Calculate area, circumference, radius, and diameter of a circle. Supports solving from radius, diameter, circumference, or area with unit selection, presets for common objects, sector/arc calculati...
The circle is one of the most fundamental shapes in mathematics and the natural world. From wheels and coins to planetary orbits and cellular structures, circles appear everywhere. The area of a circle tells you how much space is enclosed within its boundary, and computing it accurately is essential in fields ranging from engineering and architecture to agriculture and everyday life.
The classic formula A = πr² connects the radius of a circle directly to the space it encloses. Despite its simplicity, the formula has profound implications — doubling the radius does not double the area but quadruples it, because area scales with the square of the radius. This non-linear relationship catches many people off guard and is one of the reasons a dedicated calculator is so useful.
This calculator goes beyond just computing area. Enter any one measurement — radius, diameter, circumference, or even the area itself — and it will derive every other property of the circle, including sector areas and arc lengths. With built-in presets for common real-world objects and a reference comparison table, you can quickly understand the scale of different circles and how they relate to one another.
While the circle area formula is simple, real-world problems often start with a diameter measurement or a known circumference, requiring extra conversion steps. This calculator handles all four starting points and shows all derived properties in one view. The presets and reference table make it easy to build intuition about circle sizes, and the ratio visualization illustrates the critical concept that area grows with the square of the radius.
Area = π × r² Circumference = 2 × π × r Diameter = 2 × r Solving from different inputs: From diameter: r = d / 2 From circumference: r = C / (2π) From area: r = √(A / π) Sector area for angle θ: A_sector = (θ / 360) × π × r² Arc length for angle θ: L = (θ / 360) × 2πr
Result: Area = 314.1593 cm², Circumference = 62.8319 cm, Diameter = 20 cm
Using Solve From = Radius with an input of 10 cm gives a circle area of π × 10² ≈ 314.1593 cm². The same radius also gives a circumference of 2π × 10 ≈ 62.8319 cm, a diameter of 20 cm, a 10° sector area of about 8.7266 cm², and a 10° arc length of about 1.7453 cm.
Many circle problems do not start with the radius. You may measure the diameter of a plate, the circumference of a pipe, or the area of a circular garden and then need every other value. This calculator is designed for that workflow. Choose whether you are solving from radius, diameter, circumference, or area, and it derives the complete set of circle properties from that one input. That makes it useful for classroom geometry, fabrication work, and quick estimation in day-to-day projects.
The main area result tells you how much flat space is enclosed inside the circle, but the other outputs add context. Circumference gives the distance around the edge, which matters for trim, fencing, belts, or circular tracks. Diameter and radius let you convert between common measurement styles. The 10-degree sector area and arc length help when a full circle is divided into equal slices, which is common in pie charts, wheel segments, clock faces, and curved construction pieces.
The area ratio visualization in this calculator highlights one of the most important circle ideas: area grows with the square of the radius. If you double the radius, you do not get twice the area; you get four times the area. If you triple the radius, the area becomes nine times larger. The reference table of common circular objects helps turn that abstract rule into something tangible, so you can compare a coin, plate, hoop, or wheel and quickly understand how much enclosed space each one represents.
The area of a circle is A = πr², where r is the radius. If you know the diameter d, substitute r = d/2 to get A = π(d/2)² = πd²/4.
First find the radius: r = C / (2π). Then compute A = πr². For example, a circumference of 31.42 gives r ≈ 5, so A ≈ 78.54.
Because area depends on r². If you replace r with 2r, the area becomes π(2r)² = 4πr², which is four times the original area.
They mean the same thing for a circle. "Circumference" is the specific term used for the perimeter (boundary length) of a circle.
Multiply the full circle area by the fraction of the angle: A_sector = (θ/360) × πr², where θ is the central angle in degrees. Use this as a practical reminder before finalizing the result.
No. An ellipse has two radii (semi-major and semi-minor axes), and its area is π × a × b. This calculator is specifically for circles where a = b = r.
Use any consistent unit. If you enter the radius in centimeters, the area will be in square centimeters and the circumference in centimeters.
It uses the full-precision value of π available in JavaScript (about 15 significant digits). You can display up to 10 decimal places in the output.