Absolute Magnitude Calculator

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 ≈ −7.0 at its ~260 pc distance (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.

Absolute magnitude is a luminosity in disguise. Once distance is out of the way, M is just a logarithmic measure of how much light the star puts out, so you can compare any star directly against the Sun:

L / L☉ = 10^((4.83 - M) / 2.5)

Betelgeuse at M = -5.85 works out to roughly 18,700 times the Sun. One catch worth knowing: an M taken in the visual band gives you a visual luminosity, not the star’s total energy output. Betelgeuse is cool enough that most of its light leaves in the infrared where the eye and the V filter never see it, so its true bolometric luminosity is several times higher than the visual figure. The same correction runs the other way for a very hot blue star, which dumps much of its output into the ultraviolet.