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Calcimator

Telescope Limiting Magnitude

Calculate the faintest star visible through a telescope based on aperture and sky brightness conditions.

Inputs

mm
mag/arcsec²

Results

Practical Limiting Mag

14.71 mag

Theoretical Limit

14.21 mag

Naked Eye Limit6.93 mag
Magnitude Gain7.28 mag
Light Gathering816.3× eye
Dawes Resolution0.58 arcsec
Rayleigh Resolution0.69 arcsec
Stars Visible (est.)33,349,551
How to Use This Calculator
  1. Enter your Telescope Aperture (mm) — a 200 mm (8-inch) Dobsonian is a common deep-sky instrument.
  2. Enter Sky Brightness (mag/arcsec²): city skies are ~18, suburban ~20, rural ~21.5, excellent dark sites ~22.
  3. Read the Practical Limiting Magnitude — objects fainter than this number will not be visible.
  4. Compare with Naked Eye Limit (~6.5 mag) to see the Magnitude Gain your telescope provides.
  5. Use Dawes Resolution (arcsec) to determine whether close double stars can be split at your aperture.

How the result changes with Sky Brightness

Sky BrightnessPractical Limiting MagTheoretical Limit
1712.71 mag14.21 mag
1813.21 mag14.21 mag
2014.21 mag14.21 mag
2215.21 mag14.21 mag

What each input means

Telescope Aperture
Primary mirror or lens diameter in millimeters (e.g., 70 = starter, 200 = 8" Dob, 400 = 16")
Sky Brightness
Sky background brightness (18 = city center, 20 = suburban, 21.5 = rural, 22 = excellent dark site)

How this is calculated

Formula

m_lim ≈ 2.7 + 5 × log₁₀(aperture_mm)

Worked example, using the default values

  1. Identify Input Parameters
    Telescope Aperture = 200, Sky Brightness = 21 = 2 input(s) provided
  2. Calculate Practical Limiting Mag
    Practical Limiting Mag
    14.71 = 14.71
  3. Calculate Theoretical Limit
    Theoretical Limit
    14.21 = 14.21
  4. Calculate Naked Eye Limit
    Naked Eye Limit
    6.93 = 6.93
  5. Calculate Magnitude Gain
    Magnitude Gain
    7.28 = 7.28

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