Area of a Circle Calculator
Calculate the area of a circle using radius, diameter, or circumference
Calculate Circle Area
Distance from center to edge of circle
Distance from center to edge
Circle Area Results
Please enter a positive radius value
Example Calculations
Example 1: Using Radius
Given: Radius = 5 cm
Formula: Area = π × r²
Calculation: Area = π × 5² = π × 25 ≈ 78.54 cm²
Example 2: Using Diameter
Given: Diameter = 12 cm
Formula: Area = π × (d/2)²
Calculation: Area = π × (12/2)² = π × 6² = π × 36 ≈ 113.10 cm²
Example 3: Using Circumference
Given: Circumference = 31.42 cm
Step 1: Find radius: r = C/(2π) = 31.42/(2π) ≈ 5 cm
Step 2: Calculate area: Area = π × r² = π × 5² ≈ 78.54 cm²
Circle Area Formulas
From Radius
A = π × r²
Most common formula
From Diameter
A = π × (d/2)²
When diameter is known
From Circumference
A = C²/(4π)
When perimeter is known
Important Constants
Circle Area Tips
Area is always measured in square units (cm², m², etc.)
Diameter is always twice the radius (d = 2r)
Circumference = 2πr or πd
π ≈ 3.14159 (used in all circle calculations)
Area grows quadratically with radius
Understanding Circle Area
What is Circle Area?
The area of a circle is the amount of space enclosed within its circumference. It represents the total surface inside the circular boundary and is one of the most fundamental measurements in geometry.
Key Properties:
- Always measured in square units
- Proportional to the square of the radius
- Independent of the circle's position
- Always positive and finite
- π (pi) is essential for calculation
Circle Relationships
Radius to Area
A = π × r² (fundamental formula)
Diameter to Area
A = π × (d/2)² = πd²/4
Circumference to Area
A = C²/(4π)
Circle Measurements Comparison
| Radius | Diameter | Circumference | Area |
|---|---|---|---|
| 1 unit | 2 units | 6.28 units | 3.14 sq units |
| 2 units | 4 units | 12.57 units | 12.57 sq units |
| 5 units | 10 units | 31.42 units | 78.54 sq units |
| 10 units | 20 units | 62.83 units | 314.16 sq units |
Real-World Applications
Engineering & Construction
- Calculating material needed for circular surfaces
- Designing circular foundations and structures
- Planning circular gardens and landscaping
- Computing area of circular pipes and tanks
Science & Mathematics
- Physics calculations involving circular motion
- Astronomy and planetary calculations
- Biology: cell size and growth patterns
- Statistics: pie charts and data visualization