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Circle Calculator
Calculate area, circumference, and diameter of a circle
How Circle Calculations Work
Circle calculations are based on fundamental geometric formulas that relate the radius to other important measurements like area, circumference, and diameter.
Enter the radius of your circle
Click "Calculate Circle" to compute all measurements
View area, circumference, and diameter results
See the formulas and calculations used
Copy results for your records or further calculations
Circle Formulas:
Area (A): A = π × r²
Circumference (C): C = 2 × π × r
Diameter (D): D = 2 × r
Radius (r): r = D / 2 = C / (2π) = √(A/π)
Common Examples:
Radius 1: Area=3.1416, Circumference=6.2832, Diameter=2
Radius 5: Area=78.5398, Circumference=31.4159, Diameter=10
Radius 10: Area=314.1593, Circumference=62.8319, Diameter=20
Unit Circle: Radius=1, Area=π, Circumference=2π
Mathematical Constants:
π (Pi): Approximately 3.141592653589793
2π: Approximately 6.283185307179586
π²: Approximately 9.869604401089358
π is the ratio of circumference to diameter for any circle
Real-World Applications:
Engineering: Pipe diameters, wheel rotations, gear design
Construction: Circular foundations, arch design, tanks
Science: Planetary orbits, wave propagation, lenses
Daily Life: Pizza sizes, clock faces, round tables
Circle Properties:
All points on a circle are equidistant from the center
Diameter is the longest chord of a circle
Circumference is the perimeter of the circle
Area represents the space enclosed by the circle