Mathematical operators and symbols in Unicode
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
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
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
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
| ||||||||||||||||
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
| ||||||||||||||||
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 | ||||||||||||||||
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 | ||||||||||||||||
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:
Note: non-marking character |
|
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 Unicode symbols includes symbols for SI units
- Units for order of magnitude shows position of SI units
References
- ↑ 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/.
- ↑ "Unicode Character Database: Derived Core Properties". The Unicode Consortium. 19 February 2014. https://www.unicode.org/Public/UCD/latest/ucd/DerivedCoreProperties.txt.
- ↑ "Unicode Technical Annex #44: Unicode Character Database" (PDF). The Unicode Consortium. 25 September 2013. https://www.unicode.org/reports/tr44/.
- ↑ 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.
- ↑ See https://www.unicode.org/Public/UCD/latest/ucd/DerivedCoreProperties.txt
- ↑ More symbols are supported by TeX math packages, see e.g. Will Robertson, Symbols defined by unicode-math.
- ↑ The quadruple arrows U+2B45 and U+2B46 are supported by TeX math packages, per Will Robertson, Symbols defined by unicode-math.
- ↑ 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.
- ↑ 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
- Mathematical Markup Language (MathML) W3C Recommendation (2nd ed.). W3C. 10 April 2014. http://www.w3.org/TR/MathML/.
- Images of glyphs in section 6.3.3 of the Mathematical Markup Language (MathML) W3C Recommendation (2nd ed.). W3C. 21 February 2001. http://www.w3.org/TR/2001/REC-MathML2-20010221/.
 |  |
