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how to find the area of a circle

To find the area of a circle, use the formula that multiplies pi by the square of the radius.

Quick Scoop

The area of a circle is the amount of space inside its boundary. It is always measured in square units, such as square centimeters (cm²) or square meters (m²).

Core Formula

A=πr2A=\pi r^2A=πr2

  • AAA is the area of the circle.
  • rrr is the radius (distance from the center of the circle to its edge).
  • π\pi π is a constant, approximately 3.14 (or you can use the π button on a calculator).

If you only know the diameter ddd (distance all the way across the circle), remember:

r=d2r=\dfrac{d}{2}r=2d​

Then plug that radius into the area formula.

Step‑by‑Step: Given the Radius

  1. Identify the radius of the circle.
  1. Square the radius: multiply it by itself (r×rr\times rr×r).
  1. Multiply by π\pi π: A=πr2A=\pi r^2A=πr2.
  1. Attach units squared (for example, cm², m²).

Example: Radius r=5r=5r=5 cm.

  • Square the radius: 52=255^2=2552=25.
  • Multiply by π\pi π: A≈3.14×25=78.5A\approx 3.14\times 25=78.5A≈3.14×25=78.5.
  • So the area is about 78.5 cm².

Step‑by‑Step: Given the Diameter

  1. Take the diameter ddd.
  1. Find the radius: r=d/2r=d/2r=d/2.
  1. Use the same area formula A=πr2A=\pi r^2A=πr2.

Example: Diameter d=10d=10d=10 m.

  • Radius: r=10/2=5r=10/2=5r=10/2=5 m.
  • Area: A=π×52=π×25≈78.5A=\pi \times 5^2=\pi \times 25\approx 78.5A=π×52=π×25≈78.5 m².

Using Circumference Instead

If you know the circumference CCC (distance around the circle) instead of the radius, you can still find the area.

There is a direct formula:

A=C24πA=\dfrac{C^2}{4\pi}A=4πC2​

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

Simple Mental Picture

Imagine filling a round pizza pan with tiny equal squares so small they perfectly cover it. The total number of those squares (in square units) is the area, and A=πr2A=\pi r^2A=πr2 tells you how many would fit for any radius you choose.

TL;DR:

  • Use A=πr2A=\pi r^2A=πr2, where rrr is the radius.
  • If you have the diameter, halve it to get the radius first.

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