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How to Find the Area of a Circle

Learn how to find the area of a circle in minutes: formula, calculator, mistakes to avoid, and real-life examples.

Quick Formula
The essential formula you need to know
A = πr²
or
Area = π × radius²
Variables
r = radius (distance from center to edge)
π ≈ 3.14159 (pi, the mathematical constant)
Visual Guide
rcenter
Circle with radius (r)
Interactive Calculator
Enter the radius or diameter to calculate the area instantly
Practice Problems
Test your understanding with these circle area problems
Problem 1 of 4Score: 0/0

Find the area of a circle with radius 5 cm.

cm²
Common Mistakes to Avoid
Learn from these frequent errors to get accurate results
Confusing radius and diameter
Remember: diameter = 2 × radius, so radius = diameter ÷ 2
Example: If diameter is 10, radius is 5, not 10
Using wrong π approximation
Using 3.14 vs 3.14159 can give different results
Example: For r=5: 3.14×25 = 78.5, but 3.14159×25 = 78.54
Unit inconsistency
Make sure all measurements use the same units
Example: Don't mix cm and inches - stick to one unit system
How the Formula Works
Drag to see how circle sectors rearrange into a rectangle

Circle Area Calculation Principle Demo

By dividing a circle into sectors and rearranging them, we can approximate a rectangle and derive the circle area formula A = πr²

Divided Circle

r = 80px

Number of divisions: 8 sectors

After Rearrangement

πr ≈ 251pxr = 80px

Approximate rectangle area = πr × r = πr² ≈ 20106px²

Adjust Number of Divisions

The more divisions, the closer the right shape approximates a rectangle

4 sectorsCurrent: 8 sectors32 sectors

Mathematical Principle

When the number of divisions approaches infinity, the rearranged shape approaches a perfect rectangle.
Rectangle width = half of circle circumference = πr, height = radius = r
Therefore, circle area = rectangle area = πr × r = πr²

Understanding π (Pi)
The mathematical constant that makes circles work
Definition

π = circumference ÷ diameter

This ratio is the same for every circle, no matter how big or small!

Common Values
Exact: π (infinite decimal)
Decimal: 3.14159...
Fraction: 22/7 (close approximation)
Simple: 3.14 (for quick calculations)
Historical Note

Ancient Greek mathematician Archimedes (287-212 BC) was one of the first to calculate π accurately by inscribing and circumscribing polygons around circles.

Fun Fact

π is an irrational number, meaning its decimal representation never ends and never repeats. Mathematicians have calculated π to over 100 trillion digits!

Real-World Applications
See how circle area calculations are used in everyday life

Baking & Cooking

Calculate the area of circular pans, pizzas, or cakes

Example: A 12-inch pizza has area = π × 6² = 113 square inches

Architecture & Construction

Find the area of circular foundations, columns, or rooms

Example: A circular room with 8-foot radius has 201 square feet of floor space

Sports & Recreation

Calculate areas of circular courts, fields, or target zones

Example: A basketball center circle (6-foot radius) covers 113 square feet

Landscaping & Gardening

Plan circular gardens, pools, or lawn areas

Example: A circular garden bed with 4-foot radius needs 50 square feet of soil
Related Problems
Continue learning with these related geometry topics
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