# Common Symbols in Mathematics: Maths Glossary

Mathematical symbols can be confusing and can act as a real barrier to learning and understanding basic numeracy.

This page complements our numeracy skills pages and provides a quick glossary of common mathematical symbols with quick and concise definitions.

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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. As our page on Positive and Negative Numbers explains, a number without a sign is considered to be positive, so the plus is not usually necessary.

See our page on Addition for more.

### − Subtraction or Minus

This symbol has two main uses in mathematics:

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

### × or * or . Multiply

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 x (3+2).

See our page on Multiplication for more.

### ÷ or / Divide

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.

See our page on Division for more.

### = Equals

The = equals symbol is used to show the result of the calculation, 2 + 2 = 4.

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

• means not equal. For example 2 + 2 5 - 2. In computer applications (like Excel) the symbols <> mean not equal.
• means identical to. Similar, but not exactly the same as equals. 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.

### < Less Than and > Greater Than

This symbol < means less than, for example 2 < 4 means that 2 is less than 4.

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

≤ ≥ These symbols mean ‘less than or equal to’ and ‘greater than or equal to’ and are commonly used in algebra. In computer applications <= and >= are used.

≪ ≫ 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 symbol. Used commonly in algebraic functions, 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.

See our page: Special Numbers and Concepts for more on square roots.

### 2 Power

This symbol is used for the power of a number, 32, for example, means 3 to the power of 2 or 3 squared (3 x 3).

The superscripted number is the power so 43 means 4 to the power of 3 or 4 cubed, that is 4 × 4 × 4.

See our pages on Calculating Area and Calculating Volume for examples of when squared and cubed numbers are used

### . Decimal Point

. is the decimal point symbol, often referred to as simply ‘point’.

### , Thousand's Separator

A comma can be used to split larger 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.

### ( ) Brackets

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.

Learn all about percentages on our page: Introduction to Percentages

### ∞ 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-bar Mean

x-bar 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 of all the numbers from n down to 1, inclusive, i.e. n x (n−1) x (n−2) x … x 2 x 1.

### ∝ 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’.

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