Angular Unit Conversion - DD, DMS, Radians

It's important to know how to convert back and forth between various units of angular measurement.

Degrees, Minutes, Seconds to Decimal Degrees (DMS to DD):

If you put this in terms of a clock, where a degree equals one hour of time (and there are 360 hours in a complete cycle of a day), it becomes easier to understand how minutes and seconds work in relation to the degree. There are sixty minutes in an hour (or one degree), and also there are sixty seconds in a minute. Thus, 60 seconds times 60 minutes equals 3600 seconds in an hour (or in one degree of angular measurement). Now just add these together.

Note: When working with locations west of the prime meridian, longitude values may be represented with negative numbers (-84° in this case). The formula should use subtractions (-) instead of addition (+) (line 3), or the entire formula must be multiplied by -1 as a final step (line 4).  Note the "abs()" function which temporarily converts the negative value to a positive number so the addition signs can be used.  In short, be extra aware of your data and the formulas used to convert between these units.

Decimal Degrees to Degrees, Minutes, Seconds (DD to DMS):
This conversion is a bit more tricky because the minutes and seconds are combined and packed into the decimal.

For the DD value 30.443452º

• Anything to the left of the decimal is the full degree value
  D = 30º
• Multiply the decimal value by 60 to find the minutes. The value will be between zero and 59.999. The minutes value will be what is in front of the decimal again.
  M = 26' because 0.443452 * 60 = 26.60712
• Multiply the minutes decimal value by 60 to find the decimal seconds value. Again, it will be between zero and 59.999, as there are 60 seconds in a minute. Decimal seconds are acceptable.
• S = 36.4272" = 60 * 0.60712

To pull this off in a spreadsheet, create an intermediate "Calculate Minutes" field, which is referenced to build the Minutes and Seconds fields. Negative numbers require an additional step (see below).



Negative numbers will have a leading third character to deal with in front of the decimal. First, sort the dataset so these can be dealt with as a group. Change Degrees formula from =left(*Cell*, 2) to =left(*Cell*, 3) for all negative values. That's it.


DD to Radians to DD:

Radians are another unit of angular measurement, used most often in all but basic applications of geometry. So what is a radian?  It's the arc distance between two points on a circle where an angle intersects, equal to the circle's radius (Wikipedia). It's the unit of measure used to calculate a number of Excel formulas, so it's important to understand what it means, and at the very least how to use it.






DD to radians:



Or radians to DD: