Limiting Magnitude Calculator Formula

Understand the math behind the limiting magnitude calculator. Each variable explained with a worked example.

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Formulas Used

Limiting Magnitude

limiting_mag = 2 + 5 * log10(aperture)

Gain Over Naked Eye

gain_over_eye = 5 * log10(aperture / 7)

Variables

VariableDescriptionDefault
apertureAperture(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.

aperture = 200
  1. 01m_lim = 2 + 5 × log10(200)
  2. 02= 2 + 5 × 2.301 = 2 + 11.505 = 13.5
  3. 03Can see stars down to about magnitude 13.5.
  4. 04Gain over eye: 5 × log10(200/7) = 5 × 1.456 = 7.3 mag

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