View source for Mathematical operators and symbols in Unicode

{{Short description|Blackboard at the Laurent Schwartz Center for Mathematics, École Polytechnique}}
[[File:0009-cmls-2012_preview_ecran.jpg|thumb|300px|Blackboard at the Laurent Schwartz Center for Mathematics, [[École Polytechnique]]]]
{{SpecialChars}}
The [[Unicode]] Standard encodes almost all standard characters used in mathematics.<ref name="utr25">{{cite web | title = Unicode Technical Report #25: Unicode Support for Mathematics | publisher = The Unicode Consortium | date = 2 April 2012 | url = https://www.unicode.org/reports/tr25/ | format = PDF | access-date = 14 August 2014}}</ref>
Unicode Technical Report #25 provides comprehensive information about the character repertoire, their properties, and guidelines for implementation.<ref name="utr25"/>
[[Operation (mathematics)|Mathematical operators]] and [[List of mathematical symbols|symbols]] are in multiple [[Unicode block]]s.  Some of these blocks are dedicated to, or primarily contain, mathematical characters while others are a mix of mathematical and non-mathematical characters.  This article covers all Unicode characters with a derived property of "Math".<ref>{{cite web | title = Unicode Character Database: Derived Core Properties | publisher = The Unicode Consortium | date = 19 February 2014 | url = https://www.unicode.org/Public/UCD/latest/ucd/DerivedCoreProperties.txt | access-date = 14 August 2014 
}}</ref><ref>{{cite web | title = Unicode Technical Annex #44: Unicode Character Database | publisher = The Unicode Consortium | date = 25 September 2013 | url = https://www.unicode.org/reports/tr44/ | format = PDF | access-date = 14 August 2014}}</ref>
<!-- Note that capitalization below intentionally uses Unicode block name capitalization instead of the normal Wikipedia sentence case for headings. -->

==Dedicated blocks==

===Mathematical Operators block===
{{Main|Mathematical Operators (Unicode block)}}
The Mathematical Operators block (U+2200&ndash;U+22FF) contains characters for mathematical, logical, and set notation.
{{Unicode chart Mathematical Operators}}

===Supplemental Mathematical Operators block===
{{Main|Supplemental Mathematical Operators|l1=Supplemental Mathematical Operators (Unicode block)}}
The Supplemental Mathematical Operators block (U+2A00&ndash;U+2AFF) contains various mathematical symbols, including N-ary operators, summations and integrals, intersections and unions, logical and relational operators, and subset/superset relations.
{{Unicode chart Supplemental Mathematical Operators}}

===<span id="Mathematical Alphanumeric Symbols block"></span>Mathematical Alphanumeric Symbols block===
{{Main|Mathematical Alphanumeric Symbols|l1=Mathematical Alphanumeric Symbols (Unicode block)}}
The Mathematical Alphanumeric Symbols block (U+1D400&ndash;U+1D7FF) contains Latin and Greek letters and decimal digits that enable mathematicians to denote different notions with different letter styles.  The reserved code points (the "holes") in the alphabetic ranges up to U+1D551 duplicate characters in the [[#Letterlike Symbols block|Letterlike Symbols block]]. In order, these are ℎ	/	ℬ	ℰ	ℱ	ℋ	ℐ	ℒ	ℳ	ℛ	/	ℯ	ℊ	ℴ	/	ℭ	ℌ	ℑ	ℜ	ℨ	/	ℂ	ℍ	ℕ	ℙ	ℚ	ℝ	ℤ.

{{Unicode chart Mathematical Alphanumeric Symbols}}

===<span id="Letterlike Symbols block"></span>Letterlike Symbols block===
{{Main|Letterlike Symbols|l1=Letterlike Symbols (Unicode block)}}
The Letterlike Symbols block (U+2100&ndash;U+214F) includes variables.  Most alphabetic math symbols are in the Mathematical Alphanumeric Symbols block [[#Mathematical Alphanumeric Symbols block|shown above]].

