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.