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Circumference of a Circle Calculator

The circumference is the distance around a circle. Tell the calculator what you know — radius, diameter, or area — and it returns the circumference with every step shown.

Example: with I know the Diameter (d) · Value 10 → Circumference (C): 31.42.

Computed by the calculator below using its default values. Change any input to see your own numbers.

Circumference (C)
Radius / diameter
Area (A)
Steps

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Circumference formula: C = 2πr = πd

Every circle’s circumference is its diameter times π: C = πd = 2πr, with π ≈ 3.14159. So a circle with a 10 ft diameter is π × 10 ≈ 31.42 ft around, and a 7 in radius gives 2π × 7 ≈ 43.98 in. Diameter to circumference is one multiplication; going back is one division (d = C ÷ π).

How to find the circumference when you only know the area: solve A = πr² for the radius first. r = √(A ÷ π), then C = 2πr — an area of 100 gives r ≈ 5.64 and C ≈ 35.45. To measure circumference physically, wrap a flexible tape (or a string you then lay flat) once around the widest part — and that reading divided by π is also the easiest way to get a pipe or tree’s diameter.

How it’s calculated

C = 2πr = πd, with π ≈ 3.14159 (JavaScript’s full-precision Math.PI). From an area, the radius is recovered first as r = √(A ÷ π), then C = 2πr. The area row uses A = πr². Nothing is rounded until the final display (2 decimals).

Results update as you type and are estimates, not professional advice — verify important decisions with a qualified professional.

Common mistakes

  • Mixing up radius and diameter — C = 2πr but C = πd; using a diameter in the 2πr form doubles the answer.
  • Rounding π to 3 — on a 10 ft diameter that cuts the answer from 31.42 ft to 30 ft, an error of about 17 inches.
  • Reporting square units — circumference is a length (ft), not an area (ft²).

Frequently asked questions

What is the formula for the circumference of a circle?

C = 2πr from the radius, or C = πd from the diameter. They’re the same formula, since d = 2r.

How do I find circumference from the diameter?

Multiply the diameter by π ≈ 3.14159. A 12 in diameter pizza is π × 12 ≈ 37.70 in around.

How do I get the diameter from the circumference?

Divide by π: d = C ÷ π. A tree measuring 62.83 in around has a diameter of 62.83 ÷ π ≈ 20 in.

How do I measure circumference in real life?

Wrap a flexible measuring tape once around the object at its widest point, or wrap a string, mark the overlap, and measure the string flat against a ruler.

Can I find circumference from the area?

Yes: r = √(A ÷ π), then C = 2πr — equivalently C = 2√(πA). With A = 100, C ≈ 35.45.