Mathematical operators and symbols in Unicode

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Blackboard at the Laurent Schwartz Center for Mathematics, École Polytechnique

The Unicode Standard encodes almost all standard characters used in mathematics.[1] Unicode Technical Report #25 provides comprehensive information about the character repertoire, their properties, and guidelines for implementation.[1] Mathematical operators and symbols are in multiple Unicode blocks. 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".[2][3]

Dedicated blocks

Mathematical Operators block

Main page: Mathematical Operators (Unicode block)

The Mathematical Operators block (U+2200–U+22FF) contains characters for mathematical, logical, and set notation.

Supplemental Mathematical Operators block

The Supplemental Mathematical Operators block (U+2A00–U+2AFF) contains various mathematical symbols, including N-ary operators, summations and integrals, intersections and unions, logical and relational operators, and subset/superset relations.

Mathematical Alphanumeric Symbols block

The Mathematical Alphanumeric Symbols block (U+1D400–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.[4]


Letterlike Symbols block

The Letterlike Symbols block (U+2100–U+214F) includes variables. Most alphabetic math symbols are in the Mathematical Alphanumeric Symbols block shown above.

The math subset of this block is U+2102, U+2107, U+210A–U+2113, U+2115, U+2118–U+211D, U+2124, U+2128–U+2129, U+212C–U+212D, U+212F–U+2131, U+2133–U+2138, U+213C–U+2149, and U+214B.[5]


Miscellaneous Mathematical Symbols-A block

The Miscellaneous Mathematical Symbols-A block (U+27C0–U+27EF) contains characters for mathematical, logical, and database notation.

Miscellaneous Mathematical Symbols-B block

The Miscellaneous Mathematical Symbols-B block (U+2980–U+29FF) contains miscellaneous mathematical symbols, including brackets, angles, and circle symbols.

Miscellaneous Technical block

The Miscellaneous Technical block (U+2300–U+23FF) includes braces and operators.

The math subset of this block is U+2308–U+230B, U+2320–U+2321, U+237C, U+239B–U+23B5, 23B7, U+23D0, and U+23DC–U+23E2.

Geometric Shapes block

Main page: Geometric Shapes (Unicode block)

The Geometric Shapes block (U+25A0–U+25FF) contains geometric shape symbols.

The math subset of this block is U+25A0–25A1, U+25AE–25B7, U+25BC–25C1, U+25C6–25C7, U+25CA–25CB, U+25CF–25D3, U+25E2, U+25E4, U+25E7–25EC, and U+25F8–25FF.

Arrows block

Main page: Arrows (Unicode block)

The Arrows block (U+2190–U+21FF) contains line, curve, and semicircle arrows and arrow-like operators.

The math subset of this block is U+2190–U+21A7, U+21A9–U+21AE, U+21B0–U+21B1, U+21B6–U+21B7, U+21BC–U+21DB, U+21DD, U+21E4–U+21E5, U+21F4–U+21FF.[6]

Supplemental Arrows-A block

The Supplemental Arrows-A block (U+27F0–U+27FF) contains arrows and arrow-like operators.

Supplemental Arrows-A[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+27Fx ⟰ ⟱ ⟲ ⟳ ⟴ ⟵ ⟶ ⟷ ⟸ ⟹ ⟺ ⟻ ⟼ ⟽ ⟾ ⟿
Notes
1.^ As of Unicode version 13.0

Supplemental Arrows-B block

The Supplemental Arrows-B block (U+2900–U+297F) contains arrows and arrow-like operators (arrow tails, crossing arrows, curved arrows, and harpoons).

Supplemental Arrows-B[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+290x ⤀ ⤁ ⤂ ⤃ ⤄ ⤅ ⤆ ⤇ ⤈ ⤉ ⤊ ⤋ ⤌ ⤍ ⤎ ⤏
U+291x ⤐ ⤑ ⤒ ⤓ ⤔ ⤕ ⤖ ⤗ ⤘ ⤙ ⤚ ⤛ ⤜ ⤝ ⤞ ⤟
U+292x ⤠ ⤡ ⤢ ⤣ ⤤ ⤥ ⤦ ⤧ ⤨ ⤩ ⤪ ⤫ ⤬ ⤭ ⤮ ⤯
U+293x ⤰ ⤱ ⤲ ⤳ ⤴ ⤵ ⤶ ⤷ ⤸ ⤹ ⤺ ⤻ ⤼ ⤽ ⤾ ⤿
U+294x ⥀ ⥁ ⥂ ⥃ ⥄ ⥅ ⥆ ⥇ ⥈ ⥉ ⥊ ⥋ ⥌ ⥍ ⥎ ⥏
U+295x ⥐ ⥑ ⥒ ⥓ ⥔ ⥕ ⥖ ⥗ ⥘ ⥙ ⥚ ⥛ ⥜ ⥝ ⥞ ⥟
U+296x ⥠ ⥡ ⥢ ⥣ ⥤ ⥥ ⥦ ⥧ ⥨ ⥩ ⥪ ⥫ ⥬ ⥭ ⥮ ⥯
U+297x ⥰ ⥱ ⥲ ⥳ ⥴ ⥵ ⥶ ⥷ ⥸ ⥹ ⥺ ⥻ ⥼ ⥽ ⥾ ⥿
Notes
1.^ As of Unicode version 13.0

