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:

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, F₁₀. Identifying m₁ as the apparent magnitude of the star and m₂ as the absolute magnitude, the last equation becomes:

	where		m =	apparent magnitude of the star
			M =	absolute magnitude of the star
			F =	flux we receive from the star, and
			F10 =	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 F₁₀, 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