How to Calculate the Area of a Circle With the Diameter

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

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 = π​r2 where pi (π) equals 3.14 and the radius (​r​) is half the diameter.

  1. Determine the diameter

  2. 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 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.

  3. Convert diameter to radius

  4. Once you have the diameter (​d​) of the circle, you can find the radius (​r​) using the equation ​d​=2​r​. 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 is also half of the diameter. If your diameter is a simple number, you can likely calculate the radius in your head. If not, rearrange the equation to find for ​r

    r = \frac{d}{2}

    and solve.

  5. Solve for area

  6. You are now ready to use the equation for area:

    A = πr^2

    Pi (π) is a non-algebraic number that represents the ratio of the distance around the circle (circumference) to its diameter, usually estimated as 3.14. To solve for area, square the radius (radius times radius) then multiply by 3.14.

  7. Report your answer

  8. Since area is a measure of two dimensions, you always report area in square units like square inches (in2) or square feet (ft2). This is especially important when calculating the area of a circle for an assignment since an answer without correctly reported units is likely incorrect or incomplete.

    Any time you need to determine the space inside a circle or the amount of space a circle covers, you can use the equation for the area of a circle. Especially for real world applications of this skill, measuring diameter is often the simplest way to start.



About the Author

Melissa Mayer is an eclectic science writer with experience in the fields of molecular biology, proteomics, genomics, microbiology, biobanking and food science. In the niche of science and medical writing, her work includes five years with Thermo Scientific (Accelerating Science blogs), SomaLogic, Mental Floss, the Society for Neuroscience and Healthline. She has also served as interim associate editor for a glossy trade magazine read by pathologists, Clinical Lab Products, and wrote a non-fiction YA book (Coping with Date Rape and Acquaintance Rape). She has two books forthcoming covering the neuroscience of mental health.