# What does the math symbol $\propto$ mean?

I came across this symbol in my engineering class and I have never seen it before. Anyone know this?

• You know, you can always raise your hand and ask :) Likely others in the class were also not familiar with it. – Jair Taylor Aug 31 '19 at 18:32
• Well.. More like reading it in my book and came across it :) – C. K. Aug 31 '19 at 18:42

It typically means proportional to. Such that

If $$y=cx$$ for some constant $$c$$ we say

$$y\propto x$$ so that when x grows, y grows proportionally by the ratio $$c$$

Alternatively inverse proportionality is when

$$y=c\frac{1}{x}$$ so that when x gets smaller, y gets bigger proportionally by $$c$$

$$y\propto \frac{1}{x}$$ to my knowledge there isn’t a symbol specifically for inverse proportionality and $$y\propto \frac{1}{x}$$ is used instead

• Is there a symbol for inverse proportionality as well? – C. K. Aug 31 '19 at 18:34
• No I don’t think so typically $$y\propto \frac{1}{x}$$ is used – Colin Hicks Aug 31 '19 at 18:43
• This solved my question. Thanks – C. K. Aug 31 '19 at 18:44

As others have pointed out, this symbol means "is proportional to." That is, $$a \propto b$$ means that there is some constant $$C$$ such that $$a = Cb.$$

That being said, in the interests of "teaching a man to fish", it is worth pointing out that it is often possible to "reverse engineer" the meaning of specific mathematical symbols using DeTeXify. In this case, drawing the mysterious symbol gives

Either \propto or \varpropto seems to give the correct symbol. TeX often uses "var" to indicate a variation of a symbol (for example \epsilon $$\epsilon$$ vs \varepsilon $$\varepsilon$$; \theta $$\theta$$ vs \vartheta $$\vartheta$$), so "propto" seems like a reasonable guess as to what this symbol should be called. Googling this term gives a large number of results, many of which are relevant.

• This is awesome! I'll use this in the future if I come across more mystic symbols! – C. K. Aug 31 '19 at 18:45
• Glad I could be of use. Honestly, DeTeXify is one of my favorite things on the interwebs. There is also a free-to-use desktop version (you can pay something like 8 bucks to remove shareware reminders, if you desire---I think it is worth it to support a snazzy bit of hardware). – Xander Henderson Aug 31 '19 at 18:48

$$\propto$$ means "proportional to."

This symbol is often used, primarily in physics, to denote direct proportionality. so the RHS and LHS of your expression only differ by some scalar multiple.