Math Symbols in Unicode

Perm url with updates: http://xahlee.org/comp/unicode_math_operators.html

Math Symbols in Unicode

Xah Lee, 2010-06-26

This page collects math symbols in Unicode.

Some Greeks: α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς τ υ φ χ ψ ω

superscript: ⁰ ⁱ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁼ ⁽ ⁾ ⁿ

subscript: ₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋ ₌ ₍ ₎ ₐ ₑ ₒ ₓ ₔ

Roots: √ ∛ ∜

Sets: ℕ ℤ ℚ ℝ ℂ

Constants: ℯ ℵ ⅇ ⅈ ⅉ ∅ ∞ ⧜ ⧝ ⧞

Basic binary operators: × ÷ ⊕ ⊖ ⊗ ⊘ ⊙ ⊚ ⊛ ⊜ ⊝ ⊞ ⊟ ⊠ ⊡ − ∕ ∗ ∘ ∙ ⋅ ⋆

Sets

element of: ∈ ∋ ∉ ∌ ⋶ ⋽ ⋲ ⋺ ⋳ ⋻

misc: ∊ ∍ ⋷ ⋾ ⋴ ⋼ ⋵ ⋸ ⋹ ⫙ ⟒

binary relation of sets: ⊂ ⊃ ⊆ ⊇ ⊈ ⊉ ⊊ ⊋ ⊄ ⊅ ⫅ ⫆ ⫋ ⫌ ⫃ ⫄ ⫇ ⫈ ⫉ ⫊ ⟃ ⟄ ⫏ ⫐ ⫑ ⫒ ⫓ ⫔ ⫕ ⫖ ⫗ ⫘ ⋐ ⋑ ⟈ ⟉

Union: ∪ ⩁ ⩂ ⩅ ⩌ ⩏ ⩐

Intersection: ∩ ⩀ ⩃ ⩄ ⩍ ⩎

Binary operator on sets: ∖ ⩆ ⩇ ⩈ ⩉ ⩊ ⩋ ⪽ ⪾ ⪿ ⫀ ⫁ ⫂ ⋒ ⋓

N-nary operator on sets: ⋂ ⋃ ⊌ ⊍ ⊎

Joins: ⨝ ⟕ ⟖ ⟗

Order

Precede and succeed: ≺ ≻ ≼ ≽ ≾ ≿ ⊀ ⊁ ⋞ ⋟ ⋠ ⋡ ⋨ ⋩ ⪯ ⪰ ⪱ ⪲ ⪳ ⪴ ⪵ ⪶ ⪷ ⪸ ⪹ ⪺ ⪻ ⪼

less and greater: ≮ ≯ ≤ ≥ ≰ ≱ ⪇ ⪈ ≦ ≧ ≨ ≩

less and greater 2: ⋜ ⋝ ⪙ ⪚ ≶ ≷ ≸ ≹ ⋚ ⋛ ⪋ ⪌ ⪑ ⪒ ⪓ ⪔

with approx: ⪅ ⪆ ⪉ ⪊

less and greater with equivalence: ≲ ≳ ⋦ ⋧ ≴ ≵

less and greater with similarity: ⪝ ⪞ ⪟ ⪠ ⪍ ⪎ ⪏ ⪐

less and greater slanted: ⩽ ⩾ ⫹ ⫺ ⪕ ⪖ ⪛ ⪜

less and greater misc: ⪣ ⪤ ⪥ ⪦ ⪧ ⪨ ⪩ ⪪ ⪫ ⪬ ⪭ ⪮ ⪡ ⪢ ⫷ ⫸ ⩹ ⩺ ⩻ ⩼ ≬ ≪ ≫ ⋘ ⋙

Order relation with dot: ⋖ ⋗ ⩿ ⪀ ⪗ ⪘ ⪁ ⪂ ⪃ ⪄

Equality, Identity, Equivalence, Approx, Congruence

equality: ≝ ≞ ≟ ≠ ∹ ≎ ≏ ≐ ≑ ≒ ≓ ≔ ≕ ≖ ≗ ≘ ≙ ≚ ≛ ≜ ⩬ ⩭ ⩮ ⩱ ⩲ ⩦ ⩴ ⩵ ⩶ ⩷

Identity: ≡ ≢ ⩧

Equivalence: ≍ ≭ ≣ ⩸

Approx equality: ≁ ≂ ≃ ≄ ⋍ ≅ ≆ ≇ ≈ ≉ ≊ ≋ ≌ ⩯ ⩰

Misc equality:

