Absolute Magnitude Calculator
Calculate a star's absolute magnitude from apparent magnitude and distance, or find distance from magnitudes.
Includes distance modulus.
Apparent magnitude (m) is how bright a star looks from Earth. Absolute magnitude (M) is how bright it would look if placed exactly 10 parsecs (32.6 light-years) from Earth. This removes the effect of distance and lets us compare stars fairly.
The distance modulus formula:
M = m - 5 × log₁₀(d) + 5
Or equivalently:
μ = m - M = 5 × log₁₀(d / 10)
Where d is the distance in parsecs and μ is called the distance modulus.
Solving for distance:
d = 10^((m - M + 5) / 5) parsecs
Solving for apparent magnitude:
m = M + 5 × log₁₀(d) - 5
Reference stars:
- Sun: m = −26.74, M = +4.83 (about 10 pc away it would be barely visible)
- Sirius: m = −1.46, M = +1.43, distance 2.64 pc
- Rigel: m = +0.13, M = −7.84 (intrinsically one of the most luminous visible stars)
- Betelgeuse: m = +0.42, M = −5.85
The magnitude scale is logarithmic: A difference of 5 magnitudes = a factor of exactly 100 in brightness. A difference of 1 magnitude = a factor of ~2.512 (the fifth root of 100). Lower magnitude = brighter. Negative magnitude = very bright.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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