# How to Calculate the Area of a Circle With the Diameter

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A circle is one of the most universal geometric shapes, but exploring the mathematical concepts of diameter and area can sometimes feel tricky. Whether you are measuring the size of a round rug you need to purchase or determining the space you need to construct a circular garden or patio, knowing how to calculate the area of a circle from its diameter is a valuable skill. It can be further applied to semicircles or a sector of a circle.

#### TL;DR (Too Long; Didn't Read)

The area of a circle is the amount of space the circle covers. The formula for calculating the area of a circle is A = π‌r2 where pi (π) equals 3.14 and the radius (‌r‌) is half the diameter ‌r‌ = ‌d‌/2.

## Determine the diameter of the circle

The first step for calculating the area of a circle from its diameter is to find that diameter. While math problems often list this value, in the real world, you must find the diameter yourself. The diameter is the length of a line segment that begins at the edge of the circle, passes through the center of the circle, and ends at the opposite edge of the circle. To measure, you will need a ruler for small circles or a tape measure for large circles. The diameter of a circle is extremely useful when calculating the area and circumference of a circle.

## Convert diameter to radius of the circle

Once you have the diameter of the circle (‌d‌), you can find the radius (‌r‌) using the equation ‌d‌ =2‌r‌. The radius of a circle is the distance from the center of the circle to any point on the edge of the circle. The radius of a circle is half of the diameter. If your diameter is a simple number, you can likely calculate the radius in your head. If it is more difficult to work with, using a calculator will likely lead to the most accurate results. You can then use the equation:

r = \frac{d}{2}

and solve.

## Solve for area of the circle

You are now ready to use the area formula:

A = πr^2

This formula is given in terms of pi. The greek letter Pi (π) is a mathematical constant, usually approximated as 3.14 to an accuracy of two decimal places. To solve for area, square the radius of the circle (radius times radius) and multiply by 3.14.