In astronomy, absolute magnitude is the apparent magnitude, m, an object would have if it were at a standardized distance away. It allows the overall brightnesses of objects to be compared without regards to distance. Absolute Magnitude for stars and galaxies (M)
In stellar and galactic astronomy, the standard distance is 10 parsecs (about 32.616 light years, or 3×10^{14} kilometres). A star at ten parsecs has a parallax of 0.1" (100 milli arc seconds). In defining absolute magnitude it is necessary to specify the type of electromagnetic radiation being measured. When referring to total energy output, the proper term is bolometric magnitude. The dimmer an object (at a distance of 10 parsecs) would appear, the higher its absolute magnitude. The lower an object's absolute magnitude, the higher its luminosity. A mathematical equation relates apparent magnitude with absolute magnitude, via parallax. Many stars visible to the naked eye have an absolute magnitude which is capable of casting shadows from a distance of 10 parsecs; Rigel (7.0), Deneb (7.2), Naos (7.3), and Betelgeuse (_5.6). For comparison, Sirius has an absolute magnitude of 1.4 and the Sun has an absolute visual magnitude of 4.83 (it actually serves as a reference point). Absolute magnitudes generally range from 10 to +17.
Computation You can compute the absolute magnitude of a star given its apparent magnitude and distance: where is 10 parsecs (≈ 32.616 lightyears) and is the star's distance; or: where is the star's parallax and is 1 arcsec.
Example  Rigel has a visual magnitude of m_{V}=0.18 and distance about 773 lightyears.
 M_{V}Rigel = 0.18 + 5*log_{10}(32.616/773) = 6.7
 Vega has a parallax of 0.133", and an apparent magnitude of +0.03
 M_{V}Vega = 0.03 + 5*(1 + log_{10}(0.133)) = +0.65
 Alpha Centauri has a parallax of 0.750" and an apparent magnitude of _0.01
 M_{V}α Cen = _0.01 + 5*(1 + log_{10}(0.750)) = +4.37
Apparent magnitude Given the absolute magnitude , you can also calculate the apparent magnitude from any distance : Absolute Magnitude for planets (H) For planets, comets and asteroids a different definition of absolute magnitude is used which is more meaningful for nonstellar objects. In this case, the absolute magnitude is defined as the apparent magnitude that the object would have if it were one astronomical unit (au) from both the Sun and the Earth and at a phase angle of zero degrees. This is a physical impossibility, but it is convenient for purposes of calculation.
Calculations Formula for H: (Absolute Magnitude) where is the apparent magnitude of the Sun at 1 au (_26.73), is the geometric albedo of the body (a number between 0 and 1), is its radius and is 1 au (≈149.6 Gm).
Example Moon: = 0.12, = 3476/2 km = 1738 km Apparent magnitude The absolute magnitude can be used to help calculate the apparent magnitude of a body under different conditions. where is 1 au, is the phase angle, the angle between the SunBody and BodyObserver lines; by the law of cosines, we have: is the phase integral (integration of reflected light; a number in the 0 to 1 range)  Example: (An ideal diffuse reflecting sphere)  A reasonable first approximation for planetary bodies
 A fullphase diffuse sphere reflects 2/3 as much light as a diffuse disc of the same diameter
 Distances:
 is the distance betweeen the observer and the body
 is the distance between the Sun and the body
 is the distance between the obverser and the Sun
Example Moon  = +0.25
 = = 1 au
 = 384.5 Mm = 2.57 mau
 How bright is the Moon from Earth?
 Full Moon: = 0, ( ≈ 2/3)
 (Actual 12.7) A full Moon reflects 30% more light at full phase than a perfect diffuse reflector predicts.
 Quarter Moon: = 90°, (if diffuse reflector)
 (Actual approximately 11.0) The diffuse reflector formula does better for smaller phases.
See also HertzsprungRussell diagram Relates absolute magnitude or luminosity versus spectral color or surface temperature.
