You can describe a fraction of a circle by using a percentage or by describing the equivalent angle in degrees. To convert percentage into degrees, you must multiply the total number of degrees in a circle by the percent. Slopes are another entity commonly measured both ways. Percent slope describes the vertical change divided by the horizontal change, or rise over run. Degrees of slope describe the angle of incline. To convert from percent into degrees of slope, you must convert the percentage into its decimal equivalent, then find its arctangent.

Pie charts represent percentages, but the angles of the wedges are measured in degrees.

Circles

• 1. Convert the percentage into its decimal equivalent by dividing it by 100. For instance, 45 percent equals 0.45.
• 2. Multiply the decimal by 360, the total number of degrees in a circle.
  For example, 0.45 * 360 = 162.
• 3. Round the answer, if necessary and add the degree symbol or "degrees." So 45 percent of a circle equals 162º or 162 degrees.

Slopes

• 1. Convert the percentage into its decimal equivalent by dividing it by 100. For instance, 35 percent equals 0.35.
• 2. Find the arctangent (atan) of the decimal. In the example, atan(0.35) = 19.29004622
• 3. Round the answer and add the degree symbol. A 35 percent grade equals a 19º slope.