The 'distance modulus' is the difference between the apparent magnitude and absolute magnitude of a celestial object*(m - M)*, and provides a measure of the distance to the object,*r*.where m = apparent magnitude of the star M = absolute magnitude of the star, and r = distance to the star in parsecs This table shows the apparent and absolute visual magnitudes of some stars and their distances:

Star m _{v}M _{v}d (pc) Sun -26.8 4.83 Alpha Centauri -0.3 4.1 1.3 Canopus -0.72 -3.1 30.1 Rigel 0.14 -7.1 276.1 Deneb 1.26 -7.1 490.8 We can derive the expression for distance modulus by using the relation between the flux ratio of two stars and their apparent magnitudes:

where flux from stars 1 and 2 apparent magnitude of stars 1 and 2 Consider a star of luminosity

*L*and apparent magnitude*m*, at a distance*r*. Now we apply the relation for the ratio of the flux we receive from the star,*F*, and the flux we would receive if the star was at a distance of 10 parsec,*F*. Identifying_{10}*m*as the apparent magnitude of the star and_{1}*m*as the absolute magnitude, the last equation becomes:_{2}where m = apparent magnitude of the star M = absolute magnitude of the star F = flux we receive from the star, and F _{10}=flux we would receive if the star was at 10 parsecs The flux and luminosity of a star are related by:

Substituting for

*F*and*F*,_{10}*L*cancels out (luminosity is an intrinsic property of the star and does not depend on the distance to the observer), and we have:, with in parsecs

Rearranging gives the distance modulus:

, with in parsecs