Calculadora de círculo

A circle's area is π times the radius squared (A = πr²), and its circumference (the distance around it) is 2 times π times the radius (C = 2πr), or equivalently π times the diameter (C = πd). The radius is always half the diameter.

π (pi) is an irrational constant, approximately 3.14159, representing the ratio of a circle's circumference to its diameter for every circle regardless of size.

Example: a circle with radius 2 has area π × 2² ≈ 12.57 square units and circumference 2π × 2 ≈ 12.57 units — it's a coincidence at r = 2 that area and circumference match numerically, since they use different exponents of r.

Diameter mode doubles the entered value to get radius internally — a 10-inch diameter circle has radius 5 in and area π×25 ≈ 78.54 sq in.

Circumference is useful for fencing circular gardens; area is used for pizza sizing and pond liners.

Worked example with default radius 5: area = π×25 ≈ 78.54, circumference = 2π×5 ≈ 31.42. Same distance around and across differs because circumference uses 2πr while area uses πr².

Annulus (ring) area subtracts inner circle from outer — paint on a donut-shaped sign needs π(R²−r²), not this single-circle tool; run twice and subtract manually. Annulus area = π(R²−r²) — run outer and inner circles separately for ring signage, not a single radius pass. Subtract inner from outer circle areas manually when the project is a ring, not a solid disk.

Unit consistency matters — radius 5 meters gives area in square meters; mixing miles radius with inch circumference breaks dimensional analysis even though the formula symbols look the same. Radius 5 m gives area in m² — mixing mile radius with inch circumference breaks units even though symbols look identical. Keep radius and circumference in matching units before submitting dimensional-analysis homework.

Semicircle area is half πr² — radius 5 gives full circle ≈ 78.54 square units and semicircle transom ≈ 39.27 square units when ordering architectural glass for half-round windows above entry doors on commercial storefronts. Compare that half-area figure to supplier price lists that quote glass by the square foot before requesting a fabrication quote.