Unicode math symbols: what this list covers
Unicode gives mathematics more characters than any single textbook uses. Four blocks hold the operators and relations: Mathematical Operators (U2200 to U22FF, in Unicode since version 1.1 in 1993), Supplemental Mathematical Operators (U2A00 to U2AFF), Miscellaneous Mathematical Symbols-A (U27C0 to U27EF) and Miscellaneous Mathematical Symbols-B (U2980 to U29FF). The three later blocks arrived together in Unicode 3.2 in 2002, when the STIX project of the scientific publishers and the American Mathematical Society handed Unicode the symbols their journals had been setting in private fonts for decades. The letter-shaped variables live in Mathematical Alphanumeric Symbols (2001) and, for Arabic-script mathematics, in Arabic Mathematical Alphabetic Symbols (2012).
The 138 signs most people search for, from and to , , , and , are on the Math Symbols page with their meanings and keyboard shortcuts. This page holds the other 621: every remaining character of those four operator blocks that has a page here, the odd mathematical pieces from Miscellaneous Technical ( ), the styled nabla and partial signs, the Arabic mathematical letters and three Arabic root and ray signs. Together the two pages give you the whole of Unicode mathematics as plain text, which pastes into Word, Google Docs, Discord, Notion and any code editor as ordinary characters.
The grid is arranged by family rather than by code point, because that is how a specialist looks for a sign: all the forms of less-than together, with each mirror image in the row below, all subset variants together, all turnstiles together. Where a family comes in pairs (less and greater, precedes and succeeds, subset and superset) the columns line the pairs up, so a blank cell means Unicode has no mirror for that one, or the mirror is a common sign already on the main page.
How the Unicode math operators are organised and named
Unicode names describe the shape, not the meaning, and the names on this page are the long ones: is LESS-THAN ABOVE DOUBLE-LINE EQUAL ABOVE GREATER-THAN, is SUPERSET BESIDE AND JOINED BY DASH WITH SUBSET. That is deliberate. A sign like means "square image of" in one textbook and "is a substructure of" in another, so the standard records the picture and leaves the reading to the author. Only a few carry an informative alias: is noted as "Dijkstra choice", as the modal operator "was always", ("gleich stark") as tautological equivalence and as the modulo-two sum.
Within the blocks the characters run in loose families: the Supplemental block opens with the big operators , then a run of integrals to , then decorated plus, minus and times signs, unions and intersections, the logical and-or forms, a long run of equals and less-than relations, the precedes and subset families, and finally tacks, turnstiles and bars. Both the original Mathematical Operators block and the Supplemental one are completely full: 256 characters each, not one code point spare, which is why newer signs such as and (added in Unicode 6.1) had to go into Miscellaneous Mathematical Symbols-A.
The naming system also explains the pairs. Almost every relation has a mirror image that is a separate character, and the pair sits side by side in the code chart: , , , . Negations are separate characters too ( , , ), with one famous exception: FORKING is defined as NONFORKING plus the combining long solidus U0338, and because it is excluded from composition, any text that is normalised ends up with the two-character form. If a search for the single character finds nothing, that is why.
Who uses the rare math operators
Order theory and lattice theory own the curly and square families: and for a preorder, and for the information order of domain theory, and for meet and join with their big forms and . Logicians write for semantic consequence, for forcing in set theory, for "ordinarily satisfies" in non-monotonic logic, and model theorists took and for forking and non-forking independence. Linear logic reads as "lollipop", its implication that uses each hypothesis exactly once.
Database courses write the natural join of two tables as R S, with for the left, right and full outer joins and as the large join operator of relational algebra. The Z notation of formal software specification has its own run of characters: the type colon , schema composition and piping , domain and range anti-restriction , bag membership and schema hiding written with the big reverse solidus . Programmers meet , single characters that look like the ::, and of grammars and code, and the ALGOL 60 report used as the exponent mark in numbers like 16.
Analysts and physicists have the decorated integrals: for the finite-part (Hadamard) integral, for an average over a domain, for contour integrals that go around or past a pole, for a quaternion integral, and the d'Alembertian of the wave equation. Category theory marks a pullback square with and a pushout with , and writes coproducts with or . Combinatorial game theory has and , "tiny" and "miny", the infinitesimal games from Winning Ways. Geometry gets the measured angles to , the spherical angles and the three-dimensional angle , which Unicode notes was used by Euclid.
