DMS to Decimal Degrees Converter Formula

Understand the math behind the dms to decimal degrees converter. Each variable explained with a worked example.

Use the DMS to Decimal Degrees Converter

Formulas Used

Decimal Degrees

decimal = degrees + minutes / 60 + seconds / 3600

Radians

radians = (degrees + minutes / 60 + seconds / 3600) * pi / 180

Variables

VariableDescriptionDefault
degreesDegrees(°)40
minutesMinutes(')42
secondsSeconds(")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
  1. 01Decimal = 40 + 42/60 + 46.08/3600
  2. 02Decimal = 40 + 0.7 + 0.0128
  3. 03Decimal = 40.7128°

Ready to run the numbers?

Open DMS to Decimal Degrees Converter