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how to find circumference

To find the circumference of a circle, you just need one measurement and the right formula.

What “circumference” means

Circumference is the distance all the way around a circle, like the circle’s version of a perimeter.

The two main formulas

Use whichever measurement you know:

  • If you know the radius rrr (distance from center to edge):

C=2πrC=2\pi rC=2πr

  • If you know the diameter ddd (distance straight across the circle through the center):

C=πdC=\pi dC=πd

Here π\pi π (pi) is about 3.14, but you usually get a more accurate answer by using the π\pi π button on a calculator.

Quick step‑by‑step examples

Example 1: Given the radius

Radius r=3r=3r=3 cm.

  1. Use the radius formula: C=2πrC=2\pi rC=2πr.
  1. Plug in r=3r=3r=3: C=2π×3=6πC=2\pi \times 3=6\pi C=2π×3=6π cm.
  1. If you approximate π≈3.14\pi \approx 3.14π≈3.14, then C≈6×3.14=18.84C\approx 6\times 3.14=18.84C≈6×3.14=18.84 cm.

So the circumference is about 18.8 cm.

Example 2: Given the diameter

Diameter d=10d=10d=10 m.

  1. Use the diameter formula: C=πdC=\pi dC=πd.
  1. Plug in d=10d=10d=10: C=π×10=10πC=\pi \times 10=10\pi C=π×10=10π m.
  1. Using π≈3.14\pi \approx 3.14π≈3.14, C≈31.4C\approx 31.4C≈31.4 m.

So the circumference is about 31.4 m.

If you only know the area or circumference

Sometimes you’re given different information and still need the circumference.

  • From area AAA to circumference:

C=2πAC=2\sqrt{\pi A}C=2πA​

  • From circumference to radius:
    1. Radius r=C2πr=\dfrac{C}{2\pi}r=2πC​.
2. Then you can check by using C=2πrC=2\pi rC=2πr.

Tiny real‑life story to remember it

Imagine wrapping a string tightly around a round jar.

The length of that string is the jar’s circumference , and if you knew how wide the jar is across (its diameter), you’d just multiply that width by π\pi π to know how much string you need.

Fast checklist

When you see a circumference problem, ask:

  1. Do I know the radius? Use C=2πrC=2\pi rC=2πr.
  1. Do I know the diameter? Use C=πdC=\pi dC=πd.
  1. Do I know the area? Use C=2πAC=2\sqrt{\pi A}C=2πA​.

If you tell me a radius, diameter, or area, I can walk you through the exact calculation step by step.