Common Symbols in Mathematics:
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:
- - 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.
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.
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.
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.
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.
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.
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
The % symbol means percentage, or the number out of 100.
Learn all about percentages on our page: Introduction to Percentages
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 is the mean of all the possible values of x.
You will mostly come across this symbol in statistics.
See our page on Averages for more information.
! 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.
∝ 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.
∴ is a useful shorthand form of ‘therefore’, used throughout maths and science.
∵ is a useful shorthand form of ‘because’, not to be confused with ‘therefore’.