Plus Minus Symbol (±): Meaning, Uses, and How to Type It

The plus minus symbol (±) means "plus or minus": it tells you a value can be either added or subtracted, or that a measurement sits somewhere inside a stated range. You will see it in the quadratic formula, in lab reports such as 5.0 ± 0.2 mm, in confidence intervals, and in chess annotations, and you can type it with Alt + 0177 on Windows, Option + Shift + = on a Mac, or \pm in LaTeX.

This guide covers what the plus or minus sign means in each setting, how it differs from its mirror image ∓, and how to type both on every platform.

Copy and Paste the Plus Minus Sign

Copy whichever form you need:

• ± — plus-minus sign (U+00B1)
• ∓ — minus-plus sign (U+2213)
• +/− — plain-text fallback used in emails, spreadsheets, and chess books

The Plus Minus Symbol Explained

The sign is a plus with a short horizontal bar underneath; William Oughtred used it in Clavis Mathematicae in 1631. It is read aloud as "plus or minus" or, in measurement contexts, "give or take."

The symbol does two jobs:

1. Two values in one expression. Writing x = 3 ± 2 is shorthand for "x = 3 + 2 or x = 3 − 2," so x is either 5 or 1.
2. A range around a central value. Writing 5.0 ± 0.2 mm means the true length lies somewhere between 4.8 mm and 5.2 mm.

The mirror-image form ∓ (minus-plus) appears only alongside ± and means "take the opposite sign from the one you chose for ±." It is rarely used on its own.

Uses of the Plus Minus Sign

Quadratic Formula

The most familiar appearance of ± is in the solution to ax² + bx + c = 0:

x = (−b ± √(b² − 4ac)) / 2a

The sign packs both roots into a single line. For x² − 5x + 6 = 0 the formula gives x = (5 ± √(25 − 24)) / 2 = (5 ± 1) / 2, so x = 3 or x = 2.

Measurement Uncertainty

Every physical measurement comes with an uncertainty, and ± is the standard way to report it. A result written as 9.81 ± 0.03 m/s² says that the best estimate is 9.81 and that the experimenter expects the true value to fall within 0.03 of it. The number after ± is usually one standard deviation and should carry the same number of decimal places as the central value.

In papers the same convention appears as mean ± SD or mean ± SEM; always say which one you are reporting, because the two differ by a factor of √n.

Engineering Tolerances

On technical drawings, ± states how far a manufactured part may deviate from its nominal dimension and still be acceptable. A shaft labeled 10.00 ± 0.05 mm must measure between 9.95 mm and 10.05 mm. Electronic components use the same idea with percentages: a 220 Ω ± 5% resistor can legitimately measure anywhere from 209 Ω to 231 Ω.

Confidence Intervals in Statistics

A confidence interval for a population mean is written as the sample mean plus or minus a margin of error:

x̄ ± z · σ / √n

With a sample mean of 50, a known standard deviation of 2.5, a sample size of 100, and z = 1.96 for 95% confidence, the interval is 50 ± 0.49, or roughly 49.51 to 50.49.

Trigonometric Identities and ∓

The minus-plus sign earns its keep when two formulas are compressed into one. The angle-sum identities for cosine are:

cos(a ± b) = cos a cos b ∓ sin a sin b

Read the top signs together and the bottom signs together: cos(a + b) = cos a cos b − sin a sin b, and cos(a − b) = cos a cos b + sin a sin b. The ∓ signals that the sign on the right is always the opposite of the sign chosen on the left.

Chess Annotation

Chess annotators use a family of related signs to evaluate a position:

These come from the Chess Informant notation system and are now used by engines and annotated game collections worldwide.

How to Type the Plus Minus Symbol

Windows: Hold Alt and type 0177 on the numeric keypad; the leading zero matters because it selects the Windows-1252 code page. Alt + 241 (the older DOS code page) gives the same character in most programs. In Word you can also type 00B1 and press Alt + X.

Mac: Press Option + Shift + = on a US or UK keyboard, or open the Character Viewer (Control + Command + Space) and search for "plus-minus."

iPhone and iPad: Switch to the numeric keyboard (the 123 key), then press and hold the + key. The ± character appears in the pop-up. Android's Gboard offers the same long-press on +.

Plus Minus in LaTeX

In math mode, \pm produces ± and \mp produces ∓. Both are binary operators, so LaTeX automatically adds the correct spacing on each side when there is something on both sides, and tightens it when the sign is used as a prefix, as in \pm 3.

```latex
\documentclass{article}
\usepackage{amsmath}
\usepackage{siunitx}
\begin{document}
Quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Angle-sum identity:
\[ \cos(a \pm b) = \cos a \cos b \mp \sin a \sin b \]

Measurements with siunitx:
$\SI{5.0 \pm 0.2}{\milli\metre}$ and $\qty{5.0 +- 0.2}{\mm}$ and $\qty{5.0(2)}{\mm}$

Text mode: a tolerance of \textpm 0.05 mm.
\end{document}
```

For measurements, siunitx handles the spacing between number, uncertainty, and unit. Version 2 syntax is \SI{5.0 \pm 0.2}{\milli\metre}; version 3 accepts \qty{5.0 +- 0.2}{\mm} or the parenthetical \qty{5.0(2)}{\mm}, and the uncertainty-mode option chooses whether the output reads 5.0 ± 0.2 mm or 5.0(2) mm.

Outside math mode, \textpm prints the sign in the text font. It used to need the textcomp package, but since the 2020 LaTeX kernel it works without one.

Related Symbols

What Does ± Mean in a Measurement?

It states the uncertainty of the value. A reading of 12.3 ± 0.1 g means the best estimate is 12.3 g and the true mass is expected to lie between 12.2 g and 12.4 g. Reports should always state whether the number after ± is a standard deviation, a standard error, or an instrument tolerance.

What Is the Difference Between ± and ∓?

Both describe a pair of signs. On its own, ± means "plus or minus." The ∓ sign appears only in an expression that also contains ±, and it means "the opposite sign to the one you picked for ±." If you choose the plus in ±, you must use the minus in ∓, and vice versa.

Why Does the Quadratic Formula Have ±?

A quadratic equation can have two solutions, and the ± lets one formula produce both: evaluating with the plus gives one root and evaluating with the minus gives the other. When the square root is zero, the two roots are identical.

Writing Uncertainties and Tolerances Cleanly

Whether you are reporting a confidence interval or a machining tolerance, use \pm in math mode, \textpm in prose, and siunitx for anything with units. Octree, the AI LaTeX editor at useoctree.com, inserts these commands for you and compiles as you write, so the ± in your results table matches the one in your equations. For a full list of operator symbols with their LaTeX commands, see https://tools.useoctree.com/symbols/operators.