Miscellaneous Symbols and Arrows block

The Miscellaneous Symbols and Arrows block (U+2B00–U+2BFF Arrows) contains arrows and geometric shapes with various fills.

The math subset of this block is U+2B30–U+2B44, U+2B47–U+2B4C.[7]

Miscellaneous Symbols and Arrows[1][2]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+2B0x ⬀ ⬁ ⬂ ⬃ ⬄ ⬅ ⬆ ⬇ ⬈ ⬉ ⬊ ⬋ ⬌ ⬍ ⬎ ⬏
U+2B1x ⬐ ⬑ ⬒ ⬓ ⬔ ⬕ ⬖ ⬗ ⬘ ⬙ ⬚ ⬛ ⬜ ⬝ ⬞ ⬟
U+2B2x ⬠ ⬡ ⬢ ⬣ ⬤ ⬥ ⬦ ⬧ ⬨ ⬩ ⬪ ⬫ ⬬ ⬭ ⬮ ⬯
U+2B3x ⬰ ⬱ ⬲ ⬳ ⬴ ⬵ ⬶ ⬷ ⬸ ⬹ ⬺ ⬻ ⬼ ⬽ ⬾ ⬿
U+2B4x ⭀ ⭁ ⭂ ⭃ ⭄ ⭅ ⭆ ⭇ ⭈ ⭉ ⭊ ⭋ ⭌ ⭍ ⭎ ⭏
U+2B5x ⭐ ⭑ ⭒ ⭓ ⭔ ⭕ ⭖ ⭗ ⭘ ⭙ ⭚ ⭛ ⭜ ⭝ ⭞ ⭟
U+2B6x ⭠ ⭡ ⭢ ⭣ ⭤ ⭥ ⭦ ⭧ ⭨ ⭩ ⭪ ⭫ ⭬ ⭭ ⭮ ⭯
U+2B7x ⭰ ⭱ ⭲ ⭳ ⭶ ⭷ ⭸ ⭹ ⭺ ⭻ ⭼ ⭽ ⭾ ⭿
U+2B8x ⮀ ⮁ ⮂ ⮃ ⮄ ⮅ ⮆ ⮇ ⮈ ⮉ ⮊ ⮋ ⮌ ⮍ ⮎ ⮏
U+2B9x ⮐ ⮑ ⮒ ⮓ ⮔ ⮕ ⮗ ⮘ ⮙ ⮚ ⮛ ⮜ ⮝ ⮞ ⮟
U+2BAx ⮠ ⮡ ⮢ ⮣ ⮤ ⮥ ⮦ ⮧ ⮨ ⮩ ⮪ ⮫ ⮬ ⮭ ⮮ ⮯
U+2BBx ⮰ ⮱ ⮲ ⮳ ⮴ ⮵ ⮶ ⮷ ⮸ ⮹ ⮺ ⮻ ⮼ ⮽ ⮾ ⮿
U+2BCx ⯀ ⯁ ⯂ ⯃ ⯄ ⯅ ⯆ ⯇ ⯈ ⯉ ⯊ ⯋ ⯌ ⯍ ⯎ ⯏
U+2BDx ⯐ ⯑ ⯒ ⯓ ⯔ ⯕ ⯖ ⯗ ⯘ ⯙ ⯚ ⯛ ⯜ ⯝ ⯞ ⯟
U+2BEx ⯠ ⯡ ⯢ ⯣ ⯤ ⯥ ⯦ ⯧ ⯨ ⯩ ⯪ ⯫ ⯬ ⯭ ⯮ ⯯
U+2BFx ⯰ ⯱ ⯲ ⯳ ⯴ ⯵ ⯶ ⯷ ⯸ ⯹ ⯺ ⯻ ⯼ ⯽ ⯾ ⯿
Notes
1.^ As of Unicode version 13.0
2.^ Grey areas indicate non-assigned code points

Combining Diacritical Marks for Symbols 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–U+20DC, U+20E1, U+20E5–U+20E6, and U+20EB–U+20EF.

