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Circle Area from Circumference Calculator

Enter a circle's circumference to find its area, radius, and diameter.

Result

198.9437 units²
7.9577 units
15.9155 units

How it is calculated

Enter the distance around the circle, C, in any one length unit. The tool first finds the radius, r = C / (2π), then the diameter, d = 2r = C / π, and the area, A = C² / (4π). Results are shown to 4 decimals with the generic label "units" (and "units²" for the area). There is no unit conversion: if C is in centimetres, the radius and diameter are in centimetres and the area in square centimetres. The circumference must be above zero; zero or a negative value shows no result. Because the area depends on C squared, a small error in measuring the circumference has a larger effect on the area than on the radius.

Worked example

You wrap a tape around a round table top and read a circumference of 50. Radius = 50 / (2 × π) = 7.9577. Diameter = 2 × 7.9577 = 15.9155. Area = 50² / (4 × π) = 2500 / 12.5664 = 198.9437 units². If the 50 was in centimetres, the table is about 15.9 cm across with an area of roughly 198.9 cm².

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Common mistakes

  • Entering the diameter or radius in the circumference field. The tool expects the full distance around the edge, so a circle with a 10 cm diameter needs about 31.42.
  • Mixing units. The area comes out in the square of whatever unit you used, so a circumference in metres gives square metres, not square centimetres.
  • Using a tape that is not flat or not level. If it sags or spirals, the circumference is too large and the area is overstated by the square of that error.
  • Rounding the circumference too early. The area depends on the square, so keep the measurement to as many digits as you really have.
  • Assuming the shape is a true circle. For an oval or irregular outline the circumference does not give a reliable area.

About this calculator

Starting from a circle's circumference (C), the radius falls out of C = 2πr as r = C/(2π), and the diameter is simply twice that. Substituting the radius into the standard area formula πr² and simplifying gives a direct shortcut: area = C²/(4π) — no need to solve for the radius as an intermediate step.

This is handy whenever you can measure the outer edge of something circular but not its center — wrapping a tape measure around a pipe, a tree trunk, or a round tabletop — and need the enclosed area, radius, and diameter all from that single circumference reading.

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Comments (1)

  • Editorial team

    Since the area follows the square of the circumference, a small slip in the tape reading grows in the answer. A circumference of 50 gives an area of 198.9437, while 51, only 2 percent more, gives 206.9810, about 4 percent more. So measure twice, keep the tape level, and keep full precision until the end. What do you measure this way most often: pipes, trunks, tabletops or something else?

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