Circle Circumference & Area Calculator
From a circle’s radius get its circumference, area and diameter — the three measurements that depend only on the radius and π.
How it works
C = 2πr · A = πr² · d = 2r
Every measurement of a circle flows from its radius and the constant π ≈ 3.14159. The circumference (distance around) grows linearly with the radius, while the area (space inside) grows with the square of the radius — so doubling the radius doubles the circumference but quadruples the area. The diameter is simply twice the radius.
Worked example
For radius 5: circumference = 2π·5 ≈ 31.42, area = π·5² = 25π ≈ 78.54, diameter = 2·5 = 10.
Sources: Circle — Wikipedia
Frequently asked questions
What if I only know the diameter?
The radius is half the diameter, so divide by 2 first. A diameter of 10 means a radius of 5, then apply the formulas.
Why does area grow faster than circumference?
Circumference depends on r (first power) while area depends on r² (second power). Doubling r doubles the circumference but multiplies the area by four.
How do I get the radius back from the area?
Rearrange A = πr² to r = √(A/π). For example, an area of 78.54 gives r = √(78.54/π) ≈ 5.
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This calculator is for educational purposes. Double-check important results before acting on them.