Arabic mathematical alphabetic symbols
Mathematics written in Arabic script, as it is taught in Morocco, Algeria, Tunisia, Syria, Iran and parts of the Gulf, runs from right to left and uses Arabic letters as its variables, with the common ones being 𞸎 (seen, the usual x), 𞸑 (sad, the usual y) and 𞸏 (ain, z). The Arabic Mathematical Alphabetic Symbols block (U1EE00 to U1EEFF, Unicode 6.1, 2012) gives these letters a form that will not join to its neighbours and will not be mistaken for a word, exactly as the bold, italic and double-struck Latin letters do for European mathematics. Each letter exists in up to five styles that Arabic typesetters use the way Latin typesetters use italic and bold: isolated, initial, tailed, stretched and looped, plus four dotless shapes used where the dots would clash with notation.
The block lists the letters in the old abjad order (alef, beh, jeem, dal, heh, waw, zain, hah, tah, yeh, kaf, lam, meem, noon, seen, ain, feh, sad, qaf, reh, sheen, teh, theh, khah, thal, dad, zah, ghain), the order in which Arabic letters carry numerical values and label the points of a figure, not the order of a modern dictionary. The grids above follow it, with one row per style. Two operators close the block: , meem and hah joined by a tatweel, is the Arabic summation sign (from majmūʿ, "sum"), and , hah joined to dal, is the limit sign of Persian mathematics (from ḥadd, "limit"); both stretch like does. Three signs from the main Arabic block belong with them: the Arabic-Indic cube root and fourth root , which take the place of and , and the Arabic ray .
Few fonts have this block. Noto Sans Math has every letter and both operators, and DejaVu Sans about two thirds of them; XITS Math, a free font built from STIX specifically to add Arabic mathematics, is the usual choice in LuaLaTeX and XeLaTeX documents. Ordinary Arabic text fonts such as Noto Naskh Arabic show the roots and the ray but not the mathematical letters, so a page that mixes them needs a math font in its font stack.
Fonts, typing and pitfalls
Font support is the first thing to check. The 1993 Mathematical Operators block is in almost every system font, but the 2002 blocks are not: DejaVu Sans, the usual Linux fallback, has the whole original block yet fewer than a third of the Supplemental block and almost none of the Miscellaneous Mathematical Symbols, and a page without a math font shows those as empty boxes. Noto Sans Math has all 472 characters here from the four operator blocks, the styled nabla and partial signs and the complete Arabic mathematical block; the fifteen stragglers that live in other blocks ( ℇ and the small forms ﹪) come from ordinary text fonts such as Noto Sans, Noto Sans Symbols, Noto Sans Arabic or DejaVu Sans. STIX Two Math, Latin Modern Math, Cambria Math (Windows and Office) and Libertinus Math are the other fonts made for mathematical typesetting, and any of them is a sound choice for a document. Phones vary, so a message full of and may reach a friend as boxes.
Typing: the quickest route is copying from this page. In Word and Outlook, type the hex code and press Alt X (2A7D Alt X gives ). On a Mac, open the Character Viewer (Ctrl Cmd Space) and search by the Unicode name. On Linux desktops, Ctrl Shift U, the hex, then Space. In LaTeX the characters have command names: \leqslant , \preceq , \sqsubseteq , \bigsqcup , \biguplus , \Vdash , \bowtie , \ltimes , \multimap , \coprod ; with the unicode-math package under XeLaTeX or LuaLaTeX you can also paste the characters straight into the source.
Pitfalls worth knowing. and mean the same thing; the slanted form is the house style of French and Russian mathematics and of many British school texts, and a document should use one or the other, never both. and are different characters (the n-ary one takes an index underneath), as are and . are not integrals, sums or roots but the pieces used to draw tall ones line by line in terminals and old typesetters. , named "thermodynamic", was the record mark of IBM punched-card machines of the 1960s, and , the commercial minus, is the bookkeeping "less" sign of German and Swedish invoices. And the small plus, equals and percent ﹪ exist only for compatibility with old East Asian encodings; use the normal signs in anything new.
Symbols
621Click a symbol to copy it and open its page.
