The Minus-or-Plus Sign (∓): Meaning, Math, and Unicode

The minus-or-plus sign (∓) is a mathematical symbol used to indicate a choice of negative and positive values. It typically appears alongside the more common plus-minus sign (±) in equations to show that the signs strictly alternate. When an expression uses a plus for the first symbol, the corresponding part of the equation uses a minus, and vice versa.

In the Unicode standard, this symbol is officially named MINUS-OR-PLUS SIGN and sits at the code point U+2213. It belongs to the Mathematical Operators block, a collection of characters dedicated to scientific and numerical notation. Mathematicians developed this paired notation to save space, allowing them to write two related equations cleanly without duplicating lengthy, complex formulas.

You will encounter the ∓ symbol most frequently in advanced mathematics, physics, and engineering. A classic example is the cosine addition formula: cos(a ± b) = cos(a)cos(b) ∓ sin(a)sin(b). This tells the reader that if you add the angles on the left side, you must subtract the terms on the right side. Beyond equations, the symbol has a fascinating use in chess notation. Chess analysts use ∓ to indicate that the black pieces have a decisive advantage on the board, acting as the exact opposite of the ± sign, which signals a white advantage.

Typing the ∓ symbol can require a few extra steps since it does not appear on standard keyboards. On Windows, the easiest method is to type 2213 and press Alt + X in Microsoft Word, or use the built-in Character Map app. Mac users can pull up the Character Viewer by pressing Cmd + Ctrl + Space and searching for "minus." Web developers can insert it using the HTML entity ∓ or ∓, while scientists and programmers rely on the LaTeX command \mp to render it perfectly in digital documents.

The ∓ sign is the inverse sibling of the plus-minus sign (±, U+00B1). While ± means "plus or minus," ∓ explicitly means "minus or plus." These two symbols are an inseparable pair in complex formulas. It is crucial never to use them interchangeably when both appear in the same mathematical expression, as the top and bottom operators of each sign must stay strictly aligned to keep the math accurate.