Convert between Degrees, Minutes, and Seconds and Decimal Degrees

Now that you’ve become an expert at converting units and rates, we can now extend our understanding of this concept to convert units used to measure angles in trigonometry, namely degrees and radians. An angle is a geometric figure consisting of two rays with a common endpoint. The angle below is represented by the universal symbol for angles – the Greek letter theta (θ) – and it’s formed by joining the two line segments.

The degree (°) is a unit of angular measure equal to 1/360 of a revolution; thus, 360º = 1 revolution. A degree can be further split into minutes and seconds:

  • 1 minute (‘) is equal to 1/60 of a degree.
  • 1 second (”) is equal to 1/3600 of a degree.
    • These will serve as the main conversion ratios used in this lesson.

Some examples of angles written in degrees, minutes, and seconds (DMS):

  • 85° 18′ 42″ (85 degrees, 18 minutes, 42 seconds)
  • 62° 12′ (62 degrees, 12 minutes)
    • Note that minutes or seconds less than 10 are written with an initial zero.
  • 75° 06′ 03” (75 degrees, 6 minutes, 3 seconds)

Let’s learn how to convert between decimal degrees (i.e. 33°) to DMS and vice versa. The first example shows how to convert DMS to decimal degrees, while the next demonstrates the reverse process.

Now the reverse. As a challenge, try converting on your own before starting.

If you took the calculator recommendation seriously before enrolling into this course, the Casio fx-991ES Plus calculator was suggested due to its large volume of pre-programmed functions, one of which is this precise conversion. The last video outlines the steps to doing this. If you have a similar calculator, try locating these buttons – you might be lucky enough to have it!