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TallyBench / Circle Calculator
// CIRCLE CALCULATOR

Know one measurement of a circle, get the other three.

Radius, diameter, circumference and area are all fixed by any single one of them. Enter whichever you have.

Radius
Diameter
Circumference
Area

The four formulas

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.

Why that squaring matters

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.

Degrees, radians and π

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.

How do I find the radius from the area?

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.

What is the difference between circumference and perimeter?

None in substance. Circumference is simply the name given to the perimeter of a circle. Both mean the distance around the outside.

Why does doubling the radius quadruple the area?

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.

How many decimal places of π does this use?

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.