Updated · Built and checked by the PlinzoTools team, formulas tested against published sources
Calculate a circle's area and circumference from its radius.
This tool calculates both the area and circumference of a circle from a single input: its radius.
Enter the radius. Area and circumference appear instantly.
Area = πr²
Circumference = 2πr
The calculator has no unit setting: it simply works with whatever unit you type. If the radius is in centimeters, the circumference comes out in centimeters and the area in square centimeters. If it is in feet, the area is in square feet. Both results are shown to four decimal places. Keep in mind that circumference is a length while area is a surface, so you should never add them together or compare them directly. The radius must be a positive number; zero or negative values produce no result.
Suppose a hypothetical round garden bed has a diameter of 3.2 meters and you want to know how much edging to buy and how much soil surface it covers. First halve the diameter to get the radius, 1.6, and enter it.
Area = π × 1.6² = π × 2.56 ≈ 8.0425 square meters
Circumference = 2 × π × 1.6 ≈ 10.0531 meters
The edging needs to run about 10.05 meters, so in practice you would round up and add a little extra for cutting and overlap. The soil surface is roughly 8.04 square meters, which you can multiply by a planned depth to estimate volume.
The two results respond differently when the radius changes. The circumference is proportional to the radius: double the radius and the circumference doubles. The area is proportional to the square of the radius: double the radius and the area becomes four times as large. Tripling the radius makes the area nine times as large. This is why a pizza with a 16-inch diameter has much more than twice the area of one with an 8-inch diameter; it has exactly four times the area. It also explains why a small increase in pipe or wheel size can noticeably increase the cross-section or ground covered.
The tool takes a radius, but sometimes you know the other measurement instead. If you know the circumference C, the radius is C divided by 2π. If you know the area A, the radius is the square root of A divided by π. Enter the recovered radius to see the other value and to verify your work. For instance, a hypothetical circumference of 30 gives a radius of about 4.7746, and entering that will return a circumference of 30.
For real purchases, allow for waste, cutting patterns, and manufacturer sizes, because a perfect geometric figure rarely matches how materials are actually sold.
Divide the diameter by 2 to get the radius, then enter that.
The full double-precision value of π (JavaScript's Math.PI), far more precise than the common 3.14159 approximation.
Area depends on the radius multiplied by itself. Doubling the radius gives 2 × 2 = 4 times the area, whereas the circumference, which depends on the radius only once, simply doubles.
Divide the circumference by 2π, which is about 6.2832. For example, a circumference of 62.832 gives a radius of about 10.
The same unit as your input. A radius in meters gives a circumference in meters and an area in square meters. The tool does not convert between units.
No. The tool requires a positive radius, so zero and negative values show no result.
Reference: NIST Weights and Measures