A circle is a fundamental two-dimensional geometric shape defined as the set of all coplanar points equidistant from a central reference point. The distance from the center to any point on the boundary is the radius (r), while the straight line passing through the center connecting two opposite boundary points is the diameter (d = 2r). Whether calculating construction materials, designing mechanical components, or solving classical geometry proofs, circular calculations are a cornerstone of applied mathematics. This calculator computes all primary circular properties simultaneously from a single dimension. By entering the circle radius alongside an optional sector angle (θ in degrees), you receive precise values for total surface area, boundary perimeter (circumference), curved arc length, and pie-shaped sector area. All calculations utilize the mathematical constant Archimedes’ constant (π ≈ 3.14159265359). By evaluating both complete circular enclosures and angular fractional slices, this tool provides the exact geometric parameters required for engineering drafting, CNC machining layouts, landscape design, and academic trigonometry.
The area of a circle is calculated using the formula A = πr², where π is approximately 3.14159 and r is the radius. If you know the diameter (d), the formula is A = (πd²) / 4.
Circumference is calculated using the formula C = 2πr (or C = πd). It represents the total linear distance around the outer perimeter of the circle.
To find the radius from the circumference, divide the circumference by 2π: r = C / (2π). For example, if the circumference is 31.42 cm, the radius is 31.42 / 6.283 ≈ 5.00 cm.
Yes. Either divide the diameter by 2 to find the radius and calculate A = πr², or square the diameter directly and multiply by π/4: A = (πd²) / 4.
Arc length is the one-dimensional curved boundary distance along a section of the circumference, whereas sector area is the two-dimensional surface space enclosed inside the wedge bounded by the two radii and that arc.
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