Multiply Dot Symbol: What It Is and How It Is Used in Math
Explore what the multiply dot symbol means in math, how it differs from a period, and where it appears in scalar multiplication, dot products, and European decimal notation.
The multiply dot symbol is a small circle used to indicate multiplication in math. In some contexts, it also means something else.
I’ve written about the “multiply dot” symbol before. But I’ve been meaning to write an article that explains everything there is to know about this very important math symbol. So here we go!
The multiply dot symbol (·) is a small circle used to indicate multiplication in math. The symbol is sometimes called the “dot operator”, and it’s often used when you want to avoid using the multiplication sign × because of ambiguity with the variable x.
The multiply dot symbol is different from a period (.) in typography. A period is a small dot, but it’s smaller than a multiply dot. Also, a period is placed on the baseline of a font, whereas a multiply dot is centered on the cap height of a font.
For example, if you have 2 · 2 = 4, the dots are centered vertically, while periods would be lower.
In digital systems, the multiply dot is represented by the Unicode code point U+22C5. In TeX, it’s represented by the command \cdot. In LaTeX, it’s represented by the command \cdot.
The dot operator has two distinct mathematical roles:
Scalar multiplication: In arithmetic, the dot operator can be used to represent scalar multiplication. For example, 3 ⋅ 5 = fifteen.
Dot product: In linear algebra, the dot operator is used to represent the dot product of two vectors. The dot product is a number that represents how aligned two vectors are. For example, the dot product of vectors ⟨a,b⟩ and ⟨c,d⟩ is ac + bd.
When used between plain numbers, the dot and cross carry identical meaning. There is no mathematical difference between · and × between two numbers.
However, the dot is preferred over the cross in algebraic expressions because the cross symbol resembles the letter x. This can cause confusion when mixing letters and operators in an expression. The dot removes that confusion.
The multiply dot symbol is also used in European conventions as a decimal point.
In Europe, the dot is used as a decimal separator instead of a comma. However, the meaning of the dot is context-dependent; it can mean either multiplication or a decimal point depending on the situation.