Clockwise Integral ∱

How to type ∱ on Windows

The fastest method on a full-size keyboard is the Alt code Alt+8753.

1. Make sure Num Lock is on.
2. Hold down the Alt key.
3. Type 8753 on the numeric keypad (the number row will not work).
4. Release Alt. The clockwise integral symbol ∱ appears.

Note: Alt+8753 is a Unicode decimal code, not a classic code-page Alt code. It works in Microsoft Word, WordPad and some other apps, but not in Notepad or most browsers. In those apps, copy the symbol from this page instead.

No numeric keypad?

Press Win+. to open the emoji panel, choose the Symbols tab (Ω) and search for "clockwise integral". Or open Character Map from the Start menu, find ∱, click Select, then Copy.

How to type ∱ on a Mac

There is no direct keyboard shortcut for ∱ on a Mac.

For any symbol, the Character Viewer works: press Control+⌘+Space, type "clockwise integral" in the search box and double-click the result. It will be remembered under Frequently Used.

How to type ∱ on iPhone and iPad

The iOS keyboard does not include ∱, so the reliable way is to copy it from this page, then press and hold in any text field and tap Paste.

If you use it often, create a shortcut: open Settings → General → Keyboard → Text Replacement, paste ∱ in the Phrase field and type a short code such as ;clockwise in the Shortcut field. Typing that code will then insert ∱ anywhere.

How to type ∱ on Android

Copy the symbol from this page, then long-press in a text field and choose Paste. Gboard also keeps a clipboard history: tap the clipboard icon on the toolbar to paste it again later.

For a permanent shortcut, open Gboard settings → Dictionary → Personal dictionary, add ∱ as the word and a short code as the shortcut.

How to type ∱ in Microsoft Word

1. Type the Unicode hex code 2231 where you want the symbol.
2. Press Alt+X. Word converts the code into ∱.

This works on Windows in Word, Outlook and OneNote and needs no numeric keypad. You can also go to Insert → Symbol → More Symbols, set the font to a Unicode font and type 2231 in the Character code box. In Excel, the formula =UNICHAR(8753) returns the symbol.

How to type ∱ in Google Docs

Open Insert → Special characters, then either search for "clockwise integral" or draw the symbol in the sketch box. Click the result to insert it. In Google Sheets, use =CHAR(8753).

∱ in HTML, CSS and code

Because ∱ is a standard Unicode character (U+2231), you can also paste it directly into any UTF-8 file. The escaped forms above are only needed when the file encoding is uncertain or the symbol must be entered on a keyboard without it.

Where the clockwise integral symbol is used

Used in physics and engineering texts involving complex analysis or vector calculus, such as ∱E·dl for circulation around a closed loop traversed clockwise. It contrasts with ∲, the general contour integral symbol, and with ∮ which typically implies counterclockwise orientation by convention.

Frequently asked questions