The Mathematical Symbol "Circled Ring Operator (⊚)"

The ⊚ Symbol in Mathematics: Circled Ring Operator

In the extensive array of mathematical symbols, the ⊚ or "Circled Ring Operator" holds its own unique position. This article seeks to shed light on its meaning, primary usage, and a couple of illustrative examples.


The ⊚ symbol is often employed in algebraic structures and mathematical constructs where a specific binary operation or relationship needs to be highlighted. Its appearance – a ring encircled – gives a visual hint to its name and purpose.


  • Example 1: In algebraic structures:
    Consider two elements \( a \) and \( b \) of a ring \( R \). If there's a specific operation denoted by ⊚ that combines these elements, it can be represented as \( a ⊚ b \).
  • Example 2: In theoretical computer science:
    The ⊚ operator can sometimes be used to represent a special combination or operation of two data structures or elements, emphasizing a unique or modified combination methodology.

In summary, the ⊚ symbol provides a concise means to symbolize specific operations or relationships, especially in algebraic contexts. Familiarizing oneself with this notation can be essential for various mathematical discussions and proofs.

Mathematical symbol 'Circled Ring Operator'

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Codes for the ⊚ Symbol

The Symbol
Alt CodeAlt 8858
HTML Code⊚
HTML Entity⊚
CSS Code\229A
Hex Code⊚

How To Insert the ⊚ Symbol

(Method 1) Copy and paste the symbol.

The easiest way to get the ⊚ symbol is to copy and paste it into your document.

Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.

(Method 2) Use the "Alt Code."

If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8858. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML TextOutput
<b>My symbol: &#8858;</b>My symbol: ⊚

(Method 4) Use the HTML Entity Code (for webpages).

HTML TextOutput
<b>My symbol: &ocir;</b>My symbol: ⊚

(Method 5) Use the CSS Code (for webpages).

CSS and HTML TextOutput
span:after {
content: "\229A";}
<span>My symbol:</span>
My symbol: ⊚

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML TextOutput
<b>My symbol: &#x229A;</b>My symbol: ⊚
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x229A to place the ⊚ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for ⊚ is U+229A. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:
[Hold down Alt]
[Press x]

(The 229A turns into ⊚. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u229A. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u229A"
document.write("My symbol: " + str)
My symbol: ⊚