The best-known ones, with their meanings: ➗ Math Symbols
Equals and equivalence
the plain =, ≠, ≡, ≈ and ≅ are on the Math Symbols page
Less than and greater than
each column is one idea; the top row is the less-than form, the bottom row its mirror
Less than and greater than, slanted equals
⩽ and ⩾ are the slanted forms of ≤ and ≥ used in French and Russian typesetting
Less than and greater than, stacked and shaped
Precedes and succeeds
the curly order signs of order theory and lattice theory
Square order, lattices and subgroups
Element of and contains
variants of ∈ and ∋; ϶ is the "such that" of Peano
Subsets and supersets
the plain ⊂ ⊃ ⊆ ⊇ ⊄ are on the Math Symbols page
Union, intersection and the empty set
Turnstiles and tacks
proves ⊢, models ⊨ and forces ⊩ in every strength; ⊢ and ⊥ themselves are on the main page
Times, products and joins
Big operators
the n-ary forms that take limits above and below, like ∑ and ∏
Integrals
∫ ∬ ∭ ∮ ∯ ∰ are on the main page
Angles and geometry
abjad order, as in the Unicode block; each row is one of the five letter styles
The best-known ones, in their own collection
How to use them
6 situationsClick to copyUnicode Math Symbols combos
12Worth knowing
- Both the Mathematical Operators block (U2200 to U22FF) and the Supplemental Mathematical Operators block (U2A00 to U2AFF) are completely full: 256 assigned characters each, with no room for a single new sign.
- FORKING is the only character on this page that normalisation rewrites: Unicode defines it as plus the combining long solidus and excludes it from composition, so NFC or NFD text always carries the two-character form.
- and are the "Dijkstra choice" bars of guarded commands, is the exponent mark of ALGOL 60 number literals, and "thermodynamic" is the record mark of IBM punched-card equipment, so three of the symbols here come from computing history rather than mathematics.
- Unicode encodes the Arabic mathematical letters in the ancient abjad order (alef, beh, jeem, dal …), the order in which Arabic letters stand for numbers, rather than the order of a modern alphabet.
- , hah joined to dal, exists for Persian mathematics, where "ḥadd" (limit) is written as a stretched ligature over the expression, the way sits over a sum.
Questions people ask
8How many math symbols are there in Unicode?
Unicode 16.0.0 marks 2,312 code points with the Math property, of which 950 are in the category Symbol, Math. This page lists the 621 rarer operators, relations and Arabic mathematical letters; the 138 everyday signs are on the Math Symbols page, and the styled letters (𝐀 𝑎 𝔸 …) have their own pages for bold, italic, double-struck and the other alphabets.
What is the Unicode Mathematical Operators block?
It is the range U2200 to U22FF: 256 characters, from to , in Unicode since version 1.1 in 1993, with the last fourteen ( to ) added in version 3.2. Its common members ( ) are on the Math Symbols page; the remaining 136 are in the first groups of this page, next to their relatives from the Supplemental block.
Where are the basic math symbols like ?
On the Math Symbols page, which holds the 138 everyday signs with their meanings and keyboard shortcuts. This page is the continuation: the rarer characters that Unicode encodes for specialists.
What is the difference between and ?
They mean the same thing, "less than or equal to". has a horizontal bar and a slanted one. The slanted form is the usual style in French and Russian typesetting and in many British textbooks, and LaTeX gives it as \leqslant. Pick one style per document.
How do I type Unicode math symbols in Word?
Type the hex code and press Alt X: 2A7D then Alt X gives , 2AAF gives , 2A06 gives . The code is on every symbol page here. Alternatively copy the character from this page and paste it; it stays a normal text character in Word, Google Docs and email.
How do I use Unicode math symbols in LaTeX?
In pdfLaTeX load amssymb and use the command names: \leqslant , \preceq , \sqsubseteq , \Vdash , \bowtie , \multimap , \bigsqcup . With XeLaTeX or LuaLaTeX and the unicode-math package you can paste the characters directly into the source and set a font such as STIX Two Math or Latin Modern Math.
What font shows all Unicode math symbols?
Noto Sans Math covers all four operator blocks and the Arabic mathematical letters, which is everything on this page except fifteen signs from other blocks ( ℇ , the Arabic roots and the small forms) that ordinary text fonts supply. STIX Two Math, Latin Modern Math, Libertinus Math and Cambria Math are the other fonts made for mathematical typesetting. DejaVu Sans has the original 1993 block in full but less than a third of the Supplemental block, so or may show as a box without a math font.
What are the Arabic mathematical alphabetic symbols?
A Unicode block (U1EE00 to U1EEFF, added in 2012) of Arabic letters shaped for use as variables in right-to-left mathematics, in isolated, initial, tailed, stretched and looped styles, plus the summation operator and the Persian limit operator . They are to Arabic-script mathematics what the bold and italic alphabets are to Latin-script mathematics.
