Limiting Magnitude Calculator Formula
Understand the math behind the limiting magnitude calculator. Each variable explained with a worked example.
Formulas Used
Limiting Magnitude
limiting_mag = 2 + 5 * log10(aperture)Gain Over Naked Eye
gain_over_eye = 5 * log10(aperture / 7)Variables
| Variable | Description | Default |
|---|---|---|
aperture | Aperture(mm) | 200 |
How It Works
Limiting Magnitude of a Telescope
m_lim ≈ 2 + 5 log10(D) (D in mm)
This empirical formula assumes a dark sky, normal magnification, and good optics. The naked eye (7 mm pupil) reaches about +6.0.
Each doubling of aperture adds about 1.5 magnitudes (3.6× fainter stars).
Worked Example
A 200 mm (8-inch) telescope.
- 01m_lim = 2 + 5 × log10(200)
- 02= 2 + 5 × 2.301 = 2 + 11.505 = 13.5
- 03Can see stars down to about magnitude 13.5.
- 04Gain over eye: 5 × log10(200/7) = 5 × 1.456 = 7.3 mag
Frequently Asked Questions
What affects limiting magnitude in practice?
Light pollution, sky transparency, magnification, observer experience, and telescope optics quality all affect the practical limit.
What magnitude are the faintest galaxies?
Many Messier galaxies are magnitude 8-10, easily visible in a 200 mm scope. The Hubble Ultra Deep Field reaches magnitude ~30.
Does magnification help?
Moderate magnification darkens the sky background, improving contrast for faint stars. But too much magnification dims the image. Optimal is about 1× per mm of aperture for faint objects.
Ready to run the numbers?
Open Limiting Magnitude Calculator