Radius, diameter, circumference and area are all fixed by any single one of them. Enter whichever you have.
Every circle is fully determined by a single measurement, because the other three all derive from whichever one you know. Start from this page’s default, radius 5:
Enter any one of these four instead and the calculator solves for the radius first — dividing the diameter by 2, dividing the circumference by 2π, or taking the square root of (area ÷ π) — then rebuilds the other three from it. Recover a radius of 5 from an area of 78.54 and you land back on exactly the same circle.
Circumference scales directly with radius — double r and circumference exactly doubles, from 31.42 to 62.83. Area does not: double the radius from 5 to 10 and area grows from 78.54 to 314.16, a factor of 4, because area depends on r squared while circumference depends on r alone. This is why a large pizza is so much more than proportionally bigger than a medium, and why a can twice as tall and twice as wide holds eight times the volume, not twice.
This calculator uses JavaScript's built-in value of π — roughly 15 correct decimal digits — and displays results rounded to six. π itself is irrational and never terminates or repeats, so any calculator necessarily works with a truncated version; the question is only how many digits you keep. Six decimals of precision on a circle the size of the Earth's orbit would still be accurate to a handful of kilometres, which is why six is comfortably more precision than almost any real use needs.
Perimeter is the general term for the distance around any flat shape; circumference is simply what that distance is called specifically for a circle, because a circle has no straight sides to measure individually. The formula for a circle's perimeter, 2πr, is exactly as valid a perimeter calculation as base+base+side+side is for a rectangle — it just has its own name by convention. See the area calculator for how a circular sector's perimeter combines a curved arc with two straight radius edges.
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. A practical application: the Tire Size Calculator works from tyre circumference to revolutions per mile and speedometer error.