Clockwise Integral Symbol
∱ is the “clockwise integral” symbol used to indicate an integral taken in a clockwise sense.
U+2231
The symbol ∱ is known as the Clockwise Integral. It’s mainly used in mathematical notation where the orientation of a curve or path matters. You can copy it directly or insert it using its Unicode details.
Clockwise Integral Symbol Meaning
∱ (CLOCKWISE INTEGRAL, U+2231) denotes an integral with a clockwise orientation. In contexts like contour or line integrals, the direction around a closed path affects the sign or interpretation of the result, so the notation may explicitly indicate clockwise traversal. Compared with the standard integral symbol, ∱ is a specialized glyph for orientation-specific writing rather than everyday arithmetic. It is most often encountered in textbooks, lecture notes, and typeset equations related to vector calculus, complex analysis, or any setting where path direction is part of the definition.
Common uses
- •Indicating clockwise contour orientation in line or contour integrals in notes
- •Writing oriented boundary integrals in vector calculus problems
- •Labeling direction-sensitive steps in complex analysis derivations
- •Formatting math posts and cheat sheets where orientation must be explicit
- •Using the symbol in LaTeX/Unicode-capable documents as a dedicated glyph
Examples
∱ Clockwise Integral Symbol
- ∱∱ f(z) dz around the chosen clockwise loop
- ∱Evaluate ∱_C F · dr using a clockwise traversal
- ∱The clockwise orientation is shown by ∱ in the diagram
- ∱∱ ∇×G · n dS with the boundary taken clockwise
- ∱Rewrite the expression to match the clockwise integral sign ∱
Variations
Ready to copy
Technical codes
| Unicode | U+2231 | |
| HTML Entity | ∱ | |
| HTML Code | ∱ | |
| CSS | \2231 | |
| Alt Code | Alt + 8753 | |
| Decimal | 8753 |
How to type Clockwise Integral Symbol (∱)
On Windows
Hold Alt and type 8753 on the numeric keypad. In Word, type 2231 then press Alt + X.
On Mac
Switch to the Unicode Hex Input keyboard, then hold Option and type 2231. Or press Control + Command + Space and search.
On Linux
Press Control + Shift + U, type 2231, then press Enter or Space.
Anywhere
Copy ∱ with the button above and paste it wherever you need it — this works on every device and in every app, with no keyboard shortcut to remember.
FAQ
What does the Clockwise Integral symbol mean?
∱ (CLOCKWISE INTEGRAL, U+2231) denotes an integral with a clockwise orientation. In contexts like contour or line integrals, the direction around a closed path affects the sign or interpretation of the result, so the notation may explicitly indicate clockwise traversal. Compared with the standard integral symbol, ∱ is a specialized glyph for orientation-specific writing rather than everyday arithmetic. It is most often encountered in textbooks, lecture notes, and typeset equations related to vector calculus, complex analysis, or any setting where path direction is part of the definition.
What is the Unicode value for ∱?
The symbol ∱ is CLOCKWISE INTEGRAL and has Unicode code point U+2231.
How can I copy ∱ into HTML?
Use the HTML entity: ∱.
How do I use ∱ in CSS or programming strings?
CSS escape: \\2231. JavaScript (Unicode code point escape): \\u{2231}.
When should I use the clockwise integral symbol instead of ∫?
Use ∱ when your notation needs to explicitly state clockwise orientation of a contour or path; ∫ alone usually doesn’t specify direction.