# How to Calculate Roundness ••• sorapol1150/iStock/GettyImages

Roundness is a measure of the sharpness of corners and edges of a given particle and is associated with sphericity and the compactness of a shape. A circle is the most round shape, so roundness is the degree to which the object's shape differs from that of a circle. Roundness is commonly used in astronomy to classify the shapes of celestial bodies. The calculation of roundness requires the measurements of radii around the object at regular intervals.

Determine the angles at which to measure the radius of the object. Let ? be the measure of an angle in degrees such that 360/N = ? where N is an integer. The angles at which we will measure the radius of the object is then given by the set A = {1?, 2?, 3? ... N?}.

Measure the radius of an object at the angles in set A. Note that the center of the object must be defined since it may not be a circle. Astronomers typically use the center of rotation whereas a geologist will more likely use the center of mass. The radius Yi will be the distance from the center of the object to the surface of the object at angle ?i.

Define the estimated radius R of the object as the mean of measurements Y. This gives us R = ? Yi/N.

Define the lengths a and b such that a = 2? Yi cos(?i)/N and b = 2? Yi sin(?i)/N. This provides the deviation of the object from a circle of radius R as Yi - R - a x cos(?i) - b x sin(?i). This method is known as a single trace method since only one set of measurements is taken for the object.

Use a multiple trace method for greater accuracy. The object is rotated after each set of measurements before taking a new set of measurements. This allows the errors in locating the center of the object to be separated from the deviations in the object's circularity.

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