The Lesson
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.
Understanding Constants
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.
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:
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.