Circle Calculator
Calculate circle area, circumference, diameter, and radius with any known value
Calculate Circle Properties
Distance from center to edge
Circle Properties
Radius (r)
Diameter (d)
Circumference (c)
Area (A)
Circle Analysis
Example Calculation
Pizza Example
Problem: A circular pizza has a diameter of 12 inches. What is its area?
Given: Diameter (d) = 12 inches
Find radius: r = d/2 = 12/2 = 6 inches
Calculate area: A = πr² = π × 6² = π × 36 ≈ 113.1 square inches
Garden Example
Problem: A circular garden has an area of 50 m². What fence length is needed?
Given: Area (A) = 50 m²
Find radius: r = √(A/π) = √(50/π) ≈ 3.99 m
Calculate circumference: c = 2πr ≈ 2π × 3.99 ≈ 25.07 m
Circle Facts
Pi (π)
≈ 3.14159265359...
Ratio of circumference to diameter
Perfect Shape
Infinite lines of symmetry
Maximum area for given perimeter
Full Rotation
Complete circle = 360°
Or 2π radians
Unit Circle
Radius = 1
Center at origin (0,0)
Equation: x² + y² = 1
Circumference: 2π ≈ 6.283
Area: π ≈ 3.14159
Quick Tips
Diameter is always twice the radius
Area formula: A = πr² or A = πd²/4
Circumference formula: C = 2πr or C = πd
From area to radius: r = √(A/π)
From circumference to radius: r = C/(2π)
Understanding Circles
What is a Circle?
A circle is a perfectly round shape where every point on the boundary is equidistant from the center. This equal distance is called the radius. Circles are fundamental geometric shapes with unique mathematical properties.
Key Properties
- •Has the largest area for any given perimeter
- •Infinite lines of symmetry through the center
- •All diameters have the same length
- •The ratio of circumference to diameter is always π
Circle Formulas
Area: A = πr² = π(d/2)²
Circumference: C = 2πr = πd
Diameter: d = 2r
Radius from area: r = √(A/π)
Radius from circumference: r = C/(2π)
Real-World Applications
- •Engineering and architecture design
- •Calculating material needs for circular objects
- •Astronomy and planetary calculations
- •Sports field and equipment specifications
Circle Terminology
Radius
Distance from center to any point on the circle
Diameter
Line segment passing through center, connecting two points on circle
Circumference
The distance around the edge of the circle
Chord
Line segment connecting any two points on the circle