How to Determine Angular Size

The smallest angle and arc are 6 percent of the circle and circumference.

If you don't know the size of a segment's angle, you can calculate it from the size of the associated arc. The angle is a small portion of a full circle, and the arc is a small portion of the full circumference. A single ratio relates both smaller measurements to the corresponding measurement in the full circle. Calculate the angular size in radians to use this ratio without having to calculate the actual circumference.

Instructions

1. Measure the radius of the angle. For this example, imagine a radius of 8 inches.

2. Measure the arc that the angle forms. For this example, imagine an arc that measures 10 inches.

3. Divide the arc's length by the radius -- 10 / 8 = 1.25. This is the angular size, measured in radians.

Tips & Warnings

• To convert your answer to degrees, multiply by 57.3.

References

• Clark University: Measurement of Angles
• Rice University: Degree/Radian Circle

Resources

• Macquarie University: Radian and Arc Length.
• University of Notre Dame: Radian Measure
• Teachers Choice: Angle Conversions