Area of a Circle Notes

Published on: September 29, 2026

This Area of a Circle Calculator finds the space inside a circle from its radius, and shows the working line by line. A circle covers \(\pi\) times as much as the square built on its radius, so the radius is squared first and that result is then multiplied by \(\pi\). The answer is written in square units and is usually rounded, because \(\pi\) never ends. Following the same pattern every time is what makes the area of a circle easy to picture, check, and work out on your own.

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. Square the radius.
  5. Multiply by pi to get the area.

Formula:

\(A = \pi r^{2}\)
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. Square the radius.
  5. Multiply by pi to get the area.

Step 1

Step 1 - Set up the problem.

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

\(r = 7\)

Step 2

Step 2 - Write the formula.

In this problem: A circle covers \(\pi\) times as much as the square built on its radius, so the area is the radius squared and then multiplied by \(\pi\).

\(A = \pi r^{2}\)

Step 3

Step 3 - Substitute the radius into the formula.

In this problem: Replacing \(r\) with \(7\) in \(A = \pi r^{2}\) gives \(A = \pi \times 7^{2}\).

\(A = \pi \times 7^{2}\)

Step 4

Step 4 - Square the radius.

In this problem: Squaring the radius gives \(7^{2} = 7 \times 7 = 49\).

\(A = \pi \times 49\)

Step 5

Step 5 - Multiply by pi to get the area.

In this problem: Multiplying that by \(\pi\) gives \(\pi \times 49 \approx 153.94\).

\(A = \pi \times 49 \approx 153.94\)

Final Answer

\(A \approx 153.94\)
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. Square the radius.
  5. Multiply by pi to get the area.

Step 1

Step 1 - Set up the problem.

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

\(r = 2.5\)

Step 2

Step 2 - Write the formula.

In this problem: A circle covers \(\pi\) times as much as the square built on its radius, so the area is the radius squared and then multiplied by \(\pi\).

\(A = \pi r^{2}\)

Step 3

Step 3 - Substitute the radius into the formula.

In this problem: Replacing \(r\) with \(2.5\) in \(A = \pi r^{2}\) gives \(A = \pi \times 2.5^{2}\).

\(A = \pi \times 2.5^{2}\)

Step 4

Step 4 - Square the radius.

In this problem: Squaring the radius gives \(2.5^{2} = 2.5 \times 2.5 = 6.25\).

\(A = \pi \times 6.25\)

Step 5

Step 5 - Multiply by pi to get the area.

In this problem: Multiplying that by \(\pi\) gives \(\pi \times 6.25 \approx 19.63\).

\(A = \pi \times 6.25 \approx 19.63\)

Final Answer

\(A \approx 19.63\)
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. Square the radius.
  5. Multiply by pi to get the area.

Step 1

Step 1 - Set up the problem.

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

\(r = 4\)

Step 2

Step 2 - Write the formula.

In this problem: A circle covers \(\pi\) times as much as the square built on its radius, so the area is the radius squared and then multiplied by \(\pi\).

\(A = \pi r^{2}\)

Step 3

Step 3 - Substitute the radius into the formula.

In this problem: Replacing \(r\) with \(4\) in \(A = \pi r^{2}\) gives \(A = \pi \times 4^{2}\).

\(A = \pi \times 4^{2}\)

Step 4

Step 4 - Square the radius.

In this problem: Squaring the radius gives \(4^{2} = 4 \times 4 = 16\).

\(A = \pi \times 16\)

Step 5

Step 5 - Multiply by pi to get the area.

In this problem: Multiplying that by \(\pi\) gives \(\pi \times 16 \approx 50.27\).

\(A = \pi \times 16 \approx 50.27\)

Final Answer

\(A \approx 50.27\)
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. Square the radius.
  5. Multiply by pi to get the area.

Step 1

Step 1 - Set up the problem.

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

\(r = 1.5\)

Step 2

Step 2 - Write the formula.

In this problem: A circle covers \(\pi\) times as much as the square built on its radius, so the area is the radius squared and then multiplied by \(\pi\).

\(A = \pi r^{2}\)

Step 3

Step 3 - Substitute the radius into the formula.

In this problem: Replacing \(r\) with \(1.5\) in \(A = \pi r^{2}\) gives \(A = \pi \times 1.5^{2}\).

\(A = \pi \times 1.5^{2}\)

Step 4

Step 4 - Square the radius.

In this problem: Squaring the radius gives \(1.5^{2} = 1.5 \times 1.5 = 2.25\).

\(A = \pi \times 2.25\)

Step 5

Step 5 - Multiply by pi to get the area.

In this problem: Multiplying that by \(\pi\) gives \(\pi \times 2.25 \approx 7.07\).

\(A = \pi \times 2.25 \approx 7.07\)

Final Answer

\(A \approx 7.07\)