Circle Area Calculator
Calculate the area of a circle from radius or diameter. Enter any value to find all circle properties instantly.
Circle Calculator
Understanding Circle Area
What is Circle Area?
The area of a circle is the amount of space enclosed within the circle's boundary. It's measured in square units (cm², m², in², etc.) and represents the total surface contained by the circle.
The Famous Formula: A = πr²
The area of a circle equals pi (π) times the radius squared. This is one of the most important formulas in geometry:
Where:
- A = Area of the circle
- π (pi) ≈ 3.14159... (a mathematical constant)
- r = Radius (distance from center to edge)
Key Circle Relationships
Radius & Diameter
d = 2r (diameter is twice the radius)
Circumference & Radius
C = 2πr (circumference formula)
Area & Circumference
A = C² / (4π)
Special Case
When r = 2, A = C = 4π
Example Calculations
Example 1: Circle with radius 5 cm
Area = π × 5² = π × 25 = 78.54 cm²
Example 2: Circle with diameter 10 m
Radius = 10/2 = 5 m
Area = π × 5² = 78.54 m²
Example 3: Find radius if area = 100 cm²
r = √(100/π) = √(31.83) = 5.64 cm
Frequently Asked Questions
How do I find the area of a circle from radius?
Multiply pi (π ≈ 3.14159) by the radius squared. Formula: A = πr². For example, if radius is 4 cm, area = 3.14159 × 4² = 50.27 cm².
How do I find the area from diameter?
First divide the diameter by 2 to get the radius, then use A = πr². Or use the direct formula: A = π × (d/2)² = πd²/4.
How do I find radius if I know the area?
Divide the area by pi, then take the square root. Formula: r = √(A/π). For example, if area is 100 cm², radius = √(100/3.14159) = 5.64 cm.
What is pi (π)?
Pi is a mathematical constant representing the ratio of a circle's circumference to its diameter. It's approximately 3.14159265359... and is an irrational number (it goes on forever without repeating).
Why do we square the radius in the area formula?
Area is a two-dimensional measurement (length × width). Since a circle extends in two dimensions from its center, we multiply the radius by itself (r × r = r²) to capture both dimensions.
What's the difference between area and circumference?
Area (A = πr²) measures the space inside the circle in square units. Circumference (C = 2πr) measures the distance around the circle in linear units.
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