Constant vs Variable Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Constant vs Variable.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Constants are symbols with fixed, unchanging values; variables are symbols whose values can change or are yet to be determined.

\pi \approx 3.14159 is always the same (constant). x can be anything (variable).

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Constants anchor expressions with fixed values; variables provide the flexibility to represent many possible inputs.

Common stuck point: Context determines: 'm' might be a constant in one problem, variable in another.

Sense of Study hint: Ask: does this symbol change within the problem, or does it stay fixed? That tells you which role it plays.

Worked Examples

Example 1

easy
In C = 2\pi r, identify the constants and variables.

Solution

  1. 1
    \pi \approx 3.14159 is a constant—it never changes.
  2. 2
    2 is a constant coefficient.
  3. 3
    r (radius) is a variable—it can be any positive number.
  4. 4
    C (circumference) is a variable—it depends on r.

Answer

Constants: 2, \pi. Variables: C, r.
Constants have fixed values that don't change. Variables can take different values. In formulas, Greek letters like \pi and e are usually constants.

Example 2

medium
In the equation y = 3x + 5, someone says '3 is a variable because it could be any slope.' Is this correct?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
In F = ma (Newton's second law), which symbols are variables?

Example 2

medium
Is 0 a constant or a variable?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

variables