How to Find Circumference and Area of a Circle

Circles have two common measurements: circumference around the edge and area inside the circle.

Quick idea

Use circumference for distance around a circle and area for space inside the circle.

Steps

1. Find the radius. If you have the diameter, divide it by 2.
2. Use 2 times pi times radius for circumference.
3. Use pi times radius squared for area.
4. Round only at the end if the problem asks for a decimal.

Worked example

Find the area of a circle with radius 4.

Full solution

Step-by-step walkthrough

Step 1

The radius is 4.

Step 2

Square the radius first: 4 squared is 16.

Step 3

Multiply by pi to get 16 pi square units.

Common mistake

Do not confuse radius and diameter. The diameter is twice the radius.

Practice problems

1. Find the circumference when r = 3.
2. Find the area when r = 5.
3. Find the radius if the diameter is 18.

Answers

1. 6 pi
2. 25 pi
3. 9

Ask Pennpaper to explain it live

If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.

Related guides

• Area and Perimeter Explained
• How to Find the Area of a Triangle
• Pythagorean Theorem Explained