Apparent Magnitude Calculator Formula

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

Use the Apparent Magnitude Calculator

Formulas Used

Apparent Magnitude

app_magnitude = abs_magnitude + 5 * log10(distance_pc / 10)

Distance Modulus

distance_modulus = 5 * log10(distance_pc / 10)

Variables

VariableDescriptionDefault
abs_magnitudeAbsolute Magnitude (M)4.83
distance_pcDistance(pc)10

How It Works

Apparent Magnitude

Apparent magnitude (m) is how bright a star appears from Earth.

Distance Modulus

m = M + 5 log10(d / 10)

  • *M* = absolute magnitude (brightness at 10 pc)
  • *d* = distance in parsecs

    • Lower magnitudes are brighter. Each magnitude step is a factor of ≈2.512 in brightness.

    Worked Example

    The Sun has M = 4.83. How bright would it be at 10 pc?

    abs_magnitude = 4.83distance_pc = 10
    1. 01m = M + 5 log10(d/10)
    2. 02m = 4.83 + 5 log10(10/10)
    3. 03m = 4.83 + 5 × 0 = 4.83
    4. 04At 10 pc the Sun would be a modest naked-eye star.

    Ready to run the numbers?

    Open Apparent Magnitude Calculator