Circle Calculator

Radius, Diameter, Area, and Circumference

A circle is defined by a single measurement: its radius, the distance from the center to any point on the edge. The diameter is simply twice the radius, the distance straight across the circle through its center, so d = 2r. Every other measurement of a circle, its area and its circumference, can be calculated directly from the radius alone, which is why entering just one value, radius or diameter, is enough for the calculator above to fill in everything else.

Both formulas rely on the constant π (pi), the fixed ratio between a circle’s circumference and its diameter, approximately 3.14159, that holds true for every circle regardless of size. Circumference, the distance around the circle’s edge, is given by C = 2πr, or equivalently C = πd, since walking all the way around is proportional to how wide the circle is. Area, the amount of space enclosed inside the circle, is given by A = πr², because area scales with the square of the radius: doubling the radius quadruples the enclosed space, not just doubles it, which is a common source of confusion.

These formulas show up whenever a real object is round, from calculating how much fencing surrounds a circular garden (circumference) to how much material covers a round tabletop (area). Because area and circumference grow at different rates as the radius increases, comparing them is also a quick way to see why larger circles hold disproportionately more area relative to their edge length. Enter either the radius or the diameter into the calculator above, and it keeps both fields, along with the area and circumference, updated together automatically as you type.