The math subset of this block is U+2102, U+2107, U+210A&ndash;U+2113, U+2115, U+2118&ndash;U+211D, U+2124, U+2128&ndash;U+2129, U+212C&ndash;U+212D, U+212F&ndash;U+2131, U+2133&ndash;U+2138, U+213C&ndash;U+2149, and U+214B.<ref>See https://www.unicode.org/Public/UCD/latest/ucd/DerivedCoreProperties.txt</ref>

{{Unicode chart Letterlike Symbols}}

===Miscellaneous Mathematical Symbols-A block===
{{Main|Miscellaneous Mathematical Symbols-A|l1=Miscellaneous Mathematical Symbols-A (Unicode block)}}
The Miscellaneous Mathematical Symbols-A block (U+27C0&ndash;U+27EF) contains characters for mathematical, logical, and database notation.
{{Unicode chart Miscellaneous Mathematical Symbols-A}}

===Miscellaneous Mathematical Symbols-B block===
{{Main|Miscellaneous Mathematical Symbols-B|l1=Miscellaneous Mathematical Symbols-B (Unicode block)}}
The Miscellaneous Mathematical Symbols-B block (U+2980&ndash;U+29FF) contains miscellaneous mathematical symbols, including brackets, angles, and circle symbols.
{{Unicode chart Miscellaneous Mathematical Symbols-B}}

===Miscellaneous Technical block===
{{Main|Miscellaneous Technical|l1=Miscellaneous Technical (Unicode block)}}
The Miscellaneous Technical block (U+2300&ndash;U+23FF) includes braces and operators.

The math subset of this block is U+2308&ndash;U+230B, U+2320&ndash;U+2321, U+237C, U+239B&ndash;U+23B5, 23B7, U+23D0, and U+23DC&ndash;U+23E2.
{{Unicode chart Miscellaneous Technical}}

===Geometric Shapes block===
{{Main|Geometric Shapes (Unicode block)}}
The Geometric Shapes block (U+25A0&ndash;U+25FF) contains geometric shape symbols.

The math subset of this block is U+25A0&ndash;25A1, U+25AE&ndash;25B7, U+25BC&ndash;25C1, U+25C6&ndash;25C7, U+25CA&ndash;25CB, U+25CF&ndash;25D3, U+25E2, U+25E4, U+25E7&ndash;25EC, and U+25F8&ndash;25FF.
{{Unicode chart Geometric Shapes}}

===Arrows block===
{{Main|Arrows (Unicode block)}}
The Arrows block (U+2190&ndash;U+21FF) contains line, curve, and semicircle arrows and arrow-like operators.

The math subset of this block is U+2190&ndash;U+21A7, U+21A9&ndash;U+21AE, U+21B0&ndash;U+21B1, U+21B6&ndash;U+21B7, U+21BC&ndash;U+21DB, U+21DD, U+21E4&ndash;U+21E5, U+21F4&ndash;U+21FF.<ref>More symbols are supported by TeX math packages, see e.g. [https://tug.ctan.org/fonts/xcharter-math/unimath-xcharter.pdf#page=47 Will Robertson, Symbols defined by unicode-math].</ref>
{{Unicode chart Arrows}}

===Supplemental Arrows-A block===
{{Main|Supplemental Arrows-A|l1=Supplemental Arrows-A (Unicode block)}}
The Supplemental Arrows-A block (U+27F0&ndash;U+27FF) contains arrows and arrow-like operators.
{{Unicode chart Supplemental Arrows-A}}

===Supplemental Arrows-B block===
{{Main|Supplemental Arrows-B|l1=Supplemental Arrows-B (Unicode block)}}
The Supplemental Arrows-B block (U+2900&ndash;U+297F) contains arrows and arrow-like operators (arrow tails, crossing arrows, curved arrows, and harpoons).
{{Unicode chart Supplemental Arrows-B}}

===Miscellaneous Symbols and Arrows block===
{{Main|Miscellaneous Symbols and Arrows|l1=Miscellaneous Symbols and Arrows (Unicode block)}}
The Miscellaneous Symbols and Arrows block (U+2B00&ndash;U+2BFF Arrows) contains arrows and geometric shapes with various fills.