Arabic Mathematical Alphabetic Symbols block

The Arabic Mathematical Alphabetic Symbols block (U+1EE00–U+1EEFF) contains characters used in Arabic mathematical expressions.

Arabic Mathematical Alphabetic Symbols[1][2]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+1EE0x 𞸀 𞸁 𞸂 𞸃 𞸅 𞸆 𞸇 𞸈 𞸉 𞸊 𞸋 𞸌 𞸍 𞸎 𞸏
U+1EE1x 𞸐 𞸑 𞸒 𞸓 𞸔 𞸕 𞸖 𞸗 𞸘 𞸙 𞸚 𞸛 𞸜 𞸝 𞸞 𞸟
U+1EE2x 𞸡 𞸢 𞸤 𞸧 𞸩 𞸪 𞸫 𞸬 𞸭 𞸮 𞸯
U+1EE3x 𞸰 𞸱 𞸲 𞸴 𞸵 𞸶 𞸷 𞸹 𞸻
U+1EE4x 𞹂 𞹇 𞹉 𞹋 𞹍 𞹎 𞹏
U+1EE5x 𞹑 𞹒 𞹔 𞹗 𞹙 𞹛 𞹝 𞹟
U+1EE6x 𞹡 𞹢 𞹤 𞹧 𞹨 𞹩 𞹪 𞹬 𞹭 𞹮 𞹯
U+1EE7x 𞹰 𞹱 𞹲 𞹴 𞹵 𞹶 𞹷 𞹹 𞹺 𞹻 𞹼 𞹾
U+1EE8x 𞺀 𞺁 𞺂 𞺃 𞺄 𞺅 𞺆 𞺇 𞺈 𞺉 𞺋 𞺌 𞺍 𞺎 𞺏
U+1EE9x 𞺐 𞺑 𞺒 𞺓 𞺔 𞺕 𞺖 𞺗 𞺘 𞺙 𞺚 𞺛
U+1EEAx 𞺡 𞺢 𞺣 𞺥 𞺦 𞺧 𞺨 𞺩 𞺫 𞺬 𞺭 𞺮 𞺯
U+1EEBx 𞺰 𞺱 𞺲 𞺳 𞺴 𞺵 𞺶 𞺷 𞺸 𞺹 𞺺 𞺻
U+1EECx
U+1EEDx
U+1EEEx
U+1EEFx 𞻰 𞻱
Notes
1.^ As of Unicode version 13.0
2.^ Grey areas indicate non-assigned code points

Characters in other blocks

Mathematical characters also appear in other blocks. Below is a list of these characters as of Unicode version Template:Unicode version:

U+002B + PLUS SIGN
U+002D - HYPHEN-MINUS[8]
U+003C < LESS-THAN SIGN
U+003D = EQUALS SIGN
U+003E > GREATER-THAN SIGN
U+005E ^ CIRCUMFLEX ACCENT
U+007C | VERTICAL LINE
U+007E ~ TILDE
U+00AC ¬ NOT SIGN
U+00B0 ° DEGREE SIGN[9]
U+00B1 ± PLUS-MINUS SIGN
U+00D7 × MULTIPLICATION SIGN
U+00F7 ÷ DIVISION SIGN
U+03D0 ϐ GREEK BETA SYMBOL
U+03D1 ϑ GREEK THETA SYMBOL
U+03D2 ϒ GREEK UPSILON WITH HOOK SYMBOL
U+03D5 ϕ GREEK PHI SYMBOL
U+03F0 ϰ GREEK KAPPA SYMBOL
U+03F1 ϱ GREEK RHO SYMBOL
U+03F4 ϴ GREEK CAPITAL THETA SYMBOL
U+03F5 ϵ GREEK LUNATE EPSILON SYMBOL
U+03F6 ϶ GREEK REVERSED LUNATE EPSILON SYMBOL
U+0606 ؆ ARABIC-INDIC CUBE ROOT
U+0607 ؇ ARABIC-INDIC FOURTH ROOT
U+0608 ؈ ARABIC RAY
  • General Punctuation block
U+2016 ‖ DOUBLE VERTICAL LINE
U+2032 ′ PRIME
U+2033 ″ DOUBLE PRIME
U+2034 ‴ TRIPLE PRIME
U+2040 ⁀ CHARACTER TIE
U+2044 ⁄ FRACTION SLASH
U+2052 ⁒ COMMERCIAL MINUS SIGN
U+2061 note FUNCTION APPLICATION
U+2062 note INVISIBLE TIMES
U+2063 note INVISIBLE SEPARATOR
U+2064 note INVISIBLE PLUS

