Constants (Mathematics Glossary)
What Is a Constant?
A constant is a number with a fixed value - its value does not change.
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.
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.
In algebra, numbers that are not constants are called variables - they can change in value.
It is easier to understand constants with an example. Let's look at an algebraic equation.
Consider a linear equation:
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.
More Real Examples of Constants
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:
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.