⭕Circle Area Calculator — Calculate area, circumference, and sector from radius

This Circle Area Calculator computes area, circumference, diameter, and radius from any one known measurement. Enter a radius, diameter, circumference, or area value, and the calculator instantly returns all related circle properties with step-by-step formula substitution so you can verify every number.

The two most common circle formulas are Area = π × r² and Circumference = 2π × r. These formulas underpin geometry coursework, engineering design, landscaping, and manufacturing. Whether you need to find how many square feet fit inside a circular garden, calculate material needed for a circular gasket, or solve a geometry problem, this calculator gives accurate results in both metric and imperial units.

For practical projects, knowing both area and circumference matters. A circular patio needs area for material quantity (pavers, concrete, turf) and circumference for edging and border lengths. A circular pipe cross-section needs area for flow-rate calculations. This calculator returns both in a single step.

The calculator also supports diameter input, which is often easier to measure with a ruler or tape than radius. Enter diameter directly and the tool converts internally. For sector and segment calculations — common in engineering drawings — enable advanced mode to enter a central angle and compute arc length, sector area, and chord length.

For students, this calculator is useful for checking homework and understanding how changing the radius affects area quadratically. Doubling the radius increases area by four times, not two. This non-linear relationship is a core concept in geometry and calculus, and the calculator makes it easy to test with live inputs.

Units supported include millimeters, centimeters, meters, inches, feet, and yards. Results display to configurable decimal places to match needs from rough estimates to precision engineering.

For landscaping and home projects, the tool provides a quick sanity check before purchasing materials. If your circular flowerbed has a 6-foot radius, that is 113.1 square feet — not 36. The squared relationship surprises many people planning outdoor projects, making a dedicated circle area calculator more reliable than mental math.

Circle geometry follows directly from the relationship between radius, diameter, and π.

Core formulas Area: A = π × r² Circumference: C = 2π × r Diameter: d = 2r

If diameter is the input: r = d / 2, then A = π × (d/2)² = π × d² / 4

If circumference is the input: r = C / (2π), then A = π × (C/(2π))² = C² / (4π)

If area is the input: r = √(A / π), then C = 2π × √(A / π)

Sector calculations (advanced mode) Sector area = (θ / 360) × π × r² (θ in degrees) Arc length = (θ / 360) × 2π × r Chord length = 2r × sin(θ / 2)

Worked example Radius = 7 cm Area = π × 7² = π × 49 = 153.94 cm² Circumference = 2π × 7 = 43.98 cm Diameter = 2 × 7 = 14 cm