How to Calculate Diameter From Circumference

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A circle is a geometric form of which every point on the outside of the circle is the same distance away from the center. The distance around the edge of the circle is called the circumference. The distance from one side of the circle to the other, going through the center of the circle, is the diameter. The constant pi, designated by the Greek letter π, is the ratio of the circumference to the diameter of a circle. For any circle, if you divide the circumference by the diameter you get pi, an irregular number usually rounded to 3.14.

Setting Up the Formula

    Write down the formula for calculating the circumference of a circle;

    C = πd

    where ​C​ = circumference, π = 3.14 and ​d​ = diameter. Say aloud the meaning of the formula's symbols to make sure you understand, saying "Circumference equals pi times the diameter of a circle."

    Plug the numerical value for your circle's circumference into the formula; for instance, 12 inches. You should replace the symbol ​C​ with the measurement of your circle's circumference. In this example, write

    12 = 3.14 × d

    or "Twelve equals 3.14 times the diameter." Here, the parentheses denote the multiplication function.

    Solve the equation for the diameter of the circle,

    d= \frac{C}{π}

    In this example,

    d = \frac{12}{3.14}

    or "The diameter is equal to twelve divided by 3.14."

    Divide the circumference by pi to get the answer. In this case, the diameter would be 3.82 inches.



About the Author

Alexander White has been writing about science since 2005, specializing in earth science. His work has been published in the scholarly journal "Geology." White holds a B.S. in geology and an M.S. in geophysics.