Calculate the diameter, circumference and area of a circle from its radius, with full precision for π.
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A radius of 10 gives a diameter of 20, a circumference of about 62.83185307 and an area of about 314.15926536. A radius of 1 has an area of about 3.14159265, and a radius of 0.5 gives a diameter of exactly 1.
The diameter is twice the radius, the circumference is 2πr and the area is πr². The calculator uses the browser’s full double-precision value of π and rounds only when the results are displayed. Diameter and circumference come out in the same unit as the radius, while the area uses that unit squared.
Enter the radius, the distance from the centre to the edge. If you measured straight across the circle, divide that diameter by two first. A radius of 0 is accepted and returns zero for every result, while negative lengths are rejected because a radius cannot be negative.
Enter the radius, the distance from the centre to the edge. A radius of 10 gives a diameter of 20, a circumference of about 62.83185307 and an area of about 314.15926536. Diameter and circumference use the same unit as the radius, while area uses the square of that unit, such as cm² when the radius is in centimeters. If you measured straight across the circle, divide that diameter by two before entering it.
Circumference grows in proportion to the radius, but area grows with its square. A radius of 1 has an area of about 3.14159265; doubling the radius to 2 doubles the circumference but multiplies the area by four. A radius of 0.5 gives a diameter of exactly 1 and an area of about 0.78539816, a quarter of the unit-radius area. This is why a pizza 12.7 cm in radius has four times the area of one with a radius of 6.35 cm: about 506.71 cm² compared with 126.68 cm².
The calculator uses the browser’s full double-precision value of π and rounds only for display. Using 3.14 instead would give 314 for a radius of 10, about 0.05% low, which is harmless for a garden bed but noticeable in machining. For material estimates such as paint, edging or fabric, round up after calculating rather than rounding π. A radius of 0 is accepted and returns zero for every result; negative lengths are rejected because a radius cannot be negative.
| Input | Result |
|---|---|
r 10 | d 20 · C 62.83185307 · A 314.15926536 |
r 1 | d 2 · C 6.28318531 · A 3.14159265 |
r 0.5 | d 1 · C 3.14159265 · A 0.78539816 |
r 6.35 | d 12.7 · C 39.8982267 · A 126.67686977 |
r 12.7 | d 25.4 · C 79.7964534 · A 506.7074791 |
r 0 | d 0 · C 0 · A 0 |
Because the circumference grows in proportion to the radius while the area grows with its square. A radius of 12.7 has an area of about 506.71 while a radius of 6.35, exactly half as much, has about 126.68 — four times smaller. That is why a pizza of twice the radius feeds far more than twice as many people.
A little, but it can matter. With a radius of 10, using 3.14 gives an area of 314 instead of about 314.15926536, roughly 0.05% low. That is harmless for a garden bed and noticeable in machining, so let the tool keep the full value of π and round only the final figure.
Divide the diameter by two and enter that. A diameter of 1 means a radius of 0.5, which gives an area of about 0.78539816, and a diameter of 25.4 means a radius of 12.7. For material estimates such as edging or fabric, round up after calculating rather than rounding π.