How to Convert Decimal Degrees into Degrees, Minutes, Seconds

a compass graphic
(Photo by Nanette Hoogslag Premi / Getty Images)

When looking at maps and surveys, you'll sometimes find degrees given in decimal degrees (121.135 degrees) instead of the more common degrees, minutes, and seconds (121 degrees, 8 minutes, and 6 seconds). It's easy to convert from a decimal to the sexagesimal system if, for example, you need to combine data from maps that are calculated in two different systems. Or maybe you've done some math with some data in decimal degrees format and need to convert back to degrees, minutes, and seconds to plot the coordinates on a map. When you use GPS systems, for example when geocaching, you should be able to switch between the different coordinate systems on your device. 

Here's How to Do the Conversion

There are online calculators, but it's not that tough to do the calculation from decimal degrees to degrees, minutes, and seconds by hand when needed; you start by breaking down your existing figure. 

  1. The whole units of degrees will remain the same (e.g., if your figure is 121.135 degrees longitude, start with 121 degrees).
  2. Multiply the decimal portion of the figure by 60 (e.g., .135 * 60 = 8.1).
  3. The whole number becomes the minutes (8).
  4. Take the remaining decimal and multiply it by 60 (e.g., .1 * 60 = 6).
  5. The resulting number becomes the seconds (6 seconds). Seconds can remain as a decimal if needed.
  6. Take your three sets of numbers and put them together, (e.g., 121°8'6" longitude would be equivalent to 121.135 degrees longitude).

FYI

  1. After you have degrees, minutes, and seconds, it's often easier to find your location on most maps (especially topographic maps).
  2. Though there are 360 degrees in a circle, each degree is divided into 60 minutes, and each minute is divided into 60 seconds.
  3. A degree is 70 miles (113 km), a minute 1.2 miles (1.9 km), and a second is .02 miles, or 106 feet (32 m). 
  4. Use a negative sign before figures in the Southern Hemisphere and in the Western Hemisphere.