The math subset of this block is U+2B30&ndash;U+2B44, U+2B47&ndash;U+2B4C.<ref>The quadruple arrows U+2B45 and U+2B46 are supported by TeX math packages, per [https://tug.ctan.org/fonts/xcharter-math/unimath-xcharter.pdf#page=75 Will Robertson, Symbols defined by unicode-math].</ref>
{{Unicode chart Miscellaneous Symbols and Arrows}}

===Combining Diacritical Marks for Symbols block===
{{Main|Combining Diacritical Marks for Symbols|l1=Combining Diacritical Marks for Symbols (Unicode block)}}
The Combining Diacritical Marks for Symbols block contains arrows, dots, enclosures, and overlays for modifying symbol characters.

The math subset of this block is U+20D0&ndash;U+20DC, U+20E1, U+20E5&ndash;U+20E6, and U+20EB&ndash;U+20EF.
{{Unicode chart Combining Diacritical Marks for Symbols}}

===Arabic Mathematical Alphabetic Symbols block===
{{Main|Arabic Mathematical Alphabetic Symbols|l1=Arabic Mathematical Alphabetic Symbols block}}
The Arabic Mathematical Alphabetic Symbols block (U+1EE00&ndash;U+1EEFF) contains characters used in Arabic mathematical expressions.
{{Unicode chart Arabic Mathematical Alphabetic Symbols}}

==Characters in other blocks==
Mathematical characters also appear in other blocks. Below is a list of these characters as of Unicode version {{Unicode version|version=16.0}}:

