How to Calculate the Area of a Circle

Introduction

The area of a circle refers to the amount of space enclosed within its curved boundary. This concept is used in geometry, design, construction, and daily life—like measuring the surface of a round table or a circular garden.

To calculate the area of a circle, all you need is one key measurement: the radius.

Formula for Area of a Circle

Area = π × r²

• π (pi) is approximately equal to 3.1416
• r is the radius (distance from the center to the edge)

Step-by-Step Breakdown

Step 1: Measure the Radius

If you have the diameter (d), divide it by 2 to find the radius:
r = d / 2

Step 2: Square the Radius

Multiply the radius by itself:
r² = r × r

Step 3: Multiply by Pi

Multiply the squared radius by π:
Area = π × r²

Visual Representation

This diagram shows a circle with the center labeled "O" and radius "r".

Examples

Example 1: Radius is Known

Given: r = 5 cm
Area = π × 5² = 3.1416 × 25 = 78.54 cm²

Example 2: Diameter is Given

Given: d = 12 m
r = 12 / 2 = 6 m
Area = π × 6² = 3.1416 × 36 = 113.10 m²

Example 3: Using Fractional Pi

Given: r = 7 cm, use π = 22/7
Area = (22/7) × 7² = (22/7) × 49 = 154 cm²

Try the Area of a Circle Calculator

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Fun Fact

A circle’s area can also be thought of as a rectangle with:
Width = π × r     Height = r
So, Area = π × r × r = π × r²

Summary Table

Whether you're a student or a curious mind, understanding how to calculate the area of a circle is a powerful and practical skill. And when in doubt, just head over to our Area of Circle Calculator and let it do the work for you!