Complete Guide: Degrees Minutes Seconds to Decimal Degrees
Welcome to the definitive dms to decimal degrees converter and degree to degree minute second converter. In geodesy, surveying, cartography, and GPS navigation, coordinates are expressed in two primary formats: degrees minutes seconds (DMS or dd mm ss) and decimal degrees (DD). When you need to change degrees minutes seconds to decimal degrees or convert degrees to decimal coordinates for software platforms like Google Maps, ArcGIS, Leaflet, or Python GeoPandas, this degrees minutes seconds to decimal degrees calculator delivers sub-millimeter precision.
Mathematical Formula: How to Convert Degrees Minutes Seconds to Decimal Degrees
The sexagesimal coordinate system breaks each circular degree into 60 arcminutes and each minute into 60 arcseconds. To convert deg min sec to decimal degrees or convert degrees and minutes to decimal degrees, use the standard formula:
When performing degrees minutes seconds to decimal degrees conversion, hemisphere direction determines the algebraic sign:
- North (N): Positive (+)
- South (S): Negative (-) — multiply the absolute result by -1
- East (E): Positive (+)
- West (W): Negative (-) — multiply the absolute result by -1
Step-by-Step Example: Convert Degrees Minutes Seconds to Decimal
Suppose you have the coordinate 37° 46' 36.3" N:
- Degrees =
37 - Minutes =
46 / 60 = 0.766667 - Seconds =
36.3 / 3600 = 0.010083 - Add them together:
37 + 0.766667 + 0.010083 = 37.776750° - Since direction is North, the sign is positive:
+37.776750.
Reverse Math: How to Convert Decimal Degree to DMS (Degree Minute Second)
Need to convert decimal degrees to degrees or know how to convert decimal degree to dms? The reverse procedure extracts whole units sequentially:
- Whole Degrees: The integer portion of the decimal number represents the degrees (
D = trunc(DD)). - Minutes: Subtract the whole degrees from the total, then multiply the remaining decimal by 60. The integer part is your minutes (
M = trunc((DD - D) * 60)). - Seconds: Take the fractional minute remainder and multiply it by 60 (
S = ((DD - D) * 60 - M) * 60). - Hemisphere: Assign N/S for latitude or E/W for longitude based on the sign (+ or -).
Coordinate Format Comparison: DMS, DMM, and DD
| Format Notation | Name | Typical Representation | Common Use Case |
|---|---|---|---|
| DD.dddddd° | Decimal Degrees | 40.446200, -79.982222 |
Web APIs, GPS databases, GIS datasets |
| D° M' S" [NSEW] | Degrees Minutes Seconds | 40° 26' 46.32" N, 79° 58' 56.00" W |
Topographic maps, marine navigation, astronomy |
| D° M.mmm' [NSEW] | Degrees Decimal Minutes (DMM) | 40° 26.772' N, 79° 58.933' W |
Aviation navigation (VOR/DME), nautical charts |
Why Convert Between DMS and Decimal Degrees?
Whether you are working in aviation flight planning, marine navigation, drone surveying, or building location-based mobile applications, converting between dms decimal degrees is an essential daily task. Our degrees minutes seconds to decimal degrees converter ensures you never suffer latitude/longitude inversion, missed sign flips, or rounding inaccuracies.
Frequently Asked Questions (FAQ)
DD = Degrees + (Minutes / 60) + (Seconds / 3600). If the latitude is South or longitude is West, multiply the decimal degrees by -1.
=A1 + (B1/60) + (C1/3600). To account for South or West directions, multiply by -1 if the direction column indicates 'S' or 'W'.