The study of geometry requires you to deal with angles and their relation to other measurements, such as distance. When looking at straight lines, calculating the distance between two points is straightforward: simply measure the distance with a ruler, and use the Pythagorean Theorem when dealing with right triangles. When working with a circle, however, there is no instrument to accurately measure a curve. Therefore, you may have to calculate the distance between two points on a circle using mathematics.
Measure the circle's radius with a ruler, or record the figure given to you in the math problem. The radius of a circle measures the distance from the center to any point along the outside of the circle.
Multiply this measurement by two to calculate the diameter, or distance through the center of the circle.
Multiply this measurement by pi. Pi is an irrational number, but for most everyday purposes and in school, you can round it to two decimal places: 3.14. The diameter of a circle multiplied by pi gives you the circumference, or the distance around the circle.
Draw two lines from the radius of your circle, each connecting to one of the two points you're using to measure arc distance.
Measure the angle made by those lines with a protractor and record the measurement.
Set the angle you measured as a ratio of 360. According to The Geometer's Sketchpad on the Rice University website, there are 360 degrees in any circle, so any angle you measure can be taken as a ratio to determine the proportion of an arc length.
Cross-multiply your numbers using the equation: a/C = T/360. A is your arc length, C is your circumference and T is the angle you measured. Multiply C by T. Set the result equal to 360 times a. Divide both sides of the equation by 360 to solve for a.