Contour Integral

A symbol from the Math Symbols collection. Click the symbol or the button below to copy.

Symbol: ∮
Unicode: U+222E
HTML entity: ∮
Category: Math Symbols

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Download Contour Integral as a vector SVG or a raster PNG.

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SVG uses the system font stack — open in any vector editor and convert to outlines if needed. PNGs have a transparent background.

19 of 58 in the math symbols collection

About the contour integral symbol

Representing an integral over a closed path, ∮ is officially known as the Contour Integral. It is typically read as "the contour integral of" or "the line integral over a closed curve." This character belongs to the Mathematical Operators block and functions as a specialized version of the standard integral symbol, distinguished by the circle at its center which signifies the closed nature of the integration path.

In professional and academic writing, this symbol is primarily found in the fields of physics and vector calculus. It is most commonly used when expressing Maxwell’s equations to describe electromagnetic fields or when applying Cauchy's residue theorem in complex analysis. Engineers also utilize it when calculating work done in a conservative field or determining fluid flow around a closed loop.

How to type Contour Integral

Native keyboard shortcuts for each operating system — derived from the codepoint, so the steps below are always accurate.

Windows

2 options

In Word / Outlook: type 222E then press Alt + X.
Anywhere: press Win + . to open the emoji & symbol picker, then search.

macOS

2 options

Enable “Unicode Hex Input” in System Settings → Keyboard, then hold Option and type 222E.
Or: Control + Command + Space opens the Character Viewer — search by name.