How To Convert An Angle To A Decimal

In geometry, angles are measured in degrees and fractions of a degree, such as minutes and seconds. It follows that 1 degree equals to 60 minutes, while 1 minute contains 60 seconds. Hence 1 degree also comprises 3,600 (60 x 60) seconds. For many calculations, it's necessary to convert an angle value to the decimal form; for example, the angular fraction of 15 minutes equals to 0.25 degree in the decimal notation.

Step 1

Write down the angle value in the degree-minute-second form. For example, suppose you have the angle is 27 degrees, 12 minutes and 45 seconds.

Step 2

Divide the seconds by 3,600 to calculate the corresponding fraction of a degree. Continuing with the example, 45 seconds divided by 3,600 = 0.0125 degree.

Step 3

Divide the minutes by 60 to calculate the corresponding fraction of a degree. In this case, it would be 12 minutes divided by 60 = 0.2 degree.

Step 4

Add up the integer number of degrees and minute/second fractions to convert the angle magnitude into the decimal form. In this example, the angle of 27 degrees, 12 minutes and 45 seconds corresponds to 27 + 0.2 + 0.0125 = 27.2125 degrees.