Decimal Degrees to DMS Converter Formula

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

Use the Decimal Degrees to DMS Converter

Formulas Used

Degrees

degrees = deg_part

Minutes

minutes = min_part

Seconds

seconds = sec_part

Radians

radians = value * pi / 180

Variables

VariableDescriptionDefault
valueDecimal Degrees(°)40.7128
deg_partDerived value= floor(abs(value))calculated
min_totalDerived value= (abs(value) - floor(abs(value))) * 60calculated
min_partDerived value= floor((abs(value) - floor(abs(value))) * 60)calculated
sec_partDerived value= ((abs(value) - floor(abs(value))) * 60 - floor((abs(value) - floor(abs(value))) * 60)) * 60calculated

How It Works

Decimal Degrees to DMS

Conversion Steps

1. Degrees = floor of the decimal degree value 2. Minutes = floor of (fractional part x 60) 3. Seconds = remaining fraction x 60

Example

40.7128° = 40° 42' 46.08"

DMS format is commonly used on maps, in navigation, and for GPS coordinates.

Worked Example

Convert 40.7128° (New York City latitude) to DMS.

value = 40.7128
  1. 01Degrees = 40
  2. 02Fractional = 0.7128 x 60 = 42.768 minutes
  3. 03Minutes = 42
  4. 04Seconds = 0.768 x 60 = 46.08 seconds
  5. 05Result: 40° 42' 46.08"

Frequently Asked Questions

What is DMS format?

DMS stands for Degrees, Minutes, Seconds. One degree = 60 minutes, one minute = 60 seconds. It is the traditional way to express angular measurements and geographic coordinates.

Which format does GPS use?

GPS devices can use either decimal degrees or DMS. Decimal degrees (e.g., 40.7128) are simpler for calculations. DMS (40° 42' 46") is traditional for navigation. Most devices let you choose.

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