Decimal Degrees to DMS Calculator

Convert between decimal degrees (DD) and degrees-minutes-seconds (DMS) format with step-by-step solutions.

Select Conversion Direction

Result

DMS Format
--
degrees-minutes-seconds
Decimal degrees --
Degrees --
Minutes --
Seconds --
Radians --

Step-by-Step Solution

DD = D + M/60 + S/3600

Understanding Decimal Degrees and DMS

Angular measurements can be expressed in two common formats: decimal degrees (DD) and degrees-minutes-seconds (DMS). Both formats measure the same angles but represent them differently. Understanding how to convert between these formats is essential for navigation, surveying, astronomy, and geographic information systems (GIS).

Decimal Degrees (DD)

In decimal degrees, the angle is expressed as a single number with a decimal fraction. For example, 45.7625 degrees means 45 full degrees plus 0.7625 of a degree. This format is commonly used in digital mapping systems, GPS devices, and computer applications because it is easy to perform mathematical operations with decimal numbers.

Degrees-Minutes-Seconds (DMS)

In the DMS format, a degree is subdivided into 60 minutes, and each minute is subdivided into 60 seconds. This is analogous to how time is measured in hours, minutes, and seconds. For example, 45 degrees 45 minutes 45 seconds is written as 45° 45' 45".

Conversion Formulas

DD to DMS

Extract degrees, then convert the fractional part to minutes and seconds.

D = floor(DD), M = floor((DD-D)*60), S = remainder*60

DMS to DD

Combine degrees, minutes, and seconds into a single decimal value.

DD = D + M/60 + S/3600

DD to Radians

Convert decimal degrees to radians for trigonometric functions.

rad = DD x (pi / 180)

Key Relationships

Minutes and seconds subdivide degrees like time subdivides hours.

1 deg = 60' = 3600"

Step-by-Step: Converting DD to DMS

To convert a decimal degree value to DMS format, follow these steps:

  1. Extract the whole degrees: Take the integer part of the decimal degree. For 45.7625, this is 45.
  2. Calculate the minutes: Multiply the remaining decimal fraction by 60. For 0.7625 x 60 = 45.75, the minutes are 45.
  3. Calculate the seconds: Take the decimal fraction of the minutes and multiply by 60. For 0.75 x 60 = 45, the seconds are 45.
  4. Combine: The result is 45° 45' 45".

Step-by-Step: Converting DMS to DD

To convert DMS to decimal degrees:

  1. Start with the degrees value as the whole number part.
  2. Divide the minutes by 60 and add to the degrees.
  3. Divide the seconds by 3600 and add to the result.
  4. Apply a negative sign if the direction is South or West.

GPS Coordinates

GPS devices and mapping applications commonly use both DD and DMS formats for latitude and longitude. Latitude values range from -90 to 90 degrees (South to North), and longitude values range from -180 to 180 degrees (West to East). Understanding the conversion between these formats is crucial when:

  • Entering coordinates into different mapping or navigation software.
  • Reading coordinates from topographic maps (which often use DMS).
  • Performing calculations with geographic coordinates in spreadsheets or code.
  • Converting between GPS device outputs and printed map references.

Practical Examples

  • New York City: 40.7128° N = 40° 42' 46.08" N
  • London: 51.5074° N = 51° 30' 26.64" N
  • Tokyo: 35.6762° N = 35° 40' 34.32" N
  • Sydney: -33.8688° (33.8688° S) = 33° 52' 7.68" S

Precision Considerations

The precision of seconds in DMS notation directly affects geographic accuracy. One second of latitude corresponds to approximately 30.87 meters (101.3 feet) on the Earth's surface. One second of longitude varies from about 30.87 meters at the equator to 0 meters at the poles. For most surveying and navigation purposes, seconds expressed to two decimal places provide sub-meter accuracy.