Free Limiting Magnitude Calculator
Estimate the faintest star visible through a telescope: m_lim = 2 + 5 log10(D) where D is aperture in mm.
mm
Limiting Magnitude
13.5 mag
Gain Over Naked Eye7.3 mag
Limiting Magnitude vs Aperture
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).
Example Calculation
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