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Circumference to Diameter Calculator

Diameter, radius and area of a circle from its circumference alone.

Result

47.75
23.87
1,790.49

How it is calculated

The tool inverts the circle formula C = π·d. It computes d = C / π, then r = d / 2 and A = π·r². There is no unit selector: the diameter and radius come out in whatever length unit you used for the circumference, and the area comes out in that unit squared. All three values are rounded to two decimals for display, but the area is calculated from the unrounded radius, so working it out by hand from the rounded radius can differ in the last digits. Zero is accepted and gives zeros; negative numbers return no result. π is taken at full double precision.

Worked example

You wrap a tape around a tree trunk and read a circumference of 150 cm. Diameter: 150 / π ≈ 47.7465, shown as 47.75 cm. Radius: 47.7465 / 2 ≈ 23.8732, shown as 23.87 cm. Area: π × 23.8732² ≈ 1,790.49 cm², the cross-section of the trunk. Doing the area by hand with the rounded 23.87 would give 1,790.0, which is why the tool uses the unrounded radius.

Try this example →

Common mistakes

  • Dividing by 3.14 or 22/7 and then comparing with the tool. The tool uses the full value of π, so small differences appear on large circles.
  • Mixing units. If the circumference is in centimetres, the area is in square centimetres, not square metres.
  • Entering the diameter or radius in the circumference field. The result will then be a diameter that is wrong by a factor of π.
  • Measuring around a soft or irregular object without keeping the tape level. A tilted tape reads a longer circumference and gives an oversize diameter.
  • Ignoring the thickness of the tape or of the material wrapped around the object, which adds to the circumference and to the diameter you get.

About this calculator

Given a circle's circumference (C), its diameter is found by rearranging the classic formula C = πd into d = C / π. From there, the radius is simply half the diameter (r = d/2), and the area follows from A = πr², giving three related measurements from a single circumference reading.

This calculation is common whenever only the outer edge of a circular object can be measured directly — wrapping a tape measure around a tree trunk, a pipe, a wheel, or a tank — and the diameter, radius or area needs to be known. Students verifying geometry homework, engineers sizing pipes, and hobbyists building round objects from a measured wrap all rely on the same π-based relationship.

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