Bracket Symbols

The four pairs on every keyboard are ( ) parentheses (round brackets), [ ] square brackets, { } curly brackets (braces) and < >, which are strictly the less-than and greater-than signs but serve as angle brackets in HTML, email addresses and chat. The word bracket itself changes meaning across the Atlantic: in British English "brackets" means the round pair, while in American English it usually means the square pair, which is why style guides spell out "round" or "square".

Unicode holds many more. The real angle brackets are ⟨ ⟩ (mathematical left and right angle bracket) and their double form ⟪ ⟫; ⟦ ⟧ are white square brackets, also called semantic or Oxford brackets; ⦃ ⦄ white curly brackets; ⦅ ⦆ white parentheses. ⌈ ⌉ and ⌊ ⌋ are the ceiling and floor pairs. The corner pieces ⌜ ⌝ ⌞ ⌟ mark quotation in logic and editing, and ⸢ ⸣ ⸤ ⸥ are the half brackets scholars use for restored text in papyri and inscriptions.

East Asian typography adds its own families: 「 」 and 『 』 corner brackets, 【 】 and 〖 〗 lenticular brackets, 〔 〕 tortoise shell brackets, 〈 〉 and 《 》 angle brackets, and the fullwidth copies （ ） ［ ］ ｛ ｝ that take up a whole character cell so they line up with Chinese and Japanese characters. Each also exists as a vertical form (︵ ︶ ︷ ︸ ﹁ ﹂) for text that runs top to bottom.

Japanese and Chinese brackets: 「」 『』 【】 〔〕 《》

Japanese has no curly quotation marks of its own; it quotes with corner brackets. 「 」 (kagikakko) encloses speech and short quotations, and 『 』 (nijū kagikakko, the double or white corner bracket) marks a quotation inside a quotation or the title of a book. The halfwidth pair ｢ ｣ is the same bracket squeezed into half a cell for old computer systems. Chinese uses the angle pairs instead: 《 》 around the title of a book, film or newspaper and 〈 〉 around a chapter or article title inside it.

【 】, the black lenticular bracket (sumitsuki kakko), is the loud one: Japanese video and news titles put the category in it, as in 【MV】 or 【速報】, and it has spread to Chinese and Korean social media and to English-language posts that want a heavy, boxed label. Its hollow twin 〖 〗 is lighter. 〔 〕 tortoise shell brackets, named after the six-sided plates of a turtle shell, enclose editorial notes and readings in Japanese dictionaries and law texts.

Because these brackets are fullwidth, they come with built-in space on the inside, so 「like this」 needs no extra spaces. Outside Asia they are popular for aesthetic usernames and Discord names (【ＮＡＭＥ】, 『 Name 』, 「 name 」), and the Nickname Symbols and Japanese Text Symbols collections have more in that spirit.

Bracket symbols in math

Mathematics nests brackets in a fixed order, parentheses inside square brackets inside braces: {[(x + 1)(x − 1)]²}. Beyond that, each bracket shape carries a meaning. [a, b] is a closed interval and (a, b) an open one, so [0, 1) includes 0 but not 1. { } builds a set, {1, 2, 3}. ⟨ ⟩ angle brackets write an inner product ⟨u, v⟩, a generated group ⟨g⟩ or, in physics, the bra-ket notation ⟨ψ| and |φ⟩. ⌊x⌋ is the floor of x (round down) and ⌈x⌉ the ceiling (round up), a notation Kenneth Iverson introduced in 1962. ⟦ ⟧ are the semantic brackets of computer science: ⟦e⟧ means "the meaning of expression e".

A tall matrix or a system of equations needs a bracket several lines high. Unicode supplies the pieces: ⎛ ⎜ ⎝ and ⎞ ⎟ ⎠ build a parenthesis, ⎡ ⎢ ⎣ and ⎤ ⎥ ⎦ a square bracket, ⎧ ⎪ ⎨ ⎩ and ⎫ ⎪ ⎬ ⎭ a brace, one piece per line in a monospace font. The horizontal versions ⏞ ⏟ ⏜ ⏝ ⎴ ⎵ go over or under a run of terms to show what a label refers to.

In LaTeX the pairs are \langle \rangle, \lfloor \rfloor, \lceil \rceil, \{ \} and \llbracket \rrbracket (from the stmaryrd package), and \left( … \right) stretches any of them to the height of what they enclose. In HTML, write < and > for literal < and >, and ⟨ ⟩ ⌈ ⌊ for the math brackets.

Fancy and aesthetic brackets

The Dingbats block carries fourteen bracket ornaments drawn from the ITC Zapf Dingbats typeface: parentheses ❨ ❩, flattened parentheses ❪ ❫, angle brackets ❬ ❭ and the heavy ❰ ❱, the heavy angle quotation ornaments ❮ ❯, tortoise shell ❲ ❳ and curly brackets ❴ ❵. They were added in Unicode 3.2 (2002), long after the rest of the Zapf set, and render bolder and rounder than the keyboard brackets, which is why they frame usernames and headings so well: ❰ Name ❱, ❴ ✦ ❵, ❮ ❯.

The white (double-lined) brackets 〚 〛 ⟦ ⟧ ⦃ ⦄ ⦅ ⦆ ｟ ｠, the black tortoise shell ⦗ ⦘, the double parentheses ⸨ ⸩ and the French guillemets « » and ‹ › are the other favourites for bios and nicknames. The Arabic ornate parentheses ﴾ ﴿ were designed to enclose Quran verses and make a graceful frame for any text, and the Tibetan brackets ༼ ༽ are known worldwide from the ༼ つ ◕_◕ ༽つ kaomoji. Superscript and subscript parentheses ⁽ ⁾ ₍ ₎ give tiny whispers like ₍ᐢ. .ᐢ₎ and footnote-style markers like x⁽¹⁾.

How to type bracket symbols on a keyboard

On a standard US or UK keyboard, ( and ) are Shift+9 and Shift+0, [ and ] are the two keys right of P, and { and } are those keys with Shift. < and > are Shift+comma and Shift+full stop. On a phone keyboard, tap the 123 key, then #+= on iPhone or the second symbols page on Android, to reach [ ] { } < >. Everything else on this page is copied, or typed by code: on Windows hold Alt and type the plus sign followed by the hex code on the number pad (Alt + 27E8 for ⟨ when the registry tweak is on), on Mac type the hex code with the Unicode Hex Input source enabled, and on Linux press Ctrl+Shift+U, the hex code and Space.

Japanese and Chinese input methods have the brackets built in: with a Japanese IME, the [ and ] keys produce 「 and 」 directly, and typing kakko (かっこ) and pressing Space cycles through （）「」『』【】〔〕. With a Chinese IME, the same keys give 【 】 and Shift+comma and Shift+full stop give 《 》. Word and Google Docs also accept the Unicode code followed by Alt+X (Windows Word) to turn 3010 into 【.