# Why is there “modulus” word in the “distance modulus” term?

The difference of apparent (m) and absolute (M) magnitudes of an object is called "distance modulus", which is related to the distance $$d$$ to the object in parsecs with equation

$$m - M = 5 \log \Big(\frac{d}{10 \ \textrm{pc}}\Big) \tag{1}.$$

I'm trying to understand why $$m - M$$ is called "distance modulus". The word "distance" makes sense, because there is a distance d term in Eq. (1). But what is "modulus" word doing there? In math, modulus means the remainder after division of two numbers. For example, modulus of 5 and 3 is 2.

Another meaning of "modulus" is length of a vector. I don't see how either of these two meanings can be relevant to Eq. 1.

## 1 Answer

According to Oxford Dictionary of English, the word "modulus" is the diminutive of the Latin modus, meaning measure (modus, in turn, comes from Proto-Indo-European mod-os, Nocentini & Parenti 2010.

Hence, the distance modulus is a "measure of distance", just like the modulus of a vector is a way of measuring its size, and Young's modulus is a way of measuring the stiffness of a material.