Proportional Symbol Copy and Paste (∝ ∷ ∶)
Proportional to
Unicode U+221D · HTML ∝
Tap any symbol to copy it. Each tap also adds it to the box above, so you can copy several together.
Codes for every symbol on this page (Unicode, HTML, Alt, Mac, Word)
| Symbol | Name | Unicode | HTML | Windows Alt code | Mac | MS Word |
|---|---|---|---|---|---|---|
| ∝ | Proportional to | U+221D | ∝ | - | - | 221D then Alt+X |
| ∷ | Proportion (as) | U+2237 | ∷ | - | - | 2237 then Alt+X |
| ∶ | Ratio sign | U+2236 | ∶ | - | - | 2236 then Alt+X |
| α | Alpha (look-alike) | U+03B1 | α | Alt+224 | - | 03B1 then Alt+X |
The proportional symbol ∝ means "is proportional to", so y ∝ x says that y changes in the same ratio as x. If x doubles, y doubles too.
The same sign is used for both kinds of proportion: y ∝ x for direct and y ∝ 1/x for inverse. Tap ∝ in the grid above for a quick proportional symbol copy, or read on for examples from NCERT physics and chemistry.
Directly Proportional Symbol: y ∝ x
The directly proportional to symbol is simply ∝. When we say y is directly proportional to x, we write y ∝ x. The ∝ can be replaced by "= k ×", where k is a fixed number called the constant of proportionality:
y ∝ x ⇔ y = kx
So the graph of y against x is a straight line through the origin. Everyday example: if 1 kg of rice costs ₹60, then cost ∝ weight, and 5 kg costs ₹300 (here k = 60).
| Law | Written with ∝ | Condition |
|---|---|---|
| Ohm's law | V ∝ I | temperature stays the same |
| Charles's law | V ∝ T | pressure stays the same, T in kelvin |
| Hooke's law | F ∝ x | within the elastic limit |
| Newton's second law | F ∝ a | mass stays the same |
Inversely Proportional Symbol: y ∝ 1/x
There is no separate inversely proportional symbol. You use the same ∝ and put the quantity in the denominator:
y ∝ 1/x ⇔ y = k/x ⇔ xy = k
If x doubles, y becomes half. Example: if 4 workers take 6 days to finish a job, 8 workers take 3 days (4 × 6 = 8 × 3 = 24).
| Law | Written with ∝ | Condition |
|---|---|---|
| Boyle's law | P ∝ 1/V | temperature stays the same |
| Newton's law of gravitation | F ∝ 1/r² | inverse square of distance |
| Coulomb's law | F ∝ 1/r² | for two point charges |
| Wave speed | λ ∝ 1/f | speed stays the same |
People sometimes search for an "indirectly proportional symbol", but the correct term is inversely proportional, and it is written with ∝ and 1/x as shown.
Directly and Inversely Proportional Symbol Together
A quantity can depend on several others at once. Then you combine them in one statement:
- Gravitational force: F ∝ m₁m₂ and F ∝ 1/r², so F ∝ m₁m₂/r², which becomes F = Gm₁m₂/r².
- Resistance of a wire: R ∝ l (length) and R ∝ 1/A (area), so R ∝ l/A, which becomes R = ρl/A.
This is how most physics formulas are first written in class 9 to 12: proportions first, then a constant to turn ∝ into =. See the physics symbols page for what each letter stands for, and the rho symbol page for ρ.
Proportion Symbol ∷ and Ratio Sign ∶
In arithmetic, a proportion says two ratios are equal. Indian textbooks write it like this:
2 : 3 :: 4 : 6, read "2 is to 3 as 4 is to 6".
The double colon :: is the proportion symbol, and Unicode has a proper single character for it, ∷. The ratio sign ∶ looks like a normal colon but is centred for maths. In everyday typing, the keyboard : works fine. The rule to check a proportion is "product of extremes = product of means": 2 × 6 = 3 × 4 = 12.
∝ vs α: Do Not Mix Them Up
The proportionality symbol ∝ looks very much like the Greek small letter alpha α. They are different characters:
| ∝ proportional to | α alpha | |
|---|---|---|
| Shape | open on the right side, like a fish | a closed loop with a tail |
| Code | U+221D | U+03B1 |
| Used for | relations between quantities | angles, alpha particles, coefficients |
When typing, use the right one: search engines, screen readers and equation tools treat them differently. More on alpha is on the alpha symbol page.
How to Type the Proportional To Symbol
| Where | How to type ∝ |
|---|---|
| Microsoft Word | 221D then Alt+X |
| Word equation | Insert > Equation, type \propto then Space |
| Google Docs | Insert > Special characters, search "proportional" |
| Mac | Control+Command+Space, search "proportional" |
| LaTeX | \propto |
| HTML | ∝ |
| Phone | copy from this page |
There is no Windows Alt code or Mac Option key for ∝. For ∷ type 2237 then Alt+X in Word. The proportional symbol latex command \propto works in maths mode, for example $y \propto x$. More signs are on the math symbols list, including the approximately equal symbol and therefore symbol.
Frequently asked questions
What is the symbol of directly proportional?
It is ∝. Writing y ∝ x means y is directly proportional to x, so y = kx for some constant k.
What is the symbol of inversely proportional?
The same ∝ is used with a reciprocal: y ∝ 1/x. It means y = k/x, so when x increases, y decreases in the same ratio.
What is the symbol of proportional called in Unicode?
Its official name is PROPORTIONAL TO, code point U+221D. In HTML you can write ∝ and in LaTeX \propto.
What is the difference between proportion and proportional?
A proportion is a statement that two ratios are equal, like 2 : 3 :: 4 : 6. Proportional describes how two quantities change together, written with ∝.
Is ∝ the same as alpha?
No. They look alike, but ∝ is the maths sign for proportional to, and α is a Greek letter. They have different codes and meanings.