Circle Calculator

Formula

Area = πr² | C = 2πr

Area depends on the square of the radius. Circumference is the linear distance around the edge.

Worked Examples

Example 1: Radius 5

Problem:r=5

Solution:Area = π×5² ≈ 78.54. Circumference = 2×π×5 ≈ 31.42.

Result:A: 78.54, C: 31.42

Example 2: Diameter 10

Problem:d=10

Solution:r = 10/2 = 5. Same as above.

Result:A: 78.54

Frequently Asked Questions

How do I find the area of a circle?

Use the formula A = πr². If you have the diameter, divide it by 2 to get the radius first, then square it and multiply by π.

What are concentric circles?

Circles that share the same center point but have different radii (like a target or bullseye).

Background & Theory

**Circle Properties:** * **Radius (r):** Distance from center to edge. * **Diameter (d):** Distance across circle through center (d = 2r). * **Circumference (C):** Distance around the circle (Perimeter). * **Area (A):** Space inside the circle. **Formulas:** * **Diameter:** d = 2r * **Circumference:** C = 2πr = πd * **Area:** A = πr² **Pi (π):** An irrational number approximately equal to 3.14159...

History

The circle is one of the oldest geometric shapes known to humanity. The Babylonians (c. 1900 BC) approximated the value of Pi (π) as 3.125. Archimedes (c. 250 BC) gave a more accurate approximation of Pi using polygons inscribed in and circumscribed about a circle. The modern symbol "π" was introduced by William Jones in 1706 and popularized by Leonhard Euler.