Math symbols are shorthand for operations and relationships: + means add, ≠ means “is not equal to”, √ means square root and ∑ means “sum of”. The table below lists the most common ones with their meanings and examples; copy any symbol directly or open its page for keyboard shortcuts.
≠DetailsCommon math symbols table
Symbols with a link have a full reference page with copy buttons, Alt codes and Mac shortcuts where they exist, and HTML codes. Browse hundreds more in the math symbols category.
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| + | Plus sign | Addition; also marks a positive number | 3 + 4 = 7 |
| − | Minus sign | Subtraction; also marks a negative number | 9 − 5 = 4 |
| × | Multiplication sign | Multiplication (times) | 6 × 7 = 42 |
| ⋅ | Dot operator | Multiplication, and the dot product of vectors | a ⋅ b |
| ÷ | Division sign | Division | 12 ÷ 3 = 4 |
| ± | Plus-minus sign | Plus or minus; a tolerance or two solutions | x = ±2 |
| = | Equals sign | Is equal to | 2 + 2 = 4 |
| ≠ | Not equal to | Is not equal to | 5 ≠ 6 |
| ≈ | Almost equal to | Is approximately equal to | π ≈ 3.14 |
| ≡ | Identical to | Identical to, defined as, or congruent (mod n) | 17 ≡ 2 (mod 5) |
| ≅ | Approximately equal to | Congruent (geometry) or isomorphic | △ABC ≅ △DEF |
| < | Less-than sign | Is less than | 3 < 5 |
| > | Greater-than sign | Is greater than | 8 > 2 |
| ≤ | Less than or equal to | Is less than or equal to | x ≤ 10 |
| ≥ | Greater than or equal to | Is greater than or equal to | age ≥ 18 |
| ∝ | Proportional to | Varies directly with | F ∝ a |
| √ | Square root | Square root | √16 = 4 |
| ² | Superscript two | Squared (to the power of 2) | 5² = 25 |
| ∞ | Infinity | Without bound, infinitely large | x → ∞ |
| % | Percent sign | Per hundred | 25% = 0.25 |
| ‰ | Per mille sign | Per thousand | 5‰ = 0.5% |
| π | Pi | Circle constant, about 3.14159 | C = 2πr |
| ∑ | Summation | Sum of a sequence | ∑ᵢ xᵢ |
| ∏ | Product | Product of a sequence | ∏ aᵢ |
| ∫ | Integral | Integral (area under a curve) | ∫ f(x) dx |
| ∂ | Partial differential | Partial derivative | ∂f/∂x |
| ∇ | Nabla | Gradient (del) operator | ∇f |
| ∆ | Increment | Change in a quantity | Δt = t₂ − t₁ |
| ∈ | Element of | Is a member of the set | 3 ∈ A |
| ∉ | Not an element of | Is not a member of the set | 7 ∉ A |
| ⊂ | Subset of | Is a subset of | A ⊂ B |
| ∪ | Union | Elements in either set | A ∪ B |
| ∩ | Intersection | Elements in both sets | A ∩ B |
| ∅ | Empty set | The set with no elements | A ∩ B = ∅ |
| ∀ | For all | For every (universal quantifier) | ∀x ∈ ℝ |
| ∃ | There exists | There is at least one | ∃x: x² = 4 |
| ¬ | Not sign | Logical negation (not) | ¬P |
| ∧ | Logical and | Logical conjunction (and) | P ∧ Q |
| ∨ | Logical or | Logical disjunction (or) | P ∨ Q |
| ⇒ | Rightwards double arrow | Implies | x = 2 ⇒ x² = 4 |
| ⇔ | Left right double arrow | If and only if | P ⇔ Q |
| ∴ | Therefore | Therefore | ∴ x = 5 |
| ∵ | Because | Because | ∵ a = b |
| ° | Degree sign | Degrees of an angle (or temperature) | 90° |
| ∠ | Angle | Angle | ∠ABC = 45° |
| ⊥ | Up tack | Is perpendicular to | AB ⊥ CD |
| ∥ | Parallel to | Is parallel to | AB ∥ CD |
Arithmetic symbols
The basic operations are the ones most people need to type. The keyboard gives you + and =, but the “proper” multiplication, division and minus signs are separate characters:
- × multiplication sign (U+00D7) is not the letter x. In typeset math and on product labels (2 × 4 lumber, 1920 × 1080), the real sign looks cleaner and cannot be misread as a variable. In algebra, a centered dot or no symbol at all is more common: 3·x or 3x.
- ÷ division sign (U+00F7) is common in elementary math and on calculators. Beyond that level, division is usually written as a fraction or with a slash: 6/3.
- − minus sign (U+2212) is the same width as the plus sign and sits at the same height. The hyphen-minus on your keyboard (-) is shorter and is what most people type, which is fine for everyday text; typeset math uses the true minus.
- ± plus-minus (U+00B1) means “plus or minus”: a tolerance (5 ± 0.1 mm) or both roots of a quadratic.
Comparison and equality symbols
These state how two values relate. The subtle differences matter:
- = exactly equal. ≠ not equal.
- ≈ approximately equal, used for rounded values: π ≈ 3.14.
- ≡ identical to, or “equivalent by definition”. In number theory it means congruence: 17 ≡ 2 (mod 5).
- ≅ congruent, used in geometry for shapes that have the same size and shape.
- < and > strictly less than and greater than. The open side faces the larger number.
