NPF Rule Calculator — Simplified
Solve the simplified NPF rule tmax = (35·f# + 30·p) / f for any of its four quantities — maximum exposure time, aperture f-number, pixel pitch, or focal length — with step-by-step math, a live pixel-drift schematic, star-trail charts, and companion astrophotography metrics.
NPF is stricter than the 500 rule
The classic 500 rule gives t = 500/f seconds — a quick approximation that ignores aperture and pixel pitch and was calibrated for coarse-grained film. On modern high-resolution sensors the 500 rule produces visibly trailed stars. The NPF rule was developed by French astrophotographers Frédéric Michaud and others, and it yields shorter, safer exposures by adding two corrections: a 35·f# term that accounts for how sharply the aperture resolves the sky, and a 30·p term that scales with how finely the sensor samples it. For a 14mm f/2.8 on a 4.35 µm sensor, the 500 rule says 36 s; NPF says about 16 s — a factor of two stricter.
The numerator is an angular resolution budget
The two terms inside the numerator are both angular tolerances expressed in micrometres of sensor-plane drift. The 35·f# term reflects the physical limit set by diffraction and lens aberrations — a wider aperture resolves finer detail, so its tolerance in the sensor plane is larger. The 30·p term reflects the sensor's own sampling limit — a coarser pixel pitch tolerates more drift before the trail crosses a pixel boundary. Together they define the total budget, and dividing by focal length converts that sensor-plane tolerance into an angular tolerance on the sky.
Exposure scales inversely with focal length
Because focal length appears only in the denominator, tmax is inversely proportional to f. Doubling focal length halves the maximum exposure. This is why long-lens astrophotography almost always requires a tracking mount: a 200mm lens gives tmax under one second on a typical full-frame camera, far too short to gather enough light without tracking. The practical threshold for untracked shooting is roughly 50mm — beyond that, tracking becomes the only serious option.
The crop factor cancels out
A frequently confused point: the NPF rule does not need the crop factor. If you use the true focal length and the true pixel pitch, the sensor size never enters the calculation. This is because both the angular scale and the pixel geometry scale together when you switch to a smaller sensor with the same pixel pitch. What actually differs between full-frame and APS-C at the same focal length is the field of view, not the maximum exposure. Using a full-frame-equivalent focal length by mistake will give the wrong NPF time by the crop factor.
How to Use This Calculator
The NPF rule links four quantities: tmax, f#, p, and f. Pick which one you want the tool to solve, then fill in the other three.
1. Choose what to solve for
Pick tmax, f#, p, or f from the toggle. The calculator rearranges tmax = (35·f# + 30·p)/f automatically for whichever variable you choose.
2. Use realistic presets
Pixel-pitch presets cover the common cameras (Nikon D850, Sony A7R IV, Canon EOS R5, A7S III, Z6, Micro 4/3). Aperture presets span f/1.4 to f/8, focal length presets span 14mm to 300mm, and exposure presets span 4 to 60 seconds.
3. Enter the true focal length
Enter the actual lens focal length in millimetres — not the full-frame-equivalent. The crop factor cancels out in the NPF rule, so an APS-C camera at 24mm and a full-frame camera at 24mm give the same maximum exposure even though their fields of view differ.
4. Read the result and breakdown
The result card shows tmax in seconds, the pixel trail length at that exposure, the angular pixel scale, and a horizontal bar showing how the numerator splits between the aperture term 35·f# and the pixel term 30·p. A colour-coded badge classifies the exposure as ultra-short, short, typical wide-field, long, or ultra-long.
5. Check the schematic and charts
The schematic shows a zoomed sensor pixel grid alongside a simulated sky with a star trail, with a scale bar marking one pixel. The main chart plots tmax against focal length for three apertures.
6. Switch to Advanced for depth
Advanced mode adds tmax vs aperture, a star-trail-length curve showing where the 1-pixel limit falls, sensitivity metrics on all four inputs, and companion metrics including angular pixel scale, field of view, sky rotation rate, and tracking-free limit.
What This Tool Offers
Built around the simplified NPF rule tmax = (35·f# + 30·p)/f, the workhorse of modern untracked astrophotography.
Four-way solving
Solve for maximum exposure, aperture, pixel pitch, or focal length. The calculator rearranges the NPF formula for whichever variable you choose.
Live pixel-drift schematic
A sensor pixel grid on the left, a star-drifting sky on the right, and a numerator-breakdown bar showing how the aperture term and pixel term contribute to the total tolerance.
Exposure-class verdict
Each result is classified from ultra-short (long lens, tracked territory) through typical wide-field up to ultra-long (extreme wide-field, Milky Way panoramas) — with a coloured badge and plain-language description.
