DMS to Decimal Degrees Converter Formula
Understand the math behind the dms to decimal degrees converter. Each variable explained with a worked example.
Formulas Used
Decimal Degrees
decimal = degrees + minutes / 60 + seconds / 3600Radians
radians = (degrees + minutes / 60 + seconds / 3600) * pi / 180Variables
| Variable | Description | Default |
|---|---|---|
degrees | Degrees(°) | 40 |
minutes | Minutes(') | 42 |
seconds | Seconds(") | 46.08 |
How It Works
DMS to Decimal Degrees
Decimal Degrees = Degrees + Minutes/60 + Seconds/3600
Example
40° 42' 46.08" = 40 + 42/60 + 46.08/3600 = 40 + 0.7 + 0.0128 = 40.7128°
Worked Example
Convert 40° 42' 46.08" to decimal degrees.
degrees = 40minutes = 42seconds = 46.08
- 01Decimal = 40 + 42/60 + 46.08/3600
- 02Decimal = 40 + 0.7 + 0.0128
- 03Decimal = 40.7128°
Frequently Asked Questions
How accurate are DMS coordinates?
One second of latitude equals about 30.9 meters. One second of longitude varies by latitude but is about 24 meters at 40° latitude. Two decimal places of seconds gives sub-meter accuracy.
How do I handle South or West coordinates?
South latitudes and West longitudes are negative in decimal degrees. Convert the DMS to positive decimal degrees first, then add a negative sign for S or W directions.
Ready to run the numbers?
Open DMS to Decimal Degrees Converter