Photography / Night sky
Star Trails Calculator: NPF Shutter and Stacking Plan
Estimate an untracked shutter time for point stars with the 500 and complete NPF rules. Plan an intentional star-trail arc from declination, per-frame exposure and gaps, with frame count and total shooting time.
Star Trails Calculator: NPF Shutter and Stacking Plan: Uses the complete NPF expression at precision factor k = 1 and the rough 500 rule. The stacking planner assumes motion at 15 degrees per hour at the celestial equator, scaled by cos(declination), and rounds up to whole frames without adding a final gap. Runs 100% locally in your browser with zero server file uploads.
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Point stars: maximum shutter estimate
500 rule: t = 500 / (f × crop) NPF: t = (16.9N + 0.10f + 13.7p) / (f × cos δ)
NPF uses actual focal length in mm and pixel pitch in micrometres. Pixel pitch equals sensor width in mm × 1000 / image width in pixels. Precision factor k = 1 is the stricter setting. NPF often gives shorter times than the 500 rule, but the ordering depends on the inputs. Inspect a test frame; these rules are estimates for an untracked camera.
NPF formula: Frédéric Michaud, Société Astronomique du Havre.
Intentional trails: stacking planner
Target needs 120 minutes. Whole frames cover about 30.092 degrees with 116.5 minutes of open-shutter time. No gap is added after the last frame.
Rate ≈ 15 × cos δ degrees/hour Target seconds = arc / rate × 3600 Frames = ceil((target seconds + gap) / (shutter + gap)) Total seconds = frames × shutter + (frames − 1) × gap
Arc means angular path length on the celestial sphere, scaled by cos(declination), rather than rotation angle around the pole. The 15 degrees/hour model is approximate. Lens projection changes the visible trail length. Gaps can leave dotted trails; long-exposure noise reduction can add extra gaps.
NPF and the 500 rule
Frédéric Michaud, Société Astronomique du Havre, La Règle NPF: https://sahavre.fr/wp/regle-npf-rule/ . Complete formula: t = k(16.9N + 0.10f + 13.7p) / (f cos δ), with k = 1 here. N is aperture, f is actual focal length in mm and p is pixel pitch in micrometres. The author's page also describes the 500 rule as 500 / (crop times focal length).
Apparent sky motion
US Naval Observatory, sidereal time: https://aa.usno.navy.mil/data/siderealtime . Stars rotate about once per sidereal day. The planner uses the requested approximate 15 degrees/hour model; its cosine scaling represents path length along a declination circle rather than position angle around the pole. Gaps interrupt the trail.
How to use it
- Enter focal length, crop factor, aperture, pixel pitch and declination.
- Compare the 500 and complete NPF estimates for point stars.
- Set a target angular path length and frame timing to plan intentional trails.
Privacy & limitations
Night sky and camera inputs stay in your browser.
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Frequently asked questions
Why do I need pixel pitch?
Smaller pixels reveal motion sooner. Pixel pitch in micrometres is sensor width in millimetres times 1000 divided by image width in pixels. Enter actual focal length for NPF; crop factor is used only by the 500 rule.
Does the target arc mean rotation around the pole?
Here it means angular path length on the celestial sphere. That path slows by cos(declination); rotation angle around the pole is a different measure. Lens projection also affects trail length in the final photograph.
Is NPF always shorter than the 500 rule?
No. It is generally stricter for modern camera settings, but ordering depends on aperture, pixel pitch and declination. These are estimates; inspect a test exposure.
Why is declination limited below 90 degrees?
The cosine model approaches zero motion at the pole, making the estimated duration unbounded. Values from -89.9 to 89.9 degrees are supported.
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