The plus-minus sign (±) is a mathematical symbol commonly used to indicate the precision of an approximation, or as a convenient shorthand for a quantity which has two possible values opposite in sign.

This second usage is most commonly encountered in connection with square roots, e.g. in the formula for the solutions of quadratic equations:

If $ax^2\; +\; bx\; +\; c\; =\; 0$, then

$$

x = \frac{-b \pm \sqrt {b^2-4ac\ }}{2a}. In other words, the two solutions to the equation are

$$

x = \frac{-b + \sqrt {b^2-4ac\ }}{2a} and

$$

x = \frac{-b - \sqrt {b^2-4ac\ }}{2a}

but using the ± symbol allows us to compress these expressions into a single formula.

The use of ± for an approximation is closely related. For example, "5 ± 0.2" denotes a quantity that is within 0.2 units of 5; it is between 5 − 0.2 and 5 + 0.2. a percentage may also be used e.g. 230V ± 10% referring to a voltage within 10% either side of 230V (207V-253V).

Minus-plus sign

---

There is also another character, the minus-or-plus sign (∓), which is rarely seen. It only takes on significant meaning when used in conjunction with the "±" sign. It can be used alongside "±" in such expressions as "x ± y ∓ z", which can be interpreted as "x + y − z" or/and "x − y + z", but not "x + y + z" nor "x − y − z". The upper "−" in "∓" is considered attached to the "+" of "±" (and the lower symbols work in the same way) even though there is no visual indication of the dependency. The original expression can be rewritten as "x ± (y − z)" to avoid confusion, but cases such as the trig identity

$\backslash cos(x\; \backslash pm\; y)\; \backslash equiv\; \backslash cos(x)\; \backslash cos(y)\; \backslash mp\; \backslash sin(x)\; \backslash sin(y)$

are most neatly written using the "∓" sign.

In ISO-8859-1,7,8,9,13,15 and 16, the plus-minus symbol is given by the code B1_hex Since the first 256 code points of Unicode are identical to the contents of ISO-8859-1 this symbol can be found at Unicode code point 00B1. The symbol also has a HTML entity representation of ±. The rarer minus-or-plus sign (∓) is not generally found in legacy encodings and does not have a named HTML entity but is available in Unicode with codepoint U+2213.

In a pinch, a crude version of these symbols can also be formed by underlining/overlining a + sign ( +  ).

See also

---

• Plus and minus signs
• Table of mathematical symbols

Elementary arithmetic Mathematical notation

Plusminuszeichen | Signe plus ou moins | ± | Plus–minustecken | 正負號