Circle Calculator (area, circumference, radius)
Find a circle's radius, diameter, circumference, and area from any one of them, with the formulas and a worked example.
Circle formulas
Everything about a circle follows from a single number — its radius. The diameter is just twice the radius, and the circumference and area both come from the radius through π, the constant ratio of any circle's circumference to its diameter. Enter whichever measure you have and this calculator works back to the radius, then gives you the other three.
d = 2r · C = 2πr = πd · A = πr²
Going the other way is just as easy: the radius is C / (2π) from a circumference, or √(A / π) from an area.
Worked example
A circle of radius 5 has a diameter of 10, a circumference of 2π × 5 ≈ 31.42, and an area of π × 5² ≈ 78.54. Note how the circumference grows in step with the radius while the area grows with its square — double the radius and the circumference doubles, but the area quadruples.
Watch the radius-vs-diameter trap
The most common mistake is feeding a diameter into a radius formula. If you measured across the circle you have the diameter, not the radius — halve it first, or just switch this calculator's dropdown to "Diameter" and let it do the halving.
π is irrational, so the answer is rounded
Every result involving a circle is an approximation in decimal, because π has no exact decimal form. That is almost never the limiting factor: at 15 significant figures the error is far below anything you can measure. What does limit you is the input — a radius measured to the nearest millimetre cannot produce an area good to four decimal places, however many the display shows. Use the full precision shown if you are feeding the result into further working, and round only at the end.