — for reading your crop-sensor lens against advice written for full frame.
• Stacking frames — because the honest answer is often shorter than you wanted, the tool turns it into a plan: how many frames for a given total exposure, the light collected, and the noise gain. Noise averages as the square root of the frame count, so each stop of noise costs four times the frames — the table says what that means at your frame length.
• Every prime at every fast aperture — a full table of the recommended exposure for your sensor and your declination, lens by lens, yours in bold. This is the one to screenshot before a trip: it answers for the lens you did not bring the numbers for.

What it does not do

It gives a ceiling for star movement and nothing else. It does not know your lens’s coma, which smears stars at the corners at any exposure and is cured by stopping down, not by timing. It does not know your light pollution, so it cannot tell you which ISO to pair with the answer.

It assumes a fixed camera. On a star tracker the limit disappears entirely — and the landscape starts trailing instead, which is a different photograph. And it is calibrated for stars: the Moon moves against the stars as well as with them, roughly its own diameter an hour, so a lunar exposure has a tighter limit than this gives.

The 500 rule against the NPF rule

The gap, on three ordinary setups pointed at the celestial equator.

If you have ever followed the 500 rule, checked the back of the camera, thought it was fine, and then opened the file at home to find every star was a short dash — this is why. Note the middle row: a fast lens on a dense sensor is the worst case, because opening the aperture buys light without buying any tolerance.

And where you point moves it again, by the cosine of the declination: ×1 on the celestial equator, ×1.14 on the summer Milky Way core at −29°, ×2 on Cassiopeia at +60°, ×11.5 close to Polaris. Setting it honestly often buys back time you were throwing away.

Questions

Is this calculator free?

Yes. No account, no e-mail, no trial — the numbers you type are used to answer and then forgotten.

Which of the three answers should I use?

The accurate NPF one. It is the only one that knows both your camera and where you are pointing.

Where do I find my pixel pitch?

You do not need to: pick the sensor format and type the megapixels, and the tool derives it. If you want to check, it is the sensor width in millimetres divided by the pixels across, times a thousand — 6.00 µm for a 24 Mpx full frame, 3.92 µm for a 24 Mpx APS-C.

The answer is shorter than I wanted. What now?

Four ways out, and choosing between them is the whole craft. Open the lens — a stop of aperture is a stop of light for no time at all. Raise the ISO; modern sensors take more of it than their reputation suggests, and noise is easier to deal with than a trailed star, which cannot be undone. Stack, which is what the stacking block in the answer is for: twenty frames of eight seconds come out close to one clean frame of 160. Or track, and let the landscape trail instead.

Why is the recommendation rounded down?

Because it is a ceiling, not a target, and the next step up on the dial is the one that trails.

My camera has in-body stabilisation. Does that help?

No. Stabilisation corrects for the camera moving, not for the sky moving. On a tripod it should usually be off.

What counts as a trail, exactly?

The rule is calibrated so the movement stays within roughly one pixel at the centre of the frame. Printed small you could get away with two or three times that; examined at 100% on a screen, you cannot.

Does a sharper lens change the answer?

Not in this formula, which assumes the star is limited by diffraction and by the pixel. Heavy coma smears corner stars whatever the exposure, and only stopping down helps.

Sources and further reading

• The NPF rule explained, with the original formula — PetaPixel.
• The NPF rule in the field — National Parks at Night.
• Sidereal time — the 23 h 56 min 4 s the rate is derived from.