The plus–minus sign (±) is a mathematical symbol that represents two possible values: one obtained by adding a number and the other by subtracting it. It is widely used in mathematics, science, engineering, statistics, and manufacturing to express multiple solutions, measurement uncertainty, or acceptable tolerances.
For example, the expression 10 ± 2 means the value can be either 8 or 12.
Whether you’re solving algebraic equations, interpreting scientific measurements, or reading product specifications, understanding the meaning of the ± symbol is essential.
Related: You may also find our Math Calculator useful for solving mathematical expressions and equations.
What Does the Plus–Minus Sign (±) Mean?
The plus–minus sign (±) indicates that both the positive and negative versions of a value should be considered.
Symbol: ±
Name: Plus–minus sign
Common Uses:
- Showing two possible values
- Expressing measurement uncertainty
- Indicating manufacturing tolerance
- Representing ranges in science and engineering
- Writing formulas more compactly
Example
10 ± 2
This represents two values:
- 10 + 2 = 12
- 10 − 2 = 8
Instead of writing both results separately, the ± symbol combines them into one expression.
When Is the Plus–Minus Sign Used?
The plus–minus sign appears in many areas of mathematics and science.
It is commonly used to represent:
- Two mathematical solutions
- Experimental uncertainty
- Acceptable manufacturing tolerances
- Statistical variation
- Scientific measurements
Its purpose is to simplify expressions while conveying multiple possible values.
History of the Plus–Minus Sign
The plus–minus symbol became widely used during the 17th century as mathematics and science evolved. It provided mathematicians and scientists with a concise way to express values that could vary in two directions.
Today, it is recognized internationally and appears in textbooks, engineering drawings, scientific papers, calculators, and technical standards.
Plus–Minus Sign in Mathematics
In mathematics, the ± symbol often indicates that an equation has two valid solutions.
Example
x = ±5
This means:
- x = 5
- x = −5
Instead of writing two separate equations, the symbol represents both solutions at once.
This notation is especially common when solving equations involving squares or square roots.
Plus–Minus Sign in Algebra
The ± symbol is frequently used in algebraic formulas.
A well-known example is the quadratic formula:
[
x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}
]
The formula produces two possible values for x:
- One using the plus (+) sign.
- One using the minus (−) sign.
Both solutions must be calculated unless the expression under the square root equals zero, in which case the equation has only one real solution.
Plus–Minus Sign in Measurements
In measurement, the plus–minus sign indicates uncertainty or the possible variation from a measured value.
Examples
- 50 cm ± 0.5 cm
- 10 kg ± 0.1 kg
- 2.50 L ± 0.02 L
For example:
50 cm ± 0.5 cm means the actual measurement could be anywhere between:
- 49.5 cm
- 50.5 cm
This notation helps communicate the accuracy of a measurement.
Plus–Minus Sign in Engineering and Manufacturing
Engineers use the ± symbol to specify acceptable manufacturing tolerances.
For example:
25 mm ± 0.1 mm
This means a manufactured part is acceptable if its size falls between:
- 24.9 mm
- 25.1 mm
Tolerance values help ensure components fit together correctly while allowing for small variations during production.
Plus–Minus Sign in Science and Physics
In scientific fields, the ± symbol is commonly used to describe:
- Measurement uncertainty
- Experimental error
- Instrument precision
- Physical quantities with known variation
Example
Speed = 60 ± 2 km/h
This means the measured speed is expected to fall between:
- 58 km/h
- 62 km/h
Reporting uncertainty provides a more accurate representation of measured data.
Plus–Minus Sign in Statistics
In statistics, the ± symbol often represents variation around an average value.
It is commonly used with:
- Standard deviation
- Margin of error
- Confidence intervals
Example
Mean score = 75 ± 3
This indicates values are generally close to the average, typically ranging between:
- 72
- 78
The exact interpretation depends on the statistical context and the accompanying explanation.
Plus–Minus Sign vs. Minus–Plus Sign (∓)
The minus–plus sign (∓) is the companion symbol to ±.
| Symbol | Meaning |
|---|---|
| ± | Plus or minus |
| ∓ | Minus or plus |
These symbols are often used together in paired mathematical expressions to maintain the correct order of operations.
For example:
a \pm b,; c \mp d
$$
If the first expression uses the plus sign, the second uses the minus sign, and vice versa.
Common Mistakes When Using the ± Symbol
To avoid errors, keep these points in mind:
- Don’t treat ± as a single arithmetic operation.
- Always calculate both possible values when solving equations.
- Don’t use ± when only one valid solution exists.
- Remember that measurement uncertainty represents a range, not two exact values.
Checking the context helps determine how the symbol should be interpreted.
Everyday Uses of the Plus–Minus Sign
Although commonly associated with mathematics, the ± symbol appears in many everyday situations.
Examples include:
- Product specifications
- Engineering drawings
- Scientific reports
- Laboratory results
- Electronic component ratings
- Construction measurements
- Exam and textbook solutions
Whenever a value may vary slightly or two possible values exist, the plus–minus symbol provides a concise way to communicate that information.
Quick Reference Examples
| Expression | Meaning |
|---|---|
| 10 ± 2 | 8 or 12 |
| x = ±7 | x = 7 or x = −7 |
| 100 ± 5 g | Between 95 g and 105 g |
| 230 V ± 10% | Voltage may vary by 10% above or below 230 V |
Frequently Asked Questions
What does the plus–minus sign (±) mean?
The plus–minus sign indicates two possible values: one obtained by adding a number and the other by subtracting it.
How do you read the ± symbol?
It is read as “plus or minus.”
For example:
5 ± 1 is read as “five plus or minus one.”
Is ± the same as the minus sign?
No.
The minus sign (−) represents subtraction or a negative value, while the plus–minus sign (±) represents both addition and subtraction in the same expression.
When is the ± symbol used?
The symbol is commonly used in:
- Algebra
- Geometry
- Physics
- Engineering
- Statistics
- Manufacturing
- Scientific measurements
What is the difference between ± and ∓?
The ± symbol means plus or minus, while ∓ means minus or plus. They are typically used together in paired mathematical expressions.
Key Takeaways
- The plus–minus sign (±) represents two possible values.
- It is commonly used to express uncertainty, tolerance, and multiple mathematical solutions.
- In algebra, it often indicates two valid solutions to an equation.
- In science and engineering, it shows the possible variation in a measurement.
- Understanding the context helps you interpret the symbol correctly.
Final Thoughts
The plus–minus sign (±) is a simple yet powerful mathematical symbol that communicates two possible outcomes or a range of acceptable values. From solving quadratic equations to reporting scientific measurements and engineering tolerances, it plays an essential role in making mathematical and technical information concise and accurate.
Learning how to interpret and apply the ± symbol correctly will help you better understand mathematics, science, statistics, and many real-world measurements.
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