Circumference of a Circle Notes

Published on: September 29, 2026

This Circumference of a Circle Calculator finds the distance around a circle from its radius, and shows the working line by line. Twice the radius is the diameter, and every circle measures \(\pi\) diameters around, so doubling the radius and multiplying by \(\pi\) gives the circumference. The answer is a length written in units and is usually rounded. Following the same pattern every time is what makes the circumference of a circle easy to check and repeat.

Circle labeled r

In the diagram, the radius is labeled \(r\).

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the radius into the formula.
  4. Work out the circumference.

Formula:

\(C = 2\pi r\)
See Example 1 Hide Example 1

Problem

\(r = 7\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the radius into the formula.
  4. Work out the circumference.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the circumference of a circle whose radius is \(r = 7\).

\(r = 7\)

Step 2

Step 2 - Write the formula.

In this problem: Twice the radius is the diameter, and every circle is \(\pi\) diameters around, so the circumference is twice the radius multiplied by \(\pi\).

\(C = 2\pi r\)

Step 3

Step 3 - Substitute the radius into the formula.

In this problem: Replacing \(r\) with \(7\) in \(C = 2\pi r\) gives \(C = 2 \times \pi \times 7\).

\(C = 2 \times \pi \times 7\)

Step 4

Step 4 - Work out the circumference.

In this problem: Doubling the radius gives \(2 \times 7 = 14\), and multiplying that by \(\pi\) gives \(14 \times \pi \approx 43.98\).

\(C = 2 \times \pi \times 7 \approx 43.98\)

Final Answer

\(C \approx 43.98\)
See Example 2 Hide Example 2

Problem

\(r = 2.5\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the radius into the formula.
  4. Work out the circumference.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the circumference of a circle whose radius is \(r = 2.5\).

\(r = 2.5\)

Step 2

Step 2 - Write the formula.

In this problem: Twice the radius is the diameter, and every circle is \(\pi\) diameters around, so the circumference is twice the radius multiplied by \(\pi\).

\(C = 2\pi r\)

Step 3

Step 3 - Substitute the radius into the formula.

In this problem: Replacing \(r\) with \(2.5\) in \(C = 2\pi r\) gives \(C = 2 \times \pi \times 2.5\).

\(C = 2 \times \pi \times 2.5\)

Step 4

Step 4 - Work out the circumference.

In this problem: Doubling the radius gives \(2 \times 2.5 = 5\), and multiplying that by \(\pi\) gives \(5 \times \pi \approx 15.71\).

\(C = 2 \times \pi \times 2.5 \approx 15.71\)

Final Answer

\(C \approx 15.71\)
See Example 3 Hide Example 3

Problem

\(r = 4\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the radius into the formula.
  4. Work out the circumference.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the circumference of a circle whose radius is \(r = 4\).

\(r = 4\)

Step 2

Step 2 - Write the formula.

In this problem: Twice the radius is the diameter, and every circle is \(\pi\) diameters around, so the circumference is twice the radius multiplied by \(\pi\).

\(C = 2\pi r\)

Step 3

Step 3 - Substitute the radius into the formula.

In this problem: Replacing \(r\) with \(4\) in \(C = 2\pi r\) gives \(C = 2 \times \pi \times 4\).

\(C = 2 \times \pi \times 4\)

Step 4

Step 4 - Work out the circumference.

In this problem: Doubling the radius gives \(2 \times 4 = 8\), and multiplying that by \(\pi\) gives \(8 \times \pi \approx 25.13\).

\(C = 2 \times \pi \times 4 \approx 25.13\)

Final Answer

\(C \approx 25.13\)
See Example 4 Hide Example 4

Problem

\(r = 1.5\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the radius into the formula.
  4. Work out the circumference.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the circumference of a circle whose radius is \(r = 1.5\).

\(r = 1.5\)

Step 2

Step 2 - Write the formula.

In this problem: Twice the radius is the diameter, and every circle is \(\pi\) diameters around, so the circumference is twice the radius multiplied by \(\pi\).

\(C = 2\pi r\)

Step 3

Step 3 - Substitute the radius into the formula.

In this problem: Replacing \(r\) with \(1.5\) in \(C = 2\pi r\) gives \(C = 2 \times \pi \times 1.5\).

\(C = 2 \times \pi \times 1.5\)

Step 4

Step 4 - Work out the circumference.

In this problem: Doubling the radius gives \(2 \times 1.5 = 3\), and multiplying that by \(\pi\) gives \(3 \times \pi \approx 9.42\).

\(C = 2 \times \pi \times 1.5 \approx 9.42\)

Final Answer

\(C \approx 9.42\)