Telescope limiting magnitude calculator.

How limiting magnitude is estimated

The telescope gains 5 × log₁₀(D / D₀) magnitudes over the naked eye, where D is the telescope aperture and D₀ is the eye's dark-adapted pupil, both in the same units. Wikipedia writes the telescope limit as m = 5 × log₁₀(D) + N with D in centimetres and N suggested between 6.8 and 8.7, and its worked model uses a 0.7 cm (7 mm) eye pupil with N = 7.69, which is why 7 mm is the default here. Add the gain to your naked-eye limit to get the telescope's limit. Light grasp is (D / D₀)².

Worked example. A 200 mm telescope, 7 mm pupil, naked-eye limit 6.0: gain = 5 × log₁₀(200 / 7) = 7.28, so the limit is about magnitude 13.3, and the scope collects 816 times the light of your eye. An 80 mm scope gives a gain of 5.29 and a limit near 11.3.

The result is a simple estimate. Wikipedia notes that magnification darkens the background sky, which is why stars invisible to the naked eye become visible in a telescope. For a 200 mm scope its N range works out to about 13.3 to 15.2, so 13.3 is the conservative end. Sky darkness, optical quality, magnification and observer experience all shift the real answer.