{|
|- style="vertical-align:top;"
| <!-- newspaper column 1 -->
*[[Basic Latin (Unicode block)|Basic Latin block]]
{|
| U+002B || {{Large|+}} || PLUS SIGN
|- 
| U+002D || {{Large|-}} || HYPHEN-MINUS<ref>As per [https://www.unicode.org/Public/16.0.0/ucd/DerivedCoreProperties.txt Unicode 16.0.0], the ASCII hyphen-minus is not a mathematical symbol. To express the minus sign in math, {{unichar|2212|minus sign}} is used instead.</ref>
|-
| U+003C || {{Large|&lt;}} || LESS-THAN SIGN
|-
| U+003D || {{Large|1==}} || EQUALS SIGN
|-
| U+003E || {{Large|&gt;}} || GREATER-THAN SIGN
|-
| U+005E || {{Large|^}} || CIRCUMFLEX ACCENT
|-
| U+007C || {{Large|<nowiki>|</nowiki>}} || VERTICAL LINE
|-
| U+007E || {{Large|~}} || TILDE
|}
*[[Latin-1 Supplement (Unicode block)|Latin-1 Supplement block]]
{|
| U+00AC || {{Large|¬}} || NOT SIGN
|-
| U+00B0 || {{Large|°}} || DEGREE SIGN<ref>As per [https://www.unicode.org/Public/16.0.0/ucd/DerivedCoreProperties.txt Unicode 16.0.0], the degree sign is not a mathematical symbol, since it is a measurement unit symbol rather than a math symbol. Consistently, TeX packages support many non-math symbols. But this article is designed to cover only Unicode characters with a derived property of "Math".</ref>
|-
| U+00B1 || {{Large|±}} || PLUS-MINUS SIGN
|-
| U+00D7 || {{Large|×}} || MULTIPLICATION SIGN
|-
| U+00F7 || {{Large|÷}} || DIVISION SIGN
|}
*[[Greek and Coptic|Greek and Coptic block]]
{|
| U+03D0 || {{Large|ϐ}} || GREEK BETA SYMBOL
|-
| U+03D1 || {{Large|ϑ}} || GREEK THETA SYMBOL
|-
| U+03D2 || {{Large|ϒ}} || GREEK UPSILON WITH HOOK SYMBOL
|-
| U+03D5 || {{Large|ϕ}} || GREEK PHI SYMBOL
|-
| U+03F0 || {{Large|ϰ}} || GREEK KAPPA SYMBOL
|-
| U+03F1 || {{Large|ϱ}} || GREEK RHO SYMBOL
|-
| U+03F4 || {{Large|ϴ}} || GREEK CAPITAL THETA SYMBOL
|-
| U+03F5 || {{Large|ϵ}} || GREEK LUNATE EPSILON SYMBOL
|-
| U+03F6 || {{Large|϶}} || GREEK REVERSED LUNATE EPSILON SYMBOL
|}
*[[Arabic (Unicode block)|Arabic block]]
{|
| U+0606 || {{Large|؆}} || ARABIC-INDIC CUBE ROOT
|-
| U+0607 || {{Large|؇}} || ARABIC-INDIC FOURTH ROOT
|-
| U+0608 || {{Large|؈}} || ARABIC RAY
|}
*[[General Punctuation (Unicode block)|General Punctuation block]]
{|
| U+2016 || {{Large|‖}} || DOUBLE VERTICAL LINE
|-
| U+2032 || {{Large|′}} || PRIME
|-
| U+2033 || {{Large|″}} || DOUBLE PRIME
|-
| U+2034 || {{Large|‴}} || TRIPLE PRIME
|-
| U+2040 || {{Large|⁀}} || CHARACTER TIE
|-
| U+2044 || {{Large|⁄}} || FRACTION SLASH
|-
| U+2052 || {{Large|⁒}} || COMMERCIAL MINUS SIGN
|-
| U+2061 || {{small|''note''}} || FUNCTION APPLICATION
|-
| U+2062 || {{small|''note''}} || INVISIBLE TIMES
|-
| U+2063 || {{small|''note''}} || INVISIBLE SEPARATOR
|-
| U+2064 || {{small|''note''}} || INVISIBLE PLUS
|}
''Note: non-marking character''
*[[Superscripts and Subscripts|Superscripts and Subscripts block]]
{|
| U+207A || {{Large|⁺}} || SUPERSCRIPT PLUS SIGN
|-
| U+207B || {{Large|⁻}} || SUPERSCRIPT MINUS
|-
| U+207C || {{Large|⁼}} || SUPERSCRIPT EQUALS SIGN
|-
| U+207D || {{Large|⁽}} || SUPERSCRIPT LEFT PARENTHESIS
|-
| U+207E || {{Large|⁾}} || SUPERSCRIPT RIGHT PARENTHESIS
|-
| U+208A || {{Large|₊}} || SUBSCRIPT PLUS SIGN
|-
| U+208B || {{Large|₋}} || SUBSCRIPT MINUS
|-
| U+208C || {{Large|₌}} || SUBSCRIPT EQUALS SIGN
|-
| U+208D || {{Large|₍}} || SUBSCRIPT LEFT PARENTHESIS
|-
| U+208E || {{Large|₎}} || SUBSCRIPT RIGHT PARENTHESIS
|}
| <!-- newspaper column 2 -->
*[[Miscellaneous Symbols|Miscellaneous Symbols block]]
{|
| U+2605 || {{Large|★}} || BLACK STAR
|-
| U+2606 || {{Large|☆}} || WHITE STAR
|-
| U+2640 || {{Large|♀}} || FEMALE SIGN
|-
| U+2642 || {{Large|♂}} || MALE SIGN
|-
| U+2660 || {{Large|♠}} || BLACK SPADE SUIT
|-
| U+2661 || {{Large|♡}} || WHITE HEART SUIT
|-
| U+2662 || {{Large|♢}} || WHITE DIAMOND SUIT
|-
| U+2663 || {{Large|♣}} || BLACK CLUB SUIT
|-
| U+266D || {{Large|♭}} || MUSIC FLAT SIGN
|-
| U+266E || {{Large|♮}} || MUSIC NATURAL SIGN
|-
| U+266F || {{Large|♯}} || MUSIC SHARP SIGN
|}
*[[Alphabetic Presentation Forms|Alphabetic Presentation Forms block]]
{|
| U+FB29 || {{Large|﬩}} || HEBREW LETTER ALTERNATIVE PLUS SIGN
|}
*[[Small Form Variants|Small Form Variants block]]
{|
| U+FE61 || {{Large|﹡}} || SMALL ASTERISK
|-
| U+FE62 || {{Large|﹢}} || SMALL PLUS SIGN
|-
| U+FE63 || {{Large|﹣}} || SMALL HYPHEN-MINUS
|-
| U+FE64 || {{Large|﹤}} || SMALL LESS-THAN SIGN
|-
| U+FE65 || {{Large|﹥}} || SMALL GREATER-THAN SIGN
|-
| U+FE66 || {{Large|﹦}} || SMALL EQUALS SIGN
|-
| U+FE68 || {{Large|﹨}} || SMALL REVERSE SOLIDUS
|}
*[[Halfwidth and fullwidth forms|Halfwidth and Fullwidth Forms block]]
{|
| U+FF0B || {{Large|＋}} || FULLWIDTH PLUS SIGN
|-
| U+FF1C || {{Large|＜}} || FULLWIDTH LESS-THAN SIGN
|-
| U+FF1D || {{Large|＝}} || FULLWIDTH EQUALS SIGN
|-
| U+FF1E || {{Large|＞}} || FULLWIDTH GREATER-THAN SIGN
|-
| U+FF3C || {{Large|＼}} || FULLWIDTH REVERSE SOLIDUS
|-
| U+FF3E || {{Large|＾}} || FULLWIDTH CIRCUMFLEX ACCENT
|-
| U+FF5C || {{Large|｜}} || FULLWIDTH VERTICAL LINE
|-
| U+FF5E || {{Large|～}} || FULLWIDTH TILDE
|-
| U+FFE2 || {{Large|￢}} || FULLWIDTH NOT SIGN
|-
| U+FFE9 || {{Large|￩}} || HALFWIDTH LEFTWARDS ARROW
|-
| U+FFEA || {{Large|￪}} || HALFWIDTH UPWARDS ARROW
|-
| U+FFEB || {{Large|￫}} || HALFWIDTH RIGHTWARDS ARROW
|-
| U+FFEC || {{Large|￬}} || HALFWIDTH DOWNWARDS ARROW
|}
*[[Garay (Unicode block)|Garay block]]
{|
| U+10D8E || {{Large|𐶎}} || GARAY PLUS SIGN
|-
| U+10D8F || {{Large|𐶏}} || GARAY MINUS SIGN
|}
|}

