Even if part of a circle is missing, the circle still retains its general properties. The radius of a circle is an essential variable of a circle. Measuring the distance from the origin, or center point, of the circle to its outer edge, also known as its circumference, the radius is instrumental in calculating the size of the circle. If the circle has a section of it cut away by a straight line, the radius of a large or small partial circle can be found through individual measurements.
Things You'll Need
 Ruler
 Pencil or pen
 Calculator
More than Half a Circle

Find two points on the circle's circumference that are the farthest from each other, and then draw a straight line connecting them.

Measure the length of the line. The line is the diameter. For example, the line is 8 centimeters.

Divide the diameter in half to find the circle's radius. For this example, 8 centimeters divided in two is 4 centimeters. The radius is 4 centimeters.
Less than Half a Circle

Measure the length of the straight edge of the partial circle and then square the length. The length of the straight edge is 7 centimeters, and the square of 7 is 49.

Draw a perpendicular line from the middle of the straight edge to the circumference and measure the length of the line. For this example, the line is 2 centimeters.

Multiply the length of the line measured in Step 2 by 8 and then divide that amount from the square calculated in Step 1. For this example, 2 multiplied by 8 equals 16, and 49 divided by 32 equals 3.0625.

Divide the length of the line measured in Step 2 in half and then add that number to the amount calculated in Step 3. For this example, 2 divided by 2 is 1 and 1 added to 3.0625 equals 4.0625. The radius is 4.0625 centimeters.
References
 "Basic Math and Prealgebra"; Jerry Bobrow; 1995
 "The Complete Idiot's Guide to Geometry"; Denise Szecsei; 2004
 Math Open Reference: Radius of an Arc or Segment
 Cool Math: The Geometry of Circles