Limiting Magnitude Calculator
The faintest star a telescope of a given aperture shows to the eye under a dark sky — with its light-gathering power against the naked eye and how much a brighter sky costs.
A telescope’s advantage is its aperture: light grasp goes as the square of the diameter, and each factor of 2.
How the limiting magnitude calculator works
A telescope’s advantage is its aperture: light grasp goes as the square of the diameter, and each factor of 2.512 in light is one magnitude. The usual rule for the visual limit is 2.7 + 5 log₁₀(D in mm) under a dark sky with an experienced observer at moderate magnification — about 13.5 for a 150 mm telescope. Light pollution takes 2–4 magnitudes off; a camera goes far deeper by stacking exposures.
Formula: m_lim ≈ 2.7 + 5 log₁₀(D_mm) − sky penalty; light grasp = (D ÷ 7 mm)²
Worked examples
| Inputs | Limiting magnitude | Note |
|---|---|---|
| 150 mm under a dark sky | 13.6 | 13.6 |
| 50 mm binoculars in the suburbs | 9.7 | 9.7 |
| A 400 mm Dobsonian, dark sky | 15.7 | 15.7 |
FAQFrequently asked questions
Why does the formula give one number when observers disagree?
Because the real limit depends on magnification (higher magnification darkens the background and helps), eye health, experience, transparency and how long you look. Published limits differ by a magnitude or more; this is the conventional middle.
Does magnification help?
Up to a point — it spreads the sky glow but not a star, so the star stands out. The useful maximum is about 2× the aperture in millimeters; beyond that the image dims and blurs.
How much deeper does a camera go?
Far deeper: a few minutes of exposure with a modern sensor beats the eye by 4–6 magnitudes, and stacking hours goes further still. The visual limit is about the eye, not the optics.
What about the Bortle scale?
Bortle 1–3 skies match the dark setting here (naked-eye limit 6.5–7), Bortle 5–6 the suburban one, Bortle 8–9 the urban. The penalty applies to faint extended objects even more than to stars.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G and the speed of light
- IAU 2015 Resolution B3 — nominal solar and planetary conversion constants — the astronomical unit, solar mass and planetary radii
- NASA — the US space agency
Last checked: September 2026. Constants are CODATA 2018 (G, c) and IAU 2015 nominal values (solar and planetary parameters).