Telescope Limiting Magnitude Calculator

How it works

Light grasp = (D ÷ 7 mm)² × transmission; gain = 2.5 log₁₀(grasp); limiting magnitude ≈ 2.7 + 5 log₁₀(D mm) under a dark sky, adjusted ≈ 0.7 mag per magnitude of sky brightness; higher power adds up to ~1 mag by darkening the background

A telescope reaches fainter stars than the eye because its objective collects more light — proportional to the square of the aperture — and every 2.512-fold increase in light is one magnitude. The classic rule 2.7 + 5 log D gives about 14.2 for a 200 mm aperture under a dark sky; real limits move with sky brightness, transparency, seeing, optical cleanliness and the observer’s experience, and are usually a magnitude or so deeper at high magnification because the sky background darkens while stars stay point-like. Light pollution costs less than one-for-one through a telescope, but a city sky still knocks a magnitude or two off. The figure applies to stars: galaxies and nebulae spread their light over an area and are governed by contrast against the sky, so a “mag 12” galaxy can be invisible where a mag 13 star is easy.

Worked example

A 200 mm reflector (85% transmission) has 694× the light grasp of a 7 mm pupil — 7.1 magnitudes. Under a suburban mag 6.0 sky it reaches about magnitude 13.9 at moderate power and perhaps 14.1 at 120×; that takes in Neptune’s moon Triton and the quasar 3C 273, with Pluto borderline.

Frequently asked questions