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Constants (Mathematics Glossary)

What Is a Constant?

A constant is a number with a fixed value - its value does not change.

Dictionary Definition

The Merriam-Webster dictionary defines a constant as "a number that is assumed not to change value in a given mathematical discussion."

Real Examples of Constants

In algebra, some values always stay the same. They are constants.

Numbers are examples of constants - a number can only have one value. 2 can only have a value of 2.

2, 7 and -12 are examples of numbers, which are constants

Sometimes we use letters to stand in for constants. These letters will still stand in for a number which will always be the same. For example, π (pi) always has a value of 3.14.

a, b, c are constants

In algebra, numbers that are not constants are called variables - they can change in value.

Understanding Constants

It is easier to understand constants with an example. Let's look at an algebraic equation.

Consider a linear equation:

a linear equation with constants

The 2 and the 1 are both constants. They both have a fixed value.

The x and the y are variables. We can change their value.

The values of x and y must keep both sides of the equation the same. The left hand side (y) must be the same as the right hand side (2x + 1).

x = 1 ∴ y = 2x + 1 = 2 × 1 + 1 = 3

x = 2 ∴ y = 2x + 1 = 2 × 2 + 1 = 5

x = 3 ∴ y = 2x + 1 = 2 × 3 + 1 = 7

The constants are the same in each case and show which pairs of x and y are allowed by the equation.

Different constants would mean different pairs of x and y would be allowed by the equation.

a linear equation with different constants

More Real Examples of Constants

Constants appear in many different places in mathematics. The slider below has some more real examples of constants.

Algebra Lessons
Interactive Test

Here's a second test on constants.
Here's a third test on constants.


Coefficients Are a Type of Constant

A constant in front of a variable is called a coefficient.

For example, consider the equation shown below:

a constant of 2 is in front of the variable x.

2 and 1 are both constants in this equation.

The 2 is in front of the x. 2 is the coefficient of x. It means 2 × x.