The area of a circle is the total space enclosed within its boundary (circumference). It represents how much two-dimensional space the circle covers and is measured in square units such as square meters (m²), square feet (ft²), or square centimeters (cm²).
A circle is defined as the set of all points in a plane that are at a given distance (the radius) from a given point (the center). The area calculation is fundamental in geometry and has countless practical applications.
You can calculate the area of a circle using either the radius or diameter:
Using Radius: A = π × r²
Using Diameter: A = π × (d/2)² = π × d² / 4
Where:
Problem: Calculate the area of a circle with radius 5 meters.
Solution:
Problem: Calculate the area of a circle with diameter 10 cm.
Solution:
The diameter is always twice the radius. If you know the diameter, divide it by 2 to get the radius. If you know the radius, multiply by 2 to get the diameter.
Pi represents the ratio of a circle's circumference to its diameter. It's a constant (approximately 3.14159) that appears naturally in all circle calculations.
The circumference formula is C = 2πr (using radius) or C = πd (using diameter). The circumference is the distance around the circle.