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Last updated on August 19th, 2023 at 05:41 pm

In navigation, the coordinates are expressed in different ways: Degree, Minute and Seconds ( DMS ) and Decimal Degrees ( DD ). The Degree, Minutes and Seconds ( DMS ) are common format for expressing the coordinates, but the more convenient one to work with is the Decimal Degrees ( DD ). Lets convert a Sample and with the formula. The sample value that we will be using is 41°24’12.2″N 2°10’26.5″E to illustrate the conversion process.

Understanding the Conversion

The basic Formula for DMS to DD conversion is, 

1° = 60' = 3600"
1' = 1/60° = 0.01666667°
1" = 1/3600° = 2.77778e-4° = 0.000277778°

When the angle with d integer degrees, m minutes, and s seconds, the decimal degrees (dd) can be calculated. 

Example: 41°24'12.2"N 2°10'26.5"E
For latitude:
d = 41°
m = 24'
s = 12.2"

Using the formula: dd = d + m/60 + s/3600
dd_latitude = 41 + 24/60 + 12.2/3600
dd_latitude = 41 + 0.4 + 0.0033889
dd_latitude = 41.4033889°

For longitude:
d = 2°
m = 10'
s = 26.5"

Using the formula: dd = d + m/60 + s/3600
dd_longitude = 2 + 10/60 + 26.5/3600
dd_longitude = 2 + 0.1666667 + 0.0073611
dd_longitude = 2.1740278°

Therefore, the coordinates 41°24’12.2″N 2°10’26.5″E in decimal degrees are approximately 41.4033889, 2.1740278.

Conclusion

Converting Degress, Minute and Seconds to Decimal Degree simplifies the coordinate calculations and improves the usability in various applications. With the formula mentioned above, the conversion can be made effortlessly without the need of any online calculators.