Circle Area & Circumference Calculator
Circle Area Calculator
The circle calculator computes the area (space enclosed) and circumference (perimeter) of a circle given its radius.
Conversion Formula
Area = π × r². This gives the total space inside the circle. Circumference = 2 × π × r. This gives the total distance around the circle.
Step-by-Step Examples
Radius: 5 = Area: 78.53981634, Circumference: 31.41592654
π × 25 = 78.54; 2π × 5 = 31.42.
Radius: 10 = Area: 314.15926536, Circumference: 62.83185307
π × 100 = 314.16; 2π × 10 = 62.83.
Radius: 1 = Area: 3.14159265, Circumference: 6.28318531
The unit circle: area = π, circumference = 2π.
History
Archimedes approximated π around 250 BC by inscribing and circumscribing polygons around a circle, establishing the foundation for circle area calculations.
Common Use Cases
- Landscaping and garden design
- Engineering pipe and tank sizing
- Pizza size comparisons
- Wheel and tire calculations
Frequently Asked Questions
How do I calculate the area of a circle?
Multiply π (3.14159...) by the radius squared: A = πr².
What is circumference?
Circumference is the distance around the circle, calculated as C = 2πr.
What if I know the diameter instead of the radius?
Divide the diameter by 2 to get the radius, then use the formulas.
What is π (pi)?
Pi is the ratio of a circle's circumference to its diameter, approximately 3.14159. It is an irrational number.
What units is the area in?
Area is in square units. If the radius is in centimeters, the area is in square centimeters (cm²).
Can the radius be a decimal?
Yes. The calculator handles any positive decimal radius.
How do I find the radius from the area?
Use r = √(A/π). Take the area, divide by π, and take the square root.
What is the relationship between diameter and circumference?
Circumference = π × diameter. The circumference is always π times the diameter.