Area of Circle Calculator
Calculate the area of a circle from radius, diameter, or circumference with step-by-step solutions and visual representations.
Calculator
Enter your information to calculate results
Step-by-Step Calculation
Given: radius = 5 cm
Radius: r = 5.0000 cm
Area Formula: A = πr² = π × 5.00² = 78.5398 cm²
Circumference: C = 2πr = 2π × 5.00 = 31.4159 cm
Diameter: d = 2r = 2 × 5.00 = 10.0000 cm
Visual Representation
How It Works
The area of a circle calculator uses the fundamental geometric relationship between a circle's radius and its area:
Key Formula:
A = πr²
Where A = Area, r = radius, π ≈ 3.14159
The calculator can work from radius, diameter, or circumference by first converting to radius, then applying the area formula.
Conversion Formulas:
- From diameter: r = d/2
- From circumference: r = C/(2Ï€)
Examples
Pizza Example
12-inch diameter pizza:
• Radius: 6 inches
• Area: 113.1 square inches
• Circumference: 37.7 inches
Garden Plot
Circular garden, 4m radius:
• Diameter: 8 meters
• Area: 50.3 square meters
• Perimeter: 25.1 meters
Compare
Circle Properties:
- Maximum Area: Circles have the largest area for a given perimeter
- Perfect Symmetry: All points on circumference are equidistant from center
- π Relationship: All circle calculations involve π (pi)
Real-World Applications:
- Construction: Circular building footprints, pools
- Agriculture: Irrigation coverage areas
- Manufacturing: Material calculations for circular parts
- Sports: Field dimensions, track layouts
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