Decimal Degrees Converter (Degrees Minutes Seconds)
Convert latitude and longitude between degrees-minutes-seconds and decimal degrees, in either direction.
Results
Decimal degrees
40.712778
°
Degrees part
73
°
Minutes part
59
′
Seconds part
8.520
″
Side of the equator or meridian
South or West (−)
What this tool does
One degree is 60 minutes and one minute is 60 seconds, so 40° 42′ 46″ is 40 + 42÷60 + 46÷3600 = 40.7128°. Maps and GPS apps usually want decimal degrees, while charts and older records use the sexagesimal form. The sign belongs to the whole coordinate, not just the degrees: south and west are negative, and this tool takes the direction separately so that something like 0° 30′ S is not lost. For scale, five decimal places are about 1 metre on the ground and six about 11 centimetres.
Formula
decimal = D + M ÷ 60 + S ÷ 3600 · M = ⌊(decimal − D) × 60⌋ · S = (decimal − D − M ÷ 60) × 3600
Variables
| Symbol | Meaning | Unit |
|---|---|---|
dg | Degrees | ° |
mi | Minutes (′) | ′ |
sc | Seconds (″) | ″ |
sg | Side of the equator or meridian | — |
dd | Decimal degrees to convert (negative for S or W) | ° |
DEC | Decimal degrees | ° |
D | Degrees part | ° |
M | Minutes part | ′ |
S | Seconds part | ″ |
SG | Side of the equator or meridian | — |
Worked example
- Degrees40 °
- Minutes (′)42 ′
- Seconds (″)46 ″
- Side of the equator or meridian1
- Decimal degrees to convert (negative for S or W)-73.9857 °
- Decimal degrees40.712778 °
- Degrees part73 °
- Minutes part59 ′
- Seconds part8.520 ″
- Side of the equator or meridianSouth or West (−)
Limitations
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.