Coordinate Converter

Convert GPS coordinates between decimal and DMS formats

Famous Locations

Eiffel Tower48.8584, 2.2945
Statue of Liberty40.6892, -74.0445
Big Ben51.5007, -0.1246
Sydney Opera House-33.8568, 151.2153

What is a Coordinate Converter?

A coordinate converter is a tool that translates geographic coordinates between different formatting systems. The two most widely used formats are decimal degrees (DD) and degrees-minutes-seconds (DMS). Every GPS device, mapping application, and geographic information system relies on one of these formats to pinpoint locations on Earth's surface. Converting between them is a frequent necessity for anyone working with maps, navigation, or geographic data.

In the decimal degrees format, latitude and longitude are expressed as simple decimal numbers. Latitude ranges from -90 (South Pole) to +90 (North Pole), and longitude ranges from -180 (Antimeridian West) to +180 (Antimeridian East). For example, New York City's coordinates are approximately 40.7128, -74.0060. This compact format is favored by modern software, databases, and GPS receivers because it is easy to store, sort, and compute with.

The DMS format uses three components for each coordinate: degrees, minutes, and seconds. One degree equals 60 minutes, and one minute equals 60 seconds. The same New York City coordinates in DMS are 40° 42' 46" N, 74° 0' 22" W. This format is traditional in cartography, navigation, and surveying, and it appears on many official maps, legal land descriptions, and geographic references. Some older systems also use degrees and decimal minutes (DDM), which this calculator also supports.

The Coordinate Conversion Formulas

Converting between decimal degrees and DMS involves straightforward arithmetic. The key insight is that one degree contains 60 minutes and one minute contains 60 seconds, creating a base-60 (sexagesimal) subdivision system inherited from ancient Babylonian mathematics.

Decimal to DMS Conversion

Degrees = floor(|decimal|), Minutes = floor((|decimal| - Degrees) × 60), Seconds = ((|decimal| - Degrees - Minutes/60) × 3600)

Where:

  • Degrees= The whole number of degrees (0-90 for latitude, 0-180 for longitude)
  • Minutes= The whole number of minutes (0-59)
  • Seconds= The fractional seconds with decimal precision
  • Direction= N/S for latitude, E/W for longitude based on sign

DMS to Decimal Degrees Formula

Reversing the conversion from DMS to decimal degrees is equally straightforward. You add the degrees to the fractional minutes divided by 60, plus the seconds divided by 3600. If the direction is South or West, the final result is negated.

DMS to Decimal Formula

Decimal = Degrees + Minutes/60 + Seconds/3600

Where:

  • Degrees= The whole degree component of the DMS coordinate
  • Minutes= The minutes component (0-59)
  • Seconds= The seconds component (0-59.999...)
  • Direction= N or E yields positive; S or W yields negative

How to Use This Calculator

The calculator supports bidirectional conversion between decimal degrees and DMS:

  1. Select conversion mode: Choose either "Decimal