How to Calculate Acres in a Circle

How to Calculate Acres in a Circle
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Once upon a time, the acre was loosely defined as the amount of land that could be plowed in one day by one man working with one ox. While that's not a terribly useful means of measuring land today, the acre itself lingers as a measurement of land area in U.S. customary units of measure and the U.K.'s Imperial measurements. For the sake of visualization, an acre measures about three-quarters the size of a football field. With that said, if you want to calculate the number of acres in a circular area, you're going to have to do some measuring and calculating in feet first.

First Feet, Then Acres

If you already know how many square feet are in your circular area, you can skip straight to converting that measurement into acres. But if you don't know the circle's area in square feet yet, you'll have to start by measuring its radius or diameter in feet. Here's why: you need that linear (or straight line) measurement in order to calculate the circle's area. And you can't take a linear measurement in acres because, by its very definition acres involves two dimensions (length and width), while a linear measurement has only one dimension (its length).

    Measure the radius of the circle or, if it's easier, measure the diameter and then divide that by two to get the radius. The radius of the circle is the straight-line distance from its center point to any point on the circle; the diameter is the straight-line distance from any point on the circle, through the center point of the circle, and then on to the far side of the circle.

    So if you're measuring an enormous circle that has a diameter of 200 feet, you can divide this by 2 to get the circle's radius:

    200 \text{ feet} ÷ 2 = 100 \text{ feet}

    Calculate the area of the circle in square feet, using the formula ​A​ = π​r2, where ​A​ is the circle's area, ​r​ is the length of the circle's radius in feet and π is usually abbreviated as 3.14. This gives you:

    A = 3.14 × (100 \text{ ft})^2

    Which simplifies to:

    A = 31400 \text{ ft}^2

    As your final step, divide the result by 43560 to convert from square feet to acres. (One acre equals 43,560 square feet.) This gives you:

    \frac{31400 \text{ ft}^2}{43560} = 0.72 \text{ acres}

    Tips

    • Note that because an acre is very large, it's not unusual to find yourself dealing with less than one acre, as in the example just given. In fact, in 2015 the average lot size for a newly constructed single-family home was just less than 1/5 or 0.2 acre.

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