Radius, diameter, circumference and area are all fixed by any single one of them. Enter whichever you have.
Everything about a circle follows from the radius:
A radius of 5 gives a circumference of 31.4159 and an area of 78.5398. Note they are not proportional to each other: doubling the radius doubles the circumference but quadruples the area, because area depends on r².
It is the reason a 16-inch pizza is not slightly bigger than a 12-inch one but more than three-quarters bigger — 201 square inches against 113. The same relationship explains why pipe capacity rises so sharply with diameter, and why a small increase in a circular cross-section carries a disproportionate amount more.
π is the ratio of circumference to diameter, roughly 3.14159, and it is irrational — the decimal never terminates or repeats. A radian is the angle subtended by an arc equal in length to the radius, which makes a full turn 2π radians rather than 360°. Most calculus is done in radians because the derivatives come out clean only in that unit.
Divide the area by π and take the square root: r = √(A/π). For an area of 78.5398 that gives a radius of exactly 5. This calculator does it for you — select "Area" as the known value.
None in substance. Circumference is simply the name given to the perimeter of a circle. Both mean the distance around the outside.
Because area depends on the radius squared, while circumference depends on it linearly. Double r and C doubles, but A is multiplied by 2² = 4. It is the single most useful thing to remember about circles.
It uses the full double-precision value built into JavaScript, about 15 significant figures — far more precision than any physical measurement justifies. Results are rounded to six decimal places for display.
For circles as part of a larger shape, use the Area Calculator; for spheres, cylinders and cones see the Volume Calculator and Surface Area Calculator. For general arithmetic, the Scientific Calculator handles π directly.