# What is distance modulus?

Apparent magnitude, absolute magnitude and distance are related by an equation:

m - M = 5 log d - 5

m is the apparent magnitude of the object

M is the absolute magnitude of the object

d is the distance to the object in parsecs

The expression m - M is called the distance modulus and is a measure of distance to the object. An object with a distance modulus of 0 is exactly 10 parsecs away. If the distance modulus is negative, the object is closer than 10 parsecs, and its apparent magnitude is brighter than its absolute magnitude. If the distance modulus is positive, the object is farther than 10 parsecs and its apparent magnitude is less bright than its absolute magnitude.

The following table gives values of d corresponding to different values of m - M.

Distance modulus m-M Distance d (parsecs)
-4 1.6
-3 2.5
-2 4.0
-1 6.3
0 10
1 16
2 25
3 40
4 63
5 100
10 10^3
20 10^5

### Some examples to try

1. Suppose you were viewing the Sun from a planet orbiting another star 40 pc away. What would the Sun's apparent magnitude be? (The Sun has absolute magnitude M = +4.8)
2. Star A and star B are both equally bright as seen from Earth, but A is 60 pc away while B is 15 pc away. Which star is intrinsically brighter? By how much?
3. Star C has an absolute magnitude of 0.0, and an apparent magnitude of +14.0. What is the distance to star C?