Star magnitude and brightness calculator
The magnitude scale is logarithmic and backwards: five magnitudes is exactly a factor of a hundred in brightness, and brighter means smaller.
parsecs
Brightness ratio
100.0000
- Absolute magnitude at that distance
- 1.0000
- Distance modulus
- 0.0000
- Distance in light-years
- 32.616
- Pogson's ratio, one magnitude
- 1.584 893
- Magnitude difference
- 5.000
Show the working
- First magnitude = 1
- Second magnitude = 6
- Distance = 10
- Brightness ratio = 10^((6 - 1) / 2.5) = 100
- Pogson's ratio, one magnitude = 10^(1/5) = 1.584 89
- Absolute magnitude at that distance = 1 - 5 * log10(10) + 5 = 1
- Distance modulus = 5 * log10(10) - 5 = 0
- Distance in light-years = 10 * 3.2615637769 = 32.6156
- flux_ratio_db = (6 - 1) * 4 / 2.5 * 2.5 = 20
- Magnitude difference = 6 - 1 = 5
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- brightness ratio = 10^(delta m / 2.5)
- one magnitude = 100^(1/5) = 2.511 886...
- absolute magnitude M = m - 5 log10(d in parsecs) + 5
The scale was fixed so that a difference of exactly five magnitudes is a factor of exactly 100. Everything else follows from that.
The Sun is magnitude -26.74 apparent and +4.83 absolute.
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