Calculate the area of a circle

The area of a circle is the measure of the region it encloses, represented by $A=\pi r^2$ , where $r$ is the radius; given a diameter, the radius must first be found by halving it. The relationship shows that area scales with the square of the radius, so answers are expressed in square units and may be exact in terms of $\pi$ or approximated using a suitable value of $\pi$ . This scope excludes calculus-based derivations and more advanced formulas for sectors or other curved regions.

Detailed Explanation: Calculate the area of a circle

The area of a circle is found using

A=\pi r^2

where:

$A$ is the area,
$r$ is the radius,
$\pi$ is approximately $3.14$ .

If you are given the diameter, first divide it by $2$ because the radius is half the diameter.

Example: Find the area of a circle with a diameter of $10\text{ cm}$ .

Find the radius:

r=\frac{10}{2}=5\text{ cm}

Substitute the radius into the area formula:

A=\pi(5)^2

Square the radius:

A=25\pi\text{ cm}^2

This is the exact answer. To approximate it, use $\pi\approx3.14$ :

A\approx25(3.14)=78.5\text{ cm}^2

The area is therefore $25\pi\text{ cm}^2$ , or approximately $78.5\text{ cm}^2$ . Area is always written in square units.

Learn by doing: Calculate the area of a circle

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Area of a Circle from Diameter - To Pi Value

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Calculate the area of a circle

Detailed Explanation: Calculate the area of a circle

Learn by doing: Calculate the area of a circle

Practice with unlimited practice problems

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Area of a Circle from Diameter - To Pi Value