# What does it mean when someone says “…it scales with…”?

I frequently hear people say something scales with the mass m, or the length l, etc.

What does that mean?

Let's take a concrete example, the force equation F = ma.

Does this mean that F scales with m?

Or, if we have something like moment of inertia = $I = l^2$ * ...

where l denotes the length of a solid, then do we say that " the moment of inertia scales with $l^2$"?

• A number of comments that weren't going anywhere useful deleted. The best response to a comment you don't care for on a personal level is to either flag it or not but then move on. No one is going to win the internet in the comments. – dmckee Sep 3 '17 at 23:51

Unmodified the phrase probably means "is proportional to", but it can be modified to mean other functional relationships. For instance "scales quadratically with" or "scales as the square of" indicate a relationship like $$x \propto y^2\;.$$
In the sense of the Original Post's question, $F=ma$ means (in case you're trying the figure the net force magnitude from the the particle movement) that $F$ scales linearly with both the mass and the acceleration. And the meaning of that statement is that, if the mass were twice larger, than the $F$ should also be (to cause the same acceleration $a$), and if $a$ is ten times larger, than so should $F$.
Similarly, the area of a circle scales with its radius $r^2$, so for a radius 3 times as large, the corresponding area will be $3^2=9$ times larger.