Telescope Limiting Magnitude Calculator

Limiting magnitude is the faintest star a telescope can detect under ideal conditions. The larger the aperture (lens or mirror diameter), the more light the telescope gathers and the fainter the objects it can reveal.

The formula: Limiting magnitude = 2.7 + 5 × log10(aperture in mm)

This formula assumes perfect dark-sky conditions and a well-adapted eye. In practice, light pollution, atmospheric conditions, and optical quality all reduce the actual limiting magnitude.

For comparison, the naked eye can see stars down to about magnitude 6 under dark skies. Each magnitude step represents a brightness factor of about 2.512. A magnitude 1 star is 100 times brighter than a magnitude 6 star.

Common telescope apertures and their limits:

• 60mm (2.4"): ~11.6 magnitude, good for Moon, planets, bright deep-sky objects
• 80mm (3.1"): ~12.2 magnitude, shows more detail in nebulae and clusters
• 130mm (5.1"): ~13.3 magnitude, resolves globular clusters, faint galaxies
• 200mm (8"): ~14.2 magnitude, serious deep-sky observing
• 300mm (12"): ~15.1 magnitude, faint galaxies, planetary nebulae
• 400mm (16"): ~15.7 magnitude, near the visual limit for amateur astronomy

Light-gathering power compared to the naked eye: Light gathering = (Aperture / 7)² where 7mm is the typical dark-adapted pupil diameter.

Magnification is a separate consideration. Maximum useful magnification is roughly 2× the aperture in mm (a 200mm scope tops out near 400×).
Higher magnification does not reveal fainter objects. Only aperture does that, which is the single most useful thing a beginner can learn about telescope specs.

Resolution (ability to split close double stars) is also determined by aperture: Dawes' limit (arcseconds) = 115.8 / aperture in mm

That constant is Dawes’ original 4.56 arcseconds per inch converted to millimetres. It is often printed as 116, which is the same figure rounded off.

How the sky conditions change the answer. The theoretical limit above assumes a properly dark site and a fully dark-adapted eye. Almost nobody observes under those conditions, so this calculator subtracts a penalty for where you actually are:

Those penalties are worth more than aperture is. A 200 mm scope in the city reaches magnitude 10.7, while an 80 mm refractor at a dark site reaches 12.2. Driving an hour beats buying a bigger tube, and it is a good deal cheaper.