Circle Formulas

Every circle is defined by its radius r. From it, all other properties follow exactly: diameter d = 2r, circumference C = 2πr, and area A = πr². This circle calculator accepts any one known value — radius, diameter, circumference, or area — and derives the rest using exact formulas with no approximations.

Working Backward from Any Input

Given the diameter, radius = d/2. Given the circumference, radius = C/(2π). Given the area, radius = √(A/π). The calculator applies the correct inverse formula automatically based on your chosen input mode, so you never need to rearrange equations by hand.

Real-World Applications

Circle calculations appear everywhere: sizing round tables and rugs, laying out garden beds and ponds, computing pizza areas for value comparisons, designing gears and pulleys, and calculating the cross-section of pipes and cables. Choose your unit — inches, feet, centimeters, meters, millimeters, or yards — and the results follow in matching units.