Telescope Limiting Magnitude Calculator
The faintest star a telescope can show depends mostly on how much light its aperture gathers compared with the unaided eye. A larger aperture pulls in more photons and reaches fainter stars. The standard estimate adds to the naked-eye limit five times the base-10 logarithm of the ratio of the telescope aperture to the dark-adapted eye pupil. This calculator returns the estimated limiting magnitude and the light-gathering gain over the eye. The naked-eye limit and eye-pupil diameter are user-editable so you can match your own dark-sky conditions and age.
Limiting magnitude formula
gain in magnitudes = 5 * log10(aperture / eye pupil)
limiting magnitude = naked-eye limit + gain
light gain (times) = (aperture / eye pupil)^2
inches = aperture mm / 25.4
The aperture-to-pupil area ratio sets how much more light is collected. Five times the log of the diameter ratio converts that light gain into a magnitude gain, which adds to the unaided-eye limit.
Limiting magnitude notes
- This is a dark-sky estimate; light pollution makes the real limit shallower.
- A 7 mm dark-adapted pupil suits a young observer; use 5 to 6 mm if older.
- Naked-eye limit near 6 assumes a good dark site.
- Doubling aperture adds about 1.5 magnitudes of depth.
- Sky transparency and magnification shift the practical result.
Limiting magnitude: frequently asked questions
What is limiting magnitude?
Limiting magnitude is the faintest star a telescope can reveal, on the magnitude scale where larger numbers are fainter. A bigger aperture collects more light, so it reaches fainter stars. The common estimate is the naked-eye limit plus 5 times the base-10 logarithm of the ratio of telescope aperture to eye-pupil diameter.
What aperture units does the formula use?
The classic form uses millimeters: limiting magnitude equals about 2.7 plus 5 times log10 of the aperture in millimeters. This calculator uses an explicit reference based on the dark-adapted eye pupil, which is user-editable, so you can tune the assumed eye pupil and naked-eye limit.
Why is the dark-adapted eye pupil important?
The formula compares how much light the telescope gathers to how much the unaided eye gathers. The eye's dark-adapted pupil, often taken as about 7 mm for a young observer, sets the reference aperture. Older observers may use a smaller value such as 5 to 6 mm.
Is the real limiting magnitude always this faint?
No. Sky brightness, light pollution, transparency, magnification, and the observer's experience all change the practical limit. The formula gives an ideal dark-sky estimate. Under bright urban skies the true limit is much shallower.
Does higher magnification help see fainter stars?
For point sources like stars, raising magnification darkens the sky background and can reveal slightly fainter stars up to a point. The aperture sets the fundamental limit, but eyepiece choice and sky conditions shift the achievable result around it.
Official sources
- NASA Imagine the Universe: light gathering and magnitude.
- NASA Science: telescopes and stellar brightness.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.