Mathematical symbols and terminology can be confusing and can be an obstacle to learning and understanding basic mathematics.

This page complements our arithmetic skills page and provides a quick vocabulary of mathematical symbols and terminology common to concise definitions.

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## Common Mathematical Symbols

### + Addition, Plus, Positive

**The addition symbol + is usually used to indicate that two or more numbers should be added together, for example, 2 + 2.**

The + symbol can also be used to indicate a positive number although this is less common, for example, +2. Our page on Positive and Negative Numbers explains that a number without a sign is considered to be positive, so the plus is not usually necessary.

### − Subtraction, Minus, Negative

**This symbol has two main uses in mathematics:**

- − is used when one or more numbers are to be subtracted, for example, 2 − 2.
- The − symbol is also commonly used to show a minus or negative number, such as −2.

### × or * or . Multiplication

**These symbols have the same meaning; commonly × is used to mean multiplication when handwritten or used on a calculator 2 × 2, for example.**

The symbol * is used in spreadsheets and other computer applications to indicate a multiplication, although * does have other more complex meanings in mathematics.

Less commonly, multiplication may also be symbolised by a dot . or indeed by no symbol at all. For example, if you see a number written outside brackets with no operator (symbol or sign), then it should be multiplied by the contents of the brackets: 2(3+2) is the same as 2×(3+2).

### ÷ or / Division

**These symbols are both used to mean division in mathematics. ÷ is used commonly in handwritten calculations and on calculators, for example, 2 ÷ 2.**

/ is used in spreadsheets and other computer applications.

### = Equals

**The = equals symbol is used to show that the values on either side of it are the same. It is most commonly used to show the result of a calculation, for example 2 + 2 = 4, or in equations, such as 2 + 3 = 10 − 5.**

You may also come across other related symbols, although these are less common:

**≠**means not equal. For example, 2 + 2**≠****≡**means identical to. This is similar to, but not exactly the same as, equals. Therefore, if in doubt, stick to =.**≈**means approximately equal to, or almost equal to. The two sides of a relationship indicated by this symbol will**not**be accurate enough to manipulate mathematically.

This symbol

This symbol **>** means greater than, for example 4 > 2.

**≤ ≥**

**≪ ≫** These symbols are less common and mean much less than, or much greater than.

### ± Plus or Minus

**This symbol ± means ‘plus or minus'. It is used to indicate, for example, confidence intervals around a number.**

The answer is said to be ‘plus or minus' another number, or in other words, within a range around the given answer.

For example, 5 ± 2 could in practice be any number from 3 to 7.

### ∑ Sum

**The ∑ symbol means sum.**

∑ is the Greek capital sigma character. It is used commonly in algebraic functions, and you may also notice it in Excel – the AutoSum button has a sigma as its icon.

### ° Degree

**Degrees ° are used in several different ways.**

**As a measure of rotation**– the angle between the sides of a shape or the rotation of a circle. A circle is 360° and a right angle is 90°. See our section on Geometry for more.**A measure of temperature.**Degrees Celsius or Centigrade are used in most of the world (with the exception of the USA). Water freezes at 0°C and boils at 100°C. In the USA Fahrenheit is used. On the Fahrenheit scale water freezes at 32°F and boils at 212°F. See our page:**Systems of**Measurement for more information.

### ∠ Angle

**The angle symbol ∠ is used as shorthand in geometry (the study of shapes) for describing an angle.**

The expression ∠ABC is used to describe the angle at point B (between points A and C). Similarly, ∠BAC would be used to describe the angle of point A (between points B and C). For more on angles and other geometric terms see our pages on Geometry.

### √ Square Root

**√ is the symbol for square root. A square root is the number that, when multiplied by itself, gives the original number.**

For example, the square root of 4 is 2, because 2 x 2 = 4. The square root of 9 is 3, because 3 x 3 = 9.

^{n} Power

**A superscripted integer (any whole number n) is the symbol used for the power of a number.**

For example,3^{2}, means 3 to the power of 2, which is the same as 3 squared (3 x 3).

4^{3} means 4 to the power of 3 or 4 cubed, that is 4 × 4 × 4.

**Powers are also used as a shorthand way to write large and small numbers.**

Large numbers

10^{6} is 1,000,000 (one million).

10^{9} is 1,000,000,000 (one billion).

10^{12} is 1,000,000,000,000 (one trillion).

10^{100} written long-hand would be 1 with 100 0's (one Googol).

Small numbers

10^{-3} is 0.001 (one thousandth)

10^{-6} is 0.000001 (one millionth)

Powers can also be written using the **^** symbol.

10^6 = 10^{6} = 1,000,000 (one million).

### . Decimal Point

. is the decimal point symbol, often referred to simply as ‘point'. See our page on __Decimals__ for examples of its use.

### , Thousands Separator

**A comma can be used to split large numbers and make them easier to read.**

A thousand can be written as 1,000 as well as 1000 and a million as 1,000,000 or 1000000. The comma splits larger numbers into blocks of three digits.

In most English speaking countries the , does not have any mathematical function, it is simply used to make numbers easier to read.

In some other countries, especially in Europe, the comma may be used instead of a decimal point and indeed, a decimal point may be used in place of a comma as a visual separator.

### [ ], ( ) Brackets, Parentheses

**Brackets ( ) are used to determine the order of a calculation as dictated by the** BODMAS** rule.**

Parts of a calculation included within brackets are calculated first, for example

**5 + 3 × 2 = 11****(5 + 3) × 2 = 16**

### % Percentage

The % symbol means percentage, or the number out of 100.

### π Pi

π or Pi is the Greek character for the ‘p' sound. It occurs frequently in mathematics and is a mathematical constant. Pi is a circle's circumference divided by its diameter and has the value 3.141592653. It is an irrational number, which means that its decimal places continue to infinity.

### ∞ Infinity

**The ∞ symbol signifies infinity, the concept that numbers go on for ever.**

However large a number you have, you can always have a larger one, because you can always add one to it.

Infinity is not a number, but the *idea* of numbers going on for ever. You cannot add one to infinity, any more than you can add one to a person, or to love or hate.

### x¯ (x-bar) Mean

**x¯ is the mean of all the possible values of x.**

You will mostly come across this symbol in statistics.

### ! Factorial

**! is the symbol for factorial.**

n! is the product (multiplication) of all the numbers from n down to 1, inclusive, i.e. n × (n−1) × (n−2) × … × 2 × 1.

For example:

5! = 5 × 4 × 3 × 2 × 1 = 120

10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800

### | Pipe

Pipe ‘|' is also also referred to as vertical bar, vbar, pike and has many uses in mathematics, physics and computing.

Most commonly in basic mathematics, it used to denote **absolute value** or **modulus** of a real number, where |x| is the *absolute value or modulus of x*.

Mathematically, this is defined as

Simply, |x| is the non-negative value of x. For example, the modulus of 6 is 6 and the modulus of −6 is also 6.

It is also used in probability, where P(Z|Y) denotes the probability of X given Y.

### ∝ Proportional

**∝**** means ‘is proportional to**', and is used to show something that varies in relation to something else.

For example, if x = 2y, then x ∝ y.

### ∴ Therefore

∴ is a useful shorthand form of ‘therefore', used throughout maths and science.

### ∵ Because

∵ is a useful shorthand form of ‘because', not to be confused with ‘therefore'.