== See also ==
* [[Glossary of mathematical symbols]]
* [[List of logic symbols]]
* [[Greek letters used in mathematics, science, and engineering]]
* [[List of letters used in mathematics and science]]
* [[List of mathematical uses of Latin letters]]
* [[Unicode subscripts and superscripts]]
* [[Unicode symbols]]
* [[CJK Compatibility|CJK Compatibility Unicode symbols]] includes symbols for [[International System of Units|SI]] units
* [[Order of magnitude|Units for order of magnitude]] shows position of [[International System of Units|SI]] units

== References ==
{{reflist}}

==External links==
*{{cite book | title = Mathematical Markup Language (MathML) W3C Recommendation  | publisher = W3C | version = 3.0 | edition = 2nd | date = 10 April 2014 | url = http://www.w3.org/TR/MathML/}}
*Images of glyphs in [http://www.w3.org/TR/MathML2/chapter6.html#chars.16x16-tables section 6.3.3] of the {{cite book | title = Mathematical Markup Language (MathML) W3C Recommendation  | publisher = W3C
 | version = 2.0 | edition = 2nd | date = 21 February 2001 | url = http://www.w3.org/TR/2001/REC-MathML2-20010221/}}

{{Unicode navigation}}
{{Mathematical symbols notation language}}

[[Category:Unicode blocks|*]]
[[Category:Mathematical symbols]]