About the Telescope Limiting Magnitude Calculator
This telescope limiting magnitude calculator estimates the faintest star you can expect to see through a telescope of a given aperture, scaled from how faint you can see with the naked eye under your sky. It also gives the light-gathering power compared with your eye, the Dawes and Rayleigh resolution limits for splitting double stars, and the useful magnification range.
Amateur astronomers use it when choosing a first telescope, deciding whether a faint galaxy or the companion of a double star is within reach, or comparing how much an upgrade from 4 to 8 inches will really show. Enter your naked-eye limiting magnitude (NELM) — about 6 to 6.5 at a dark rural site, 4 to 5 in the suburbs, 3 or less in a city.
The estimate assumes a dark-adapted eye whose pupil sets the naked-eye light grasp, perfect optics and steady air. Real-world limits vary by about ±1 magnitude with observer experience, magnification, optical transmission, central obstruction and seeing; experienced observers using averted vision often go fainter.
With the default inputs, the limiting magnitude is 13.28 mag. Change any value above to recalculate instantly.
How to use the telescope limiting magnitude calculator
- 1Enter your telescope’s aperture in millimetres.
- 2Estimate your naked-eye limiting magnitude from how dark your sky is.
- 3Adjust the pupil diameter if you are older or know your own value.
- 4Read the limiting magnitude and how many magnitudes the scope adds.
- 5Check the Dawes and Rayleigh limits to see which double stars you can split.
Formula and method
A telescope collects light in proportion to the area of its aperture, so compared with your eye it gathers (D/d)² times more, where d is your pupil diameter. Because the magnitude scale is logarithmic (5 magnitudes = 100× in brightness), that light grasp becomes a gain of 2.5·log₁₀((D/d)²) = 5·log₁₀(D/d) magnitudes added to your naked-eye limit.
Resolution is set by diffraction. The Dawes limit (116/D in mm, from 4.56″ per inch) is an empirical limit for splitting equal-brightness double stars; the Rayleigh criterion 1.22λ/D at 550 nm gives about 138/D arcseconds. The useful magnification range runs from D/d (exit pupil equals your pupil) to about 2× the aperture in mm (50× per inch).
- m_lim
- Faintest stellar magnitude visible through the telescope
- NELM
- Naked-eye limiting magnitude at your site
- D
- Telescope aperture (mm)
- d
- Dark-adapted eye pupil diameter (mm)
- λ
- Wavelength of light, 550 nm (green)
Worked examples
8-inch (200 mm) telescope under dark skies
200 ÷ 7 = 28.6, so the scope gathers 816× more light than the eye — a gain of 5·log₁₀(28.6) = 7.28 magnitudes. With NELM 6 the limit is about magnitude 13.3, enough for thousands of galaxies. Dawes limit: 116 ÷ 200 = 0.58″.
70 mm refractor from the suburbs (NELM 5, 6 mm pupil)
Light grasp is (70/6)² = 136×, adding 5.33 magnitudes to the naked-eye limit of 5, for about magnitude 10.3. It can split doubles down to roughly 1.7″.
4-inch (102 mm) scope at a very dark site (NELM 6.5)
6.5 + 5·log₁₀(102/7) = 6.5 + 5.82 ≈ 12.3. The Dawes limit is 116 ÷ 102 ≈ 1.14″ and the Rayleigh limit about 1.36″.
16-inch (406 mm) Dobsonian at a dark site
A 406 mm mirror collects (406/7)² = 3,364× more light, reaching about magnitude 15.3. In practice the atmosphere rarely allows more than about 300–400× even though 812× is the theoretical useful maximum.
Frequently asked questions
What is limiting magnitude?+
It is the brightness of the faintest star you can see, on the astronomical magnitude scale where larger numbers mean fainter objects. The naked eye reaches about magnitude 6 under dark skies; each additional magnitude is 2.512 times fainter.
What is the Dawes limit?+
An empirical rule found by William Dawes in the 1860s: a telescope of aperture D inches can just separate two equally bright stars about 4.56/D arcseconds apart — about 116/D in millimetres. It is slightly tighter than the theoretical Rayleigh criterion.
How faint can an 8-inch telescope see?+
Roughly magnitude 13 to 14 under dark skies, depending on the observer and conditions. This formula gives about 13.3 for a 200 mm aperture with a naked-eye limit of 6; experienced observers with averted vision may reach 14 or more.
Does magnification affect limiting magnitude?+
Yes, moderately. Higher magnification darkens the sky background more than it dims stars, so stellar limiting magnitude usually improves up to a point. The formula here is a typical-case estimate, not a function of eyepiece choice.
Why does light pollution reduce what a telescope can show?+
A telescope magnifies the sky glow along with the stars, so a brighter background hides faint stars and galaxies. That is why the naked-eye limit at your site is part of the calculation: every magnitude lost to light pollution is lost through the eyepiece too.