Telescope Limiting Magnitude Calculator
Every telescope has a limiting magnitude: the faintest star it can show under ideal dark-sky conditions with a dark-adapted eye. The standard formula relating limiting magnitude to aperture is m = 2 + 5 * log10(D), where D is the aperture in millimeters. This formula is an empirical approximation widely used in amateur astronomy. A 100 mm telescope reaches about magnitude 12, while a 200 mm instrument can reach magnitude 13.5. Enter your telescope's aperture below to find its theoretical limiting magnitude and see how it compares to common reference objects in the sky.
Limiting magnitude formula
m(lim) = 2 + 5 * log10(D)
Where D is the aperture in millimeters and log10 is the base-10 logarithm. The naked-eye limiting magnitude under excellent skies is approximately 6.5. The gain over naked eye equals the telescope limiting magnitude minus 6.5.
Magnitude by aperture reference
60 mm: ~m 11.0. 100 mm: ~m 12.0. 150 mm: ~m 12.9. 200 mm: ~m 13.5. 300 mm: ~m 14.4. 400 mm: ~m 15.0. 500 mm: ~m 15.5. These are theoretical maxima under ideal conditions. Real-world performance depends on sky quality, collimation, eyepiece quality, and observer experience.
Limiting magnitude: frequently asked questions
What is limiting magnitude?
Limiting magnitude is the faintest stellar magnitude that a telescope can detect under ideal dark-sky conditions. The magnitude scale is logarithmic: each step of 1 magnitude represents a brightness factor of about 2.512. Higher numbers mean fainter objects.
What is the formula for telescope limiting magnitude?
The standard formula is: m = 2 + 5 * log10(aperture in mm). For example, a 100 mm aperture gives m = 2 + 5 * log10(100) = 2 + 10 = 12. This is an approximation assuming good skies and a dark-adapted eye.
Does magnification affect limiting magnitude?
Yes, but indirectly. Higher magnification darkens the sky background, improving contrast for point sources (stars). However, this formula is based on aperture alone, which is the primary driver of light-gathering ability.
What can I see at magnitude 12?
At magnitude 12 you can resolve many globular clusters into individual stars, see details in larger galaxies, and observe many planetary nebulae. The naked eye under dark skies typically reaches magnitude 6 to 6.5.
How does sky quality affect limiting magnitude?
Light pollution reduces limiting magnitude. This formula assumes an ideal Bortle Class 1 or 2 sky. Under suburban skies (Bortle 6), subtract 1 to 2 magnitudes. Under city skies (Bortle 8-9), subtract 3 or more magnitudes.
Official sources
- NASA Goddard Space Flight Center: imagine.gsfc.nasa.gov.
- USNO Astronomical Almanac Online: aa.usno.navy.mil.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.