∝
∝ Proportional To Symbol
The proportional-to symbol (∝) says two quantities scale together: y ∝ x means y = kx for some constant k.
Also known as: proportional to symbol, proportional symbol, varies as, directly proportional sign.
Codes
| Symbol | ∝ | |
| Unicode | U+221D | |
| HTML entity (named) | ∝ | |
| HTML entity (decimal) | ∝ | |
| HTML entity (hex) | ∝ | |
| CSS | \221D | |
| LaTeX | \propto | |
| Windows Alt code | Alt + 8733 |
How to type ∝ (Proportional To Symbol)
Windows221D, Alt + X
In Word, type 221D then press Alt + X. Elsewhere, copy ∝ above or use Character Map (search “proportional”).
Mac
No default keystroke. Open Character Viewer (Control + Cmd + Space) and search “proportional to”, or copy ∝ above.
Microsoft Word221D, Alt + X
Type 221D, then press Alt + X to convert it to ∝.
Google Docs
Insert → Special characters, then search “proportional”. In an equation, \propto followed by a space also works.
LaTeX\propto
Use \propto in math mode: y \propto x.
Usage
- y ∝ x means y is directly proportional to x — double x and you double y. Formally, y = kx for some non-zero constant k, the constant of proportionality.
- Inverse proportion drops the variable into a denominator: y ∝ 1/x. Ohm's law and the inverse-square law are both written this way before the constants are pinned down.
- In Bayesian statistics, ∝ does a lot of work: writing the posterior as p(θ|x) ∝ p(x|θ)p(θ) lets you drop the normalising constant and still say something true.
- Which one to use: ∝ (U+221D) is the proportional-to relation. It is not the Greek letter alpha α (U+03B1), even though the glyph is nearly identical in many fonts — α is a variable, ∝ is a relation, and they typeset with different spacing.