The Lesson

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

Lesson Slides

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