Note: non-marking character

U+207A ⁺ SUPERSCRIPT PLUS SIGN
U+207B ⁻ SUPERSCRIPT MINUS
U+207C ⁼ SUPERSCRIPT EQUALS SIGN
U+207D ⁽ SUPERSCRIPT LEFT PARENTHESIS
U+207E ⁾ SUPERSCRIPT RIGHT PARENTHESIS
U+208A ₊ SUBSCRIPT PLUS SIGN
U+208B ₋ SUBSCRIPT MINUS
U+208C ₌ SUBSCRIPT EQUALS SIGN
U+208D ₍ SUBSCRIPT LEFT PARENTHESIS
U+208E ₎ SUBSCRIPT RIGHT PARENTHESIS
U+2605 ★ BLACK STAR
U+2606 ☆ WHITE STAR
U+2640 ♀ FEMALE SIGN
U+2642 ♂ MALE SIGN
U+2660 ♠ BLACK SPADE SUIT
U+2661 ♡ WHITE HEART SUIT
U+2662 ♢ WHITE DIAMOND SUIT
U+2663 ♣ BLACK CLUB SUIT
U+266D ♭ MUSIC FLAT SIGN
U+266E ♮ MUSIC NATURAL SIGN
U+266F ♯ MUSIC SHARP SIGN
U+FB29 ﬩ HEBREW LETTER ALTERNATIVE PLUS SIGN
U+FE61 ﹡ SMALL ASTERISK
U+FE62 ﹢ SMALL PLUS SIGN
U+FE63 ﹣ SMALL HYPHEN-MINUS
U+FE64 ﹤ SMALL LESS-THAN SIGN
U+FE65 ﹥ SMALL GREATER-THAN SIGN
U+FE66 ﹦ SMALL EQUALS SIGN
U+FE68 ﹨ SMALL REVERSE SOLIDUS
U+FF0B ＋ FULLWIDTH PLUS SIGN
U+FF1C ＜ FULLWIDTH LESS-THAN SIGN
U+FF1D ＝ FULLWIDTH EQUALS SIGN
U+FF1E ＞ FULLWIDTH GREATER-THAN SIGN
U+FF3C ＼ FULLWIDTH REVERSE SOLIDUS
U+FF3E ＾ FULLWIDTH CIRCUMFLEX ACCENT
U+FF5C ｜ FULLWIDTH VERTICAL LINE
U+FF5E ～ FULLWIDTH TILDE
U+FFE2 ￢ FULLWIDTH NOT SIGN
U+FFE9 ￩ HALFWIDTH LEFTWARDS ARROW
U+FFEA ￪ HALFWIDTH UPWARDS ARROW
U+FFEB ￫ HALFWIDTH RIGHTWARDS ARROW
U+FFEC ￬ HALFWIDTH DOWNWARDS ARROW

See also

References

  1. ↑ 1.0 1.1 "Unicode Technical Report #25: Unicode Support for Mathematics" (PDF). The Unicode Consortium. 2 April 2012. https://www.unicode.org/reports/tr25/. 
  2. ↑ "Unicode Character Database: Derived Core Properties". The Unicode Consortium. 19 February 2014. https://www.unicode.org/Public/UCD/latest/ucd/DerivedCoreProperties.txt. 
  3. ↑ "Unicode Technical Annex #44: Unicode Character Database" (PDF). The Unicode Consortium. 25 September 2013. https://www.unicode.org/reports/tr44/. 
  4. ↑ 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.
  5. ↑ See https://www.unicode.org/Public/UCD/latest/ucd/DerivedCoreProperties.txt
  6. ↑ More symbols are supported by TeX math packages, see e.g. Will Robertson, Symbols defined by unicode-math.
  7. ↑ The quadruple arrows U+2B45 and U+2B46 are supported by TeX math packages, per Will Robertson, Symbols defined by unicode-math.
  8. ↑ As per Unicode 15.1.0, the ASCII hyphen-minus is not a mathematical symbol. To express the minus sign in math, U+2212 − MINUS SIGN is used instead.
  9. ↑ As per Unicode 15.1.0, 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".

External links



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