Derived hints everywhere
Each field shows the value converted to related units — pixel trail length, angular pixel scale, field of view, sky rotation rate, and the practical untracked focal-length limit.
Three linked charts
tmax vs focal length for three apertures, tmax vs aperture for three focal lengths, and star-trail length vs exposure time with the 1-pixel NPF limit marked.
Reference tables
A camera pixel-pitch database, an NPF lookup grid across focal lengths and apertures, and a comparison table of the 500 rule, NPF, and other exposure rules.
Reference Tables & Conversions
An exposure-rule comparator, an NPF lookup grid, and a camera pixel-pitch reference.
Exposure-rule comparator (enter f#, p, and f)
NPF Lookup Grid (seconds)
Computed from tmax = (35·f# + 30·p)/f with p = 4.35 µm. Rows are the focal length f, columns are the aperture f#.
| f \ f# | f/1.4 | f/1.8 | f/2.8 | f/4 | f/5.6 | f/8 |
|---|
Camera Pixel-Pitch Reference
Common cameras used for astrophotography and their pixel pitch. Larger pixels mean longer NPF exposures at the same focal length and aperture.
| Camera | Sensor | Resolution | Pixel pitch (µm) | NPF @ 14mm f/2.8 (s) |
|---|---|---|---|---|
| Sony A7S III | Full-frame | 12 MP | 8.40 | 24.3 |
| Nikon Z6 / Z6 II | Full-frame | 24 MP | 5.94 | 19.1 |
| Canon EOS R6 | Full-frame | 20 MP | 6.56 | 20.4 |
| Canon EOS 5D Mark IV | Full-frame | 30 MP | 5.36 | 18.4 |
| Nikon D850 | Full-frame | 46 MP | 4.35 | 16.3 |
| Canon EOS R5 | Full-frame | 45 MP | 4.40 | 16.4 |
| Sony A7 IV | Full-frame | 33 MP | 5.12 | 18.0 |
| Sony A7R IV / V | Full-frame | 61 MP | 3.76 | 15.1 |
| Nikon Z7 / Z7 II | Full-frame | 46 MP | 4.35 | 16.3 |
| Fujifilm X-T4 | APS-C | 26 MP | 3.76 | 15.1 |
| Sony a6600 | APS-C | 24 MP | 3.91 | 15.4 |
| OM System OM-1 | Micro 4/3 | 20 MP | 3.30 | 14.1 |
Variable Reference
| Symbol | Meaning | Typical range | Units |
|---|---|---|---|
| tmax | Maximum untracked exposure | 0.1 – 60 | seconds |
| f# | Lens aperture f-number | 1.0 – 16 | dimensionless |
| p | Pixel pitch | 2.0 – 10 | micrometres |
| f | Focal length | 4 – 2000 | millimetres |
| ε | NPF tolerance (approx. 1 pixel) | — | pixels |
| θpix | Angular pixel scale, 206.265·p/f | 1 – 200 | arcsec/pixel |
| ω | Sky rotation rate, 15.041·cos(δ) | 0 – 15 | arcsec/s |
What Does tmax = (35·f# + 30·p) / f Measure?
The NPF rule gives the longest shutter speed for which stars remain point-like in an untracked exposure. It is the practical answer to the central constraint of untracked astrophotography: the sky moves, the camera does not, and any exposure longer than about one pixel of drift will smear the stars into visible trails. The formula was developed by French astrophotographers in the 2010s and has become the standard reference for the modern high-resolution digital sensor.
The three letters N, P, F stand for the three corrections that the rule applies beyond the classic 500 rule: N for Npf itself (a refinement factor), P for pixel pitch, and F for focal length. The simplified form used here collapses the constant terms into the numerator (35·f# + 30·p), which makes the rule fast enough to compute in your head on a night shoot and accurate enough to match the vast majority of practical situations.
NPF Rule Formula
The simplified form used throughout this calculator is:
where tmax is in seconds, f# is the aperture f-number, p is the pixel pitch in micrometres, and f is the focal length in millimetres. Rearranged for the other three unknowns:
p = (tmax · f − 35 · f#) / 30
f = (35 · f# + 30 · p) / tmax
The stricter, declination-aware form of the rule multiplies the simplified result by an extra factor of cos(δ) — the angle of the field above the celestial equator. Objects near the celestial pole move more slowly across the sky and tolerate longer exposures:
NPF Rule Variables
| Symbol | Meaning | Notes |
|---|---|---|
| tmax | Maximum exposure time | Longest shutter speed for acceptable star roundness |
| f# | Aperture f-number | Wide apertures reduce the numerator but gather more light |
| p | Pixel pitch | Larger pixels tolerate more drift; smaller pixels are stricter |
| f | Focal length | The only variable in the denominator; t scales as 1/f |
| δ | Declination of the field | Optional correction; near the pole, longer exposures are possible |
| θpix | Angular pixel scale | 206.265 · p / f, in arcseconds per pixel |
| ω | Sky rotation rate | 15.041 arcsec/s at the equator, times cos(δ) elsewhere |
How Each Variable Affects the Exposure
Focal length has the strongest effect: tmax is exactly proportional to 1/f, so doubling focal length halves the exposure. This is the reason telephoto astrophotography demands tracking — a 200mm lens on a modern full-frame body typically yields tmax under one second, well below what is needed to capture a decent signal. Aperture and pixel pitch enter the numerator, so their effect is milder and more subtle: a wider aperture (smaller f#) reduces the numerator and therefore shortens tmax, which is counterintuitive at first — but the reward is that much more light per second, and the wider aperture resolves the sky more sharply, so stars drift across more of the sensor's optical resolution and trail sooner.
Pixel pitch is the most camera-specific term. Cameras with large pixels (like the 12 MP Sony A7S III at 8.40 µm) tolerate substantially longer exposures than the 61 MP Sony A7R IV at 3.76 µm — over 60% longer at the same focal length and aperture. This is one reason the A7S III is a favourite among astrophotographers despite its modest resolution: its large pixels are both more sensitive per pixel and more forgiving of sky motion.
The 35·f# term captures the fact that aperture controls the sharpest angular detail the lens can transmit. A wide-open f/1.4 lens has a much smaller diffraction-limited spot than an f/8 lens stopped down, so its angular tolerance is larger and the numerator grows. The 30·p term captures the fact that the sensor itself can only sample down to roughly one pixel — any drift smaller than a pixel is invisible. Together they define the total tolerance, and dividing by focal length converts that tolerance from micrometres in the sensor plane to an angular limit on the sky.
The crop factor does not appear anywhere in the formula. This is important and often misunderstood. If you keep the pixel pitch the same and switch from full-frame to APS-C, the field of view narrows but the star drift per pixel per second is identical, because the focal length is identical. What changes is only how much of the sky is captured. Confusion arises because many photographers are used to quoting "equivalent" focal lengths, which are full-frame-equivalent values that do not belong in the NPF calculation.
NPF Rule Calculation Examples
tmax = (35 × 2.8 + 30 × 4.35) / 14 = (98 + 130.5) / 14 = 16.32 s
tmax = (98 + 130.5) / 24 = 9.52 s
tmax = (35 × 1.4 + 30 × 8.40) / 24 = (49 + 252) / 24 = 12.54 s
tmax = (35 × 1.8 + 30 × 4.35) / 50 = (63 + 130.5) / 50 = 3.87 s
tmax = (35 × 2 + 30 × 4.40) / 135 = (70 + 132) / 135 = 1.50 s
tmax = (35 × 4 + 30 × 4.35) / 300 = (140 + 130.5) / 300 = 0.90 s — tracking mandatory
Frequently Asked Questions
The acronym NPF is generally attributed to the three terms of the original French formula: N for the number of pixels of drift tolerated (typically 1), P for the pixel pitch, and F for the focal length. Some sources attribute it to the initials of the astrophotographers who popularised it, and others describe it as "Nouvelle Règle Photographique" (new photographic rule). The precise etymology is less important than the formula itself, which has become the standard reference for untracked exposures on digital sensors.
The 500 rule — t = 500/f — was developed in the film era, when grain was coarse and stars could be considered acceptably round even with several pixels of drift. Digital sensors resolve far finer detail, so the same drift that was invisible on film becomes a visible trail on a modern 45 MP or 61 MP sensor. The NPF rule corrects for this by adding a 30·p pixel term that scales the tolerance with the sensor's sampling limit, and a 35·f# aperture term that reflects the lens's resolving power. In practice NPF gives exposures 2–3× shorter than the 500 rule, which is why it is the modern standard for untracked astrophotography.
No — and this is one of the most commonly misunderstood aspects of the NPF rule. The formula uses the true focal length, not the full-frame equivalent, and the pixel pitch, not the sensor size. If you change from full-frame to APS-C with the same pixel pitch and the same lens, the star drift per pixel per second is identical because the focal length is identical. What changes is the field of view. Confusion arises because many photographers habitually convert focal lengths to full-frame equivalents, which is fine for framing decisions but wrong for NPF calculations. Always enter the physical focal length marked on the lens.
It seems counterintuitive at first: a wider aperture lets in more light, so you would expect a longer exposure to be tolerable. But the NPF rule is not about light — it is about angular resolution. A wider aperture resolves finer angular detail, so the same star drift produces a sharper, more visible trail. The 35·f# term encodes this: a smaller f# reduces the numerator, so tmax shrinks. The trade is worthwhile: even though the maximum untracked exposure is shorter at f/1.4 than at f/2.8, the amount of light gathered per second is four times higher, so the total signal in the image is usually better with the wider aperture despite the shorter exposure.
Yes, with caveats. The simplified NPF rule is calibrated for a drift of roughly one pixel, which most photographers find acceptable when the resulting image is downsampled for screen or small prints. If you plan to print large or crop deeply, you may want to halve the result as a safety margin. If your field is far from the celestial equator, you can relax it by the cos(δ) factor. The rule also assumes a static tripod; any wind, ground vibration, or mirror/shutter shock will blur the image regardless of how short the exposure is. Many astrophotographers shoot slightly shorter than the NPF result and stack multiple frames to recover the lost signal.
The NPF time is calculated for a field at the celestial equator, where stars move fastest across the sky. As you point closer to the celestial pole, the apparent angular motion slows by a factor of cos(δ), where δ is the declination of the field centre. So a Milky Way shot pointed at δ = 30° allows tmax / cos(30°) ≈ 1.15× the equatorial value, and one at δ = 60° allows 2× the value. Near the pole the correction grows very large, but so do projection distortions near the frame edge, so most photographers cap the relaxation at about δ = 60°.
Halve or third the NPF result. The rule is calibrated for roughly one pixel of trail, which corresponds to a slightly elongated star about 1.4× longer than wide when the drift is diagonal. For pixel-perfect roundness, target a drift of about 0.5 pixels, which gives tmax/2. Alternatively, use the full rigorous NPF formula with an explicit pixel tolerance parameter and set it to 0.5 instead of 1.0. The trade is that you either lose light or need more frames stacked to reach the same signal-to-noise ratio — tracking mounts exist precisely to remove this trade-off.
The NPF rule is specific to untracked astrophotography, but the underlying physics — an angular tolerance set by aperture and pixel pitch, divided by focal length — appears in other contexts. Long-exposure handheld photography uses a similar reasoning with the shutter speed set by hand-shake frequency rather than sky rotation. Satellite trails and aircraft tracks are governed by the same angular-drift calculation. The NPF rule is essentially a special case of a general angular-motion budget, which is why it is sometimes taught in the context of imaging system design rather than as a photography heuristic.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| t_max | Maximum exposure time | s |
| f_number | Lens aperture (f-number) | |
| pixel_pitch | Camera sensor pixel pitch | µm |
| focal_length | Lens focal length | mm |
What it means
The NPF (or 500‑rule alternative) is a more precise formula for maximum exposure time in untracked astrophotography. It considers the aperture (f‑number) and pixel size (in µm), giving a shorter, more realistic time than the 500 rule, especially for modern high‑resolution sensors. It reduces trailing at the pixel level. It is used by advanced astrophotographers to capture sharp images with minimal trailing. Understanding this helps in achieving the best possible image quality in wide‑field astrophotography.
Worked example
NPF Rule (Simplified) – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| f_number | 2.8 |
| pixel_pitch (µm) | 4.3 |
| focal_length (mm) | 24 |
| Parameter | Value |
|---|---|
| f_number | 1.8 |
| pixel_pitch | 5.9 |
| focal_length | 35 |
Common mistakes
- NPF rule: t_max = (35 × f_number + 30 × pixel_pitch) / focal_length.
- f_number: The aperture f‑ratio – dimensionless.
- Pixel pitch: The size of one pixel in microns (µm).
- Focal length: In mm.
- Result: Maximum exposure time in seconds – more accurate than 500 rule.
Applications
The NPF rule (simplified) provides a more accurate formula for maximum exposure time before star trailing, considering pixel size and aperture. t_max = (35 * f_number + 30 * pixel_pitch) / focal_length. This accounts for the actual resolution of the camera sensor. Advanced astrophotographers use it for precise exposure planning to avoid trailing when using high‑resolution sensors and long focal lengths. By applying the NPF rule, photographers can maximise exposure time without star trails, essential for capturing faint objects in tracked or untracked setups. This improves image quality and reduces the need for stacking many short exposures.
- Precise exposure time calculation for high‑resolution astrophotography
- Optimisation of settings for tracked and untracked imaging
- Selection of appropriate lenses and camera settings
- Reduction of star trailing in deep‑sky images
- Education on modern astrophotography techniques
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