How to Calculate the Radius and Diameter of an Oval

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An oval is also referred to as an ellipse. Because of its oblong shape, the oval features two diameters: the diameter that runs through the shortest part of the oval, or the semi-minor axis, and the diameter that runs through the longest part of the oval, or the semi-major axis. Each axis perpendicularly bisects the other, cutting each other into two equal parts and creating right angles where they meet. There are also two radii, one for each diameter. To calculate the radii and diameters, or axes, of the oval, use the focus points of the oval -- two points that lie equally spaced on the semi-major axis -- and any one point on the perimeter of the oval.

The Semi-Minor Axis

    Measure the distance between one focus point to the point on the oval’s perimeter to determine a. In this example, a will equal 5 cm.

    Measure the distance between the other focus point to that same point on the perimeter to determine b. In this example, b will equal 3 cm.

    Add a and b together and square the sum. For example, 5 cm plus 3 cm equals 8 cm, and 8 cm squared equals 64 cm^2.

    Measure the distance between the two focus points to figure out f; square the result. In this example, f equals 5 cm, and 5 cm squared equals 25 cm^2.

    Subtract the sum in step four from the sum in step three. For example, 64 cm^2 minus 25 cm^2 equals 39 cm^2.

    Calculate the square root of the sum from step five. For example, the square root of 39 equals 6.245, rounded to the nearest thousandth. Therefore, the semi-minor axis, or shortest diameter, is 6.245 cm.

    Divide the semi-minor axis measurement in half to figure its radius. For example, 6.245 cm divided by two equals 3.122 cm.

The Semi-Major Axis

    Repeat the measuring process from the previous section to figure out a and b. In this example, we'll use the same numbers: 5 cm and 3 cm.

    Add a and b together. The result is the semi-major axis. For example, 5 cm plus 3 cm equals 8 cm, so the semi-major axis is 8 cm.

    Halve the result from step one to figure the radius. Eight divided by two equals four, so the other radius is 4 cm.

References

About the Author

Based in Royal Oak, Mich., Christine Wheatley has been writing professionally since 2009. She contributes to several websites, specializing in articles about fitness, diet and parenting. Wheatley has a Bachelor of Arts in art from Calvin College.

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