Apparent Magnitude Converter

Brightness Ratio Examples

1 magnitude difference: 2.512× brighter
2 magnitude difference: 6.31× brighter
3 magnitude difference: 15.85× brighter
5 magnitude difference: 100× brighter

Magnitude Scale Ranges

Negative magnitudes: Very bright (Sun, Moon, planets)
0 to +3: Bright stars
+3 to +6: Naked eye visible
+6 to +30: Telescope required

Distance Modulus

m - M = 5 log₁₀(d) - 5
At 10 pc: m = M (definition)
At 100 pc: m - M = 5
At 1000 pc: m - M = 10

Luminosity Calculation

L/L☉ = 10^((4.83 - M)/2.5)
M = 4.83: L = 1 L☉ (Sun)
M = -0.17: L = 100 L☉
M = -5.17: L = 10,000 L☉

Example 1: Sirius Distance Modulus

Apparent magnitude (m): -1.46
Absolute magnitude (M): +1.42
Distance modulus: -1.46 - 1.42 = -2.88
Distance: 10^((-2.88+5)/5) = 2.64 pc = 8.6 ly

Example 2: Betelgeuse Luminosity

Absolute magnitude (M): -5.85
Sun absolute magnitude: +4.83
Difference: 4.83 - (-5.85) = 10.68
Luminosity: 10^(10.68/2.5) = 126,000 L☉

Example 3: Brightness Comparison

Sirius: m = -1.46
Vega: m = +0.03
Difference: 1.49 magnitudes
Brightness ratio: 2.512^1.49 = 3.94×

Example 4: Absolute Magnitude from Distance

Star at 100 pc, m = +10
M = m - 5 log₁₀(d/10)
M = 10 - 5 log₁₀(100/10)
M = 10 - 5(1) = +5