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how do you find the perimeter of a circle

You find the perimeter of a circle using the circumference formula. The perimeter of a circle is just another name for its circumference.

Basic formula

The key formulas are:

  • Using the radius rrr:

Perimeter=C=2πr\text{Perimeter}=C=2\pi rPerimeter=C=2πr

This means “two times pi times the radius.”

  • Using the diameter ddd:

Perimeter=C=πd\text{Perimeter}=C=\pi dPerimeter=C=πd

This works because the diameter is 2r2r2r, so 2πr=π(2r)=πd2\pi r=\pi(2r)=\pi d2πr=π(2r)=πd.

Here π\pi π is about 3.143.143.14, or more accurately 3.14159...3.14159...3.14159....

Step‑by‑step method

  1. Identify what you’re given:
    • If you know the radius , use C=2πrC=2\pi rC=2πr.
    • If you know the diameter , use C=πdC=\pi dC=πd.
  1. Multiply:
    • Radius case: multiply the radius by 2, then multiply by π\pi π.
    • Diameter case: multiply the diameter directly by π\pi π.
  1. Round your answer to a sensible number of decimal places (often 2).

Example with radius

A circle has radius 777 cm.

  • Use C=2πrC=2\pi rC=2πr.
  • C=2×π×7C=2\times \pi \times 7C=2×π×7.
  • Using π≈3.14\pi \approx 3.14π≈3.14: C≈2×3.14×7=43.96C\approx 2\times 3.14\times 7=43.96C≈2×3.14×7=43.96 cm.

Example with diameter

A circle has diameter 101010 inches.

  • Use C=πdC=\pi dC=πd.
  • C=π×10C=\pi \times 10C=π×10.
  • With π≈3.1416\pi \approx 3.1416π≈3.1416: C≈31.416C\approx 31.416C≈31.416 inches.

If you only know the area (extra)

Sometimes you only know the area AAA and still want the perimeter. You can use a derived formula:

C=2πAC=2\sqrt{\pi A}C=2πA​

This comes from combining the area formula A=πr2A=\pi r^2A=πr2 with C=2πrC=2\pi rC=2πr.

Quick “real life” way

If you have a real circular object (like a plate or a lid) and no measurements:

  • Wrap a string once around the edge.
  • Mark where it completes one loop.
  • Straighten the string and measure it with a ruler.
    That length is the circle’s perimeter.

TL;DR:
To find the perimeter of a circle, multiply either the radius by 2π2\pi 2π or the diameter by π\pi π:

C=2πrorC=πdC=2\pi r\quad \text{or}\quad C=\pi dC=2πrorC=πd

Information gathered from public forums or data available on the internet and portrayed here.