Circle Calculator

Calculate area, circumference, radius, and diameter of a circle from any known measurement. Perfect for geometry, construction, and design.

Enter the measurement you know

Area = PIr^2\nCircumference = 2PIr = PId\nDiameter = 2r\nRadius = d/2\n\nWhere:\nPI (pi) ≈ 3.14159\nr = radius\nd = diameter
Example 1 (From Radius):\nRadius = 10 cm\n\nDiameter = 2 * 10 = 20 cm\nCircumference = 2PI * 10 = 62.83 cm\nArea = PI * 10^2 = 314.16 cm^2\n\nExample 2 (From Area):\nArea = 100 cm^2\n\nRadius = sqrt(100/PI) = 5.64 cm\nDiameter = 2 * 5.64 = 11.28 cm\nCircumference = 2PI * 5.64 = 35.45 cm

What is the formula for the area of a circle?

The area of a circle is calculated using the formula: A = PIr^2, where A is the area, PI (pi) is approximately 3.14159, and r is the radius. For example, a circle with radius 5 cm has an area of PI * 5^2 = 78.54 cm^2.

How do I find the circumference of a circle?

The circumference is the distance around the circle, calculated as: C = 2PIr or C = PId, where r is radius and d is diameter. Since diameter = 2 * radius, both formulas give the same result.

What is the difference between radius and diameter?

Radius is the distance from the center of the circle to any point on the edge. Diameter is the distance across the circle through the center, which is exactly twice the radius. If radius = 5, then diameter = 10.

Can I calculate the radius if I know the area?

Yes! Rearrange the area formula: r = sqrt(A/PI). For example, if area = 100 cm^2, then radius = sqrt(100/PI) = sqrt31.83 = 5.64 cm. This calculator can work backwards from area or circumference.

What are real-world uses for circle calculations?

Common applications include: calculating pizza sizes, determining garden bed areas, sizing circular pools, measuring pipe cross-sections, designing round tables, calculating wheel circumference, planning circular driveways, and engineering calculations.