Circle Calculator

For a circle with radius r: Area = pi x r^2. Circumference = 2 x pi x r = pi x d. Diameter = 2r. If you know any one measurement, you can find all others. Pi (pi) ≈ 3.14159265358979.

First find radius: r = C / (2 x pi). Then area = pi x r^2. Shortcut: Area = C^2 / (4 x pi). Example: circumference = 31.416, area = (31.416)^2 / (4 x pi) ≈ 78.54 square units.

Circumference is specifically the perimeter (boundary length) of a circle. Perimeter is the general term for the boundary length of any 2D shape. All circles have circumference; other shapes have perimeter. C = 2 x pi x r = pi x d.

Pi (pi) ≈ 3.14159265... is the ratio of any circle circumference to its diameter: C/d = pi. It is irrational (never ending decimal) and transcendental (cannot be expressed as a root of a polynomial). Pi appears in countless formulas beyond circles: sphere volumes, wave equations, Fourier transforms, and probability.

Area of semicircle = (pi x r^2) / 2. The straight edge has length 2r. Perimeter = pi x r + 2r = r(pi + 2). For a quarter circle: Area = (pi x r^2) / 4. For a sector with angle theta (degrees): Area = (theta/360) x pi x r^2.