# 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.

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 (**2***x* + **1**).

*x* = 1 ∴ *y* = **2***x* + **1** = **2** × 1 + **1** = 3

*x* = 2 ∴ *y* = **2***x* + **1** = **2** × 2 + **1** = 5

*x* = 3 ∴ *y* = **2***x* + **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.

##### Curriculum

##### Interactive Test

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Here's a second test on constants.

Here's a third test on constants.

##### Note

# 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*.