Circle Calculator
Calculate area, circumference, diameter, and radius of circles with step-by-step solutions for geometry, construction, and design projects.
Calculator
Enter your information to calculate results
Formulas Used
Area: A = πr² = π × 5.00² = 78.5398
Circumference: C = 2πr = 2π × 5.00 = 31.4159
Diameter: d = 2r = 2 × 5.00 = 10.0000
Circle Properties
Ï€ (Pi): 3.14159...
Radius to Diameter: d = 2r
Area to Radius: r = √(A/π)
Circumference to Radius: r = C/(2Ï€)
Area to Circumference: C = 2√(πA)
Diameter to Area: A = π(d/2)²
How It Works
The circle calculator uses fundamental geometric relationships to calculate all circle properties from any single measurement:
Key Formulas:
- Area: A = πr² (pi times radius squared)
- Circumference: C = 2Ï€r (2 times pi times radius)
- Diameter: d = 2r (2 times radius)
- Radius from Area: r = √(A/π)
All calculations use the mathematical constant π (pi) ≈ 3.14159265359 for maximum accuracy.
Examples
Real-World Examples
Pizza (12" diameter):
• Radius: 6 inches
• Area: 113.1 square inches
• Circumference: 37.7 inches
Construction Examples
Round table (4 ft diameter):
• Radius: 2 feet
• Area: 12.57 square feet
• Circumference: 12.57 feet
Compare
Circle vs Other Shapes:
- Efficiency: Circles have the largest area for a given perimeter
- Symmetry: Perfect rotational symmetry around center
- Applications: Wheels, pipes, tanks, sports fields
- Calculations: All properties related through π (pi)
Practical Tips:
- Use π ≈ 3.14 for quick mental calculations
- Diameter is always twice the radius
- Area grows with the square of radius
- Circumference grows linearly with radius
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