Circle Calculator
Calculate a circle's diameter, circumference, and area from its radius. Enter a radius to get all three measurements instantly, computed with Math.PI.
How It's Calculated
Formula
d = 2r\\ C = 2\pi r\\ A = \pi r^2A circle is fully defined by a single measurement — its radius, the distance from the center to any point on the edge. Once you know the radius, every other basic measurement follows directly: the diameter is simply twice the radius (the length straight across the circle through its center), the circumference is the distance around the circle's edge, and the area is the amount of flat space the circle encloses. This calculator applies all three formulas using Math.PI for maximum available precision, so the same radius always produces consistent diameter, circumference, and area figures.
Worked Examples
Standard case: radius = 5
- Diameter: d = 2r = 2 × 5 = 10
- Circumference: C = 2πr = 2 × π × 5 ≈ 31.4159
- Area: A = πr² = π × 5² = π × 25 ≈ 78.5398
Larger radius: radius = 10
- Diameter: d = 2r = 2 × 10 = 20
- Circumference: C = 2πr = 2 × π × 10 ≈ 62.8319
- Area: A = πr² = π × 10² = π × 100 ≈ 314.1593
Frequently Asked Questions
What is the difference between diameter and radius?
The radius is the distance from the circle's center to its edge. The diameter is the full distance straight across the circle through the center — always exactly twice the radius (d = 2r). If you only know the diameter, divide it by 2 to get the radius before using this calculator.
Why does the circumference formula use 2πr instead of πd?
They're the same formula written two ways: since d = 2r, πd and 2πr are always equal. This calculator takes radius as the input, so it applies C = 2πr directly rather than first converting to diameter and back.
How precise is the value of π used here?
This calculator uses Math.PI, which provides roughly 15-16 significant decimal digits of precision — far more precision than any practical measurement of a physical circle's radius could support. For everyday use, results are accurate to the number of decimal places shown.
What happens if I enter a radius of 0 or a negative number?
A radius of 0 or less does not describe a real circle, so the calculator will not produce diameter, circumference, or area figures for it. Enter any radius strictly greater than 0.
Can I use this for very large or very small circles?
Yes. The formulas scale correctly for any positive radius, from tiny fractional values (like 0.001) to very large ones (like 1,000,000), without losing accuracy or producing invalid results.