- ≤ and ≥ less than or equal to, greater than or equal to. People without these on the keyboard often write <= and >=, which is also how most programming languages spell them.
- ∝ proportional to: y ∝ x means y is a constant multiple of x.
Algebra, calculus and analysis symbols
- √ square root; ∛ and ∜ are the cube and fourth root.
- ² and ³ squared and cubed. For other powers, see the superscript and subscript characters, or use your editor’s superscript formatting.
- ∞ infinity, used in limits and intervals: x → ∞.
- ∑ sum of a sequence; ∏ product of a sequence.
- ∫ integral, the area under a curve.
- ∂ partial derivative, used when a function has several variables.
- ∇ nabla (del), the gradient operator in vector calculus.
- ∆ change in a quantity: Δx is the change in x. (The Greek letter Δ is used for the same purpose.)
- π pi, approximately 3.14159.
Set theory and logic symbols
- ∈ is an element of: 3 ∈ ℕ. ∉ is not an element of.
- ⊂ and ⊆ subset and subset-or-equal. Textbooks differ on whether ⊂ means proper subset, so check your course’s convention.
- ∪ and ∩ union (everything in either set) and intersection (only what is in both).
- ∅ the empty set. It is not the Greek letter phi or the Scandinavian letter Ø, although they look similar.
- ∀ and ∃ for all, and there exists, the two quantifiers of logic.
- ∧, ∨ and ¬ logical and, or, and not.
- ⇒ and ⇔ implies, and if and only if.
- ∴ and ∵ therefore and because, used in proofs and step-by-step working.
Geometry symbols
- ° degrees of an angle: a right angle is 90°.
- ∠ angle: ∠ABC. ∟ right angle.
- ⊥ perpendicular, ∥ parallel.
- ′ and ″ prime and double prime: minutes and seconds of arc, feet and inches, or labels such as A′ for a transformed point. They are not apostrophes or quotation marks.
How to type math symbols
Windows
Several common math symbols have Alt codes. Hold Alt, type the number on the numeric keypad with Num Lock on, then release. The top-row number keys will not work.
| Symbol | Alt code |
|---|---|
| ° degree | Alt + 248 or Alt + 0176 |
| ± plus-minus | Alt + 241 or Alt + 0177 |
| × multiplication | Alt + 0215 |
| ÷ division | Alt + 246 or Alt + 0247 |
| ≈ approximately equal | Alt + 247 |
| ≤ less than or equal | Alt + 243 |
| ≥ greater than or equal | Alt + 242 |
| √ square root | Alt + 251 |
| ∞ infinity | Alt + 236 |
| ² squared | Alt + 253 or Alt + 0178 |
There is no Alt code for ≠, ∑ or ∫. For those, use the Windows + . panel’s Symbols tab or Character Map. The Alt code finder lists every symbol that does have one.
Mac
The standard U.S. Mac layout has Option-key shortcuts for many math symbols:
| Symbol | Mac shortcut |
|---|---|
| ≠ | Option + = |
| ≈ | Option + X |
| ≤ / ≥ | Option + , / Option + . |
| ± | Option + Shift + = |
| ÷ | Option + / |
| √ | Option + V |
| ∞ | Option + 5 |
| ∑ / ∏ | Option + W / Option + Shift + P |
| ∫ | Option + B |
| ∂ | Option + D |
| ∆ | Option + J |
| π | Option + P |
| ° | Option + Shift + 8 |
For anything else, open the Character Viewer with Control + Command + Space and search by name.
Microsoft Word and Google Docs
In Word, type a symbol’s hex code point and press Alt + X; for example 2260 then Alt + X gives ≠. Word’s equation editor (Insert > Equation) also has a full math symbol palette. In Google Docs, use Insert > Special characters, or Insert > Equation for formulas.
Phones
Phone keyboards include + and = on the symbol layer, and some, such as Gboard, also offer × and ÷. Press and hold symbol keys to see what variants your keyboard provides. For anything else, copy from SymbolHero, or set up a text replacement on iPhone (Settings > General > Keyboard > Text Replacement) so a short code like “neq” expands to ≠.
HTML
Many math symbols have named entities: ≠ ≠, ≤ ≤, ≥ ≥, × ×, ÷ ÷, − −, √ √, ∞ ∞, ∑ ∑. The full list is in the HTML entity reference.
Common mistakes
- Using look-alike letters. x for ×, the letter o for °, and ß for β are common substitutions that look wrong in print and break search.
- Mixing up ∑ and Σ. The summation operator (U+2211) and the Greek capital sigma (U+03A3) are different characters. Either renders fine in most documents, but be consistent. See the Greek alphabet guide for more look-alikes.
- Symbols showing as boxes. Rare math symbols can be missing from basic fonts. Switch to a font with math coverage such as Cambria Math on Windows, or see why symbols show as boxes.
Frequently asked questions
What is the symbol for “approximately equal to”?
≈ (U+2248). On Windows it is Alt + 247; on a Mac, Option + X.
What does ∴ mean?
“Therefore.” It introduces a conclusion in a proof or calculation. Its upside-down counterpart ∵ means “because”.
What is the difference between ≡ and =?
= states that two values are equal. ≡ usually means identical for every value of the variables, equal by definition, or congruent in modular arithmetic.
How do I type the not equal sign?
On a Mac press Option + =. On Windows there is no Alt code; copy ≠ from this page, use the Symbols tab in the Windows + . panel, or type 2260 then Alt + X in Word.