What Does ± Mean Next to a Number?

What the ± symbol means

The sign ± combines the plus sign (+) and minus sign (−). In ordinary mathematical notation, it says to consider both adding and subtracting the number that follows it. For example, 10 ± 2 represents 10 + 2 and 10 − 2: the values 12 and 8.

In measurement and science, the same notation often describes a central value together with an uncertainty or tolerance. A measurement written as 10 ± 2 units usually means the measured value is 10 units, with an uncertainty of 2 units. If that uncertainty is treated as a simple range, the possible interval is from 8 to 12 units.

So ± does not have one universal interpretation beyond “plus or minus.” The surrounding words, equation, and conventions tell you whether it is listing two calculations, expressing an approximate range, or describing uncertainty.

How to read it in a calculation

When ± appears in an equation, it can stand for two separate cases. Solve once using the plus sign, then again using the minus sign. This is especially common when a formula has two possible solutions.

For instance, the equation x = 5 ± 3 gives two values: x = 8 or x = 2. It does not mean that x is somehow both values at once; it is compact notation for the pair of results. In some contexts, one of the results may later be ruled out by the conditions of the problem.

In a formula, the symbol may apply to a whole expression, so parentheses matter. If an expression is written as a ± (b + c), the two cases are a + (b + c) and a − (b + c). Follow the grouping symbols and the definitions supplied by the problem rather than assuming the sign applies only to the nearest digit.

Ranges, tolerances, and measurements

When attached to a measured or specified value, ± commonly communicates how far the value may vary from a center point. A part with a specified length of 50 ± 1 millimeters, for example, has a nominal length of 50 millimeters and an allowed variation of 1 millimeter either way. Under that straightforward tolerance convention, the acceptable range is 49 to 51 millimeters.

For a measurement such as 20 ± 0.5 centimeters, the central estimate is 20 centimeters and the stated uncertainty is 0.5 centimeter. A simple interval interpretation runs from 19.5 to 20.5 centimeters. But the notation alone may not tell you what kind of uncertainty is meant, how it was calculated, or how likely values within that interval are.

In technical writing, uncertainty can be defined in different ways. It might represent instrument resolution, a tolerance set by a manufacturer, or a statistical uncertainty calculated from data. A scientific report may specify a confidence level or other method separately. Do not assume that ± automatically means a particular probability, such as “95% certain,” unless the source explicitly says so.

Why the context matters

These uses are related but not interchangeable. In algebra, ± often instructs you to create two branches of a solution. In a specification, it may define an acceptable range. In a scientific result, it can express uncertainty around an estimate. The same printed notation can therefore do different jobs.

Equation: calculate both the plus and minus cases.
Specification: check whether the surrounding text defines a permitted tolerance.
Measurement: identify how the uncertainty was determined and what it represents.
Informal statement: treat it as an approximate range only if that is clearly intended.

Units matter, too. In “30 ± 2 cm,” both the value and its variation are in centimeters. A notation such as “30 cm ± 2” is generally intended to mean the same thing, but good technical writing keeps units and definitions clear to prevent mistakes.

The symbol ± is easy to confuse with other signs, but they communicate different relationships:

+ or −: Each is one operation or sign; ± presents both possibilities.
−: A minus sign can indicate subtraction or a negative value, not a two-sided variation by itself.
≈: “Approximately equal to” says a value is close to another value; it does not specify the size of the difference.
≤ or ≥: These mean “less than or equal to” and “greater than or equal to.” They set a one-sided boundary rather than a symmetric variation.
∓: Read “minus or plus.” It is often paired with ± to show opposite sign choices in related expressions.

For example, “about 10” gives an approximate value without a defined range. “10 ± 2” gives a stated amount of variation, though the reason for that variation still depends on context.

Common misunderstandings

A frequent mistake is to treat the number after ± as a percentage. In “100 ± 5,” the 5 is an absolute difference in the units of the stated value unless a percent sign is shown or the source defines it otherwise. By contrast, “100 ± 5%” indicates a percentage variation: 5% of 100 is 5, giving a simple range of 95 to 105.

Another mistake is assuming the central value is necessarily the only meaningful answer. In a calculation, ± may produce two valid answers. In a measurement, the central value is commonly an estimate, and the accompanying uncertainty provides important information about its precision.

Also, a symmetric notation does not guarantee that every value in the interval is equally likely or even possible. It states a plus-and-minus amount; interpreting probability or distribution requires further information. When the stakes are practical—such as checking a component against a specification—consult the applicable instructions or standard rather than relying on an informal reading.

Frequently Asked Questions

How do you calculate a number with ±?

Calculate two results: add the following number for one case and subtract it for the other. For 7 ± 4, the results are 11 and 3.

Does ± mean a range?

It often describes a range centered on a value, such as 10 ± 2 meaning 8 through 12 under a simple interval interpretation. In equations, it can instead indicate two separate solutions.

Does ± mean plus or minus a percentage?

Only when a percent sign or the surrounding definition makes that clear. Without one, the amount after ± is ordinarily an absolute amount in the relevant units.

What does ± mean in a measurement?

It usually gives an uncertainty or tolerance around the reported value. The notation by itself does not explain how that amount was determined or what probability interpretation applies.

What is the difference between ± and ∓?

± means “plus or minus,” while ∓ means “minus or plus.” They are often used together when two expressions must take opposite sign choices.

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