⊗ Circled Times Symbol: Meaning, Math Usage, and How to Type It

The ⊗ symbol, officially known as the Circled Times or tensor product symbol, represents a multiplication sign enclosed within a circle. In mathematics, it primarily denotes the tensor product of vector spaces, matrices, or other algebraic structures. In physics, it visually illustrates a vector—such as a magnetic field—pointing away from the viewer and into the page, resembling the tail feathers of a retreating arrow.

Added to the Unicode Standard in 1993, ⊗ resides in the Mathematical Operators block under the code point U+2297. Mathematicians and physicists developed this specific notation in the late 19th and early 20th centuries to distinguish complex operations from standard multiplication. Enclosing mathematical operators in circles became a highly effective, standard way to show that a mathematical operation applies to higher-dimensional spaces or non-standard mathematical fields.

You will spot the circled times symbol across several different disciplines. Beyond tensor products in advanced algebra, electrical engineers and computer scientists sometimes use it to represent the convolution operation or the exclusive OR (XOR) logic gate, though the circled plus (⊕) is more common for XOR. Outside of STEM fields, UI designers occasionally borrow ⊗ as a stylized "close" or "cancel" button, or to denote a crosshair or target in modern gaming interfaces.

Typing the ⊗ symbol varies depending on your platform and operating system. On a Windows PC, you can type 2297 and press Alt + X in Microsoft Word, or simply grab it from the Windows Character Map. On a Mac, pull up the Character Viewer (Control + Command + Space) and search for "circled times." If you are coding for the web, use the HTML entity ⊗ to display it cleanly. For mathematical and academic writing in LaTeX, the command \otimes renders the symbol perfectly.

The circled times operator sits alongside several visual and mathematical siblings. It directly pairs with ⊕ (Circled Plus, U+2295), which represents a direct sum. It also acts as a specialized extension of the standard × (Multiplication Sign, U+00D7). If you need a significantly larger version for complex mathematical equations, Unicode provides the N-ary Circled Times Operator (⨂, U+2A02), which functions much like the standard summation symbol but is designed specifically for large-scale tensor products.