Misc relations: ⊏ ⊐ ⊑ ⊒ ⊓ ⊔ ⋢ ⋣ ⋤ ⋥ ⊲ ⊳ ⊴ ⊵ ⋪ ⋫ ⋬ ⋭ ⫴ ⫵

Logic

Logic: ¬ ⫬ ⫭ ⊨ ⊭ ∀ ∁ ∃ ∄ ∴ ∵ ⊦ ⊬ ⊧ ⊩ ⊮ ⊫ ⊯ ⊪ ⊰ ⊱

Logic binary: ∧ ∨ ⊻ ⊼ ⊽ ⋎ ⋏ ⟑ ⟇ ⩑ ⩒ ⩓ ⩔ ⩕ ⩖ ⩗ ⩘ ⩙ ⩚ ⩛ ⩜ ⩝ ⩞ ⩟ ⩠ ⩢ ⩣ ⨇ ⨈

Logic n-nary: ⋀ ⋁

n-nary operators: ∑ ⨀ ⨁ ⨂ ⨃ ⨄ ⨅ ⨆ ∏ ∐ ∔

Geometry

Geometry: ∣ ∤ ⫮ ⌅ ⌆ ℓ ⫛

Ratio and proportion: ∝ ∶ ∷ ∺

Parallel and perpendicular: ∥ ∦ ⫲ ⫳ ⋕ ⟂ ⫡

Right angle: ∟ ⊾ ⦜ ⦝ ⊿

Angles: ∠ ∡ ⦛ ⦞ ⦟ ⦢ ⦣ ⦤ ⦥ ⦦ ⦧ ⦨ ⦩ ⦪ ⦫ ⦬ ⦭ ⦮ ⦯ ⦓ ⦔ ⦕ ⦖ ⟀

Spherical angle: ∢ ⦠ ⦡

...

Pairs: ⌈ ⌉ ⌊ ⌋ ⦋ ⦌ ⟦ ⟧ ⦍ ⦎ ⦏ ⦐

pairs 2: ⟮ ⟯ ⟨ ⟩ ⟪ ⟫ ⦃ ⦄ ⦅ ⦆ ⦇ ⦈ ⦉ ⦊ ⟬ ⟭ ⦗ ⦘ ⦑ ⦒ ⧼ ⧽

integrals: ∫ ∬ ∭ ∮ ∯ ∰ ∱ ∲ ∳ ⨋ ⨌ ⨍ ⨎ ⨏ ⨐ ⨑ ⨒ ⨓ ⨔ ⨕ ⨖ ⨗ ⨘ ⨙ ⨚ ⨛ ⨜

Derivative: ∂ ′ ″ ‴ ∆

vector: ⨯ ∇ ⊹

Misc indicators: ∎ ± ∓ ⋮ ⋯ ⋰ ⋱

Misc symbols:

Tacks: ⊣ ⊢ ⊥ ⊤ ⟘ ⟙ ⟛ ⟝ ⟞ ⟟ ⫧ ⫨ ⫩ ⫪ ⫫ ⫞ ⫟ ⫠

Turnstiles: ⫢ ⫣ ⫤ ⫥ ⟚

Z notation: ⦁ ⦂ ⩤ ⩥ ⨟ ⨠ ⨡ ⨾

Tilde Operators: ∼ ∽ ⩪ ⩫ ⩳

Misc Operators: ⋄ ⫶ ⫼ ⫾

Misc products: ≀ ⨿ ⨼ ⨽ ⧢ ⋉ ⋊ ⋋ ⋌

Plus variations: ⨢ ⨣ ⨤ ⨥ ⨦ ⨧ ⨨ ⨭ ⨮

Solidus: ⫻ ⫽

minus sign variations: ∸ ⨩ ⨪ ⨫ ⨬

maps: ⊶ ⊷ ⊸ ⟜ ⧟

Unsorted: ∾ ⊺ ⋇ ⟌ ⟠ ⋔ ⫚ ⋈ ⟁ ⟅ ⟆ ⟊ ⟐ ⟓ ⟔ ⟡ ⟢ ⟣ ⟤ ⟥ ⦀ ⦙ ⦚ ⧘ ⧙ ⧚ ⧛ ⦰ ⦱ ⦲ ⦳ ⦴ ⦵ ⦶ ⦷ ⦸ ⦹ ⦺ ⦻ ⦼ ⦽ ⦾ ⦿ ⧀ ⧁ ⧂ ⧃ ⧄ ⧅ ⧆ ⧇ ⧈ ⧉ ⧑ ⧒ ⧓ ⧔ ⧕ ⧖ ⧗ ⧠ ⧡ ⧣ ⧤ ⧥ ⧦ ⧧ ⧨ ⧩ ⧪ ⧫ ⧬ ⧭ ⧮ ⧯ ⧰ ⧱ ⧲ ⧳ ⧴ ⧵ ⧶ ⧷ ⧸ ⧹ ⧺ ⧻ ⧾ ⨉ ⨊ ⨞ ⧊ ⧋ ⧌ ⧍ ⨹ ⨺ ⨻ ⧎ ⧏ ⧐ ⨰ ⨱ ⨲ ⨳ ⨴ ⨵ ⨶ ⨷ ⨸ ⩡ ⩨ ⩩ ⫍ ⫎ ⫝̸ ⫝ ⫦ ⫯ ⫰ ⫱

What Chars Are Included

These are roughly “all” math related symbols under the Basic Multilingual Plane (BMP). The total number of chars on this page is about 766.

For few hundred arrows, see: Arrows in Unicode. There are also a few hundred drawing shapes, used together for example to tile into a large braket or boxes, corner, for matrixes, etc. You can see them here: unicode_shapes.txt. There are also few hundred dingbats in unicode, some could be used for math, but are not considered math symbols here.

There are more math symbols but are outside of BMP, and i'm not aware of any fonts that shows much of chars outside BMP. In particular, there are several set of specially rendered alphabets, such as double struck capital letters, Fraktur (aka gothic), bold slanted... They are outside of BMP. You can see them here: unicode_math_alphanum.txt. You can see also part of the operator set grouped by code point, here: unicode_math_operators.txt

Note: this page will be improved over the coming months. e.g. The bunch of less used misc symbols at the bottom can still use some categorizing.

I See Blank Squares?

If some shows up as square, that's probably because you don't have the right font, or your browser is old and isn't configured properly, or your browser simply does not work well. Exact reason can be complex. As of 2010-06-27, latest versions of the following browsers on Windows Vista show all characters (assuming you have the right font first): Google Chrome, Opera, Firefox.

To get proper fonts, see: Best Unicode Fonts.

To find out the unicode name and code point of the char, use emacs. See: xub Unicode Browser mode for Emacs.

Unicode Names for Symbol's Meaning

The symbols are roughly grouped by purpose, and with respect to the symbol's semantic meaning, as opposed to their appearance.

For example, there are many similar looking symbols, and in different fonts they may look different or identical. e.g. ~ ∼ ∿ ∽ ≈. The first is “tilde”, the second is “tilde operator”, third is “sine wave”, 4th is “reversed tilde”, 5th is “almost equal to”.

Another example: ⩳ ≌ ⩯ ⩰. Their names are:

  • EQUALS SIGN ABOVE TILDE OPERATOR
  • ALL EQUAL TO
  • ALMOST EQUAL TO WITH CIRCUMFLEX ACCENT
  • APPROXIMATELY EQUAL OR EQUAL TO

The unicode names give indication of the symbol's meaning. There are some 20 more symbols that's made up wavy line(s) and or horizontal line(s). Best to go by the symbol's name in your choice a symbol, because what you see as rendered by a font may be very different from another font, and often font designers simply got the shape wrong, especially for less common chars.

Formal Language, not Glyphs with no Grammar

Also, i've organized these symbols with respect to their use in calculational proof and formal language. e.g. use in computer proof languages (e.g. Hol, Coq, Isabelle, OCaml) or computer algebra systems (e.g. Mathematica). The symbol's meaning are precisely defined and parsed by a compiler. This is in contrast to traditional math (e.g. LaTeX) where the symbols serve as a picture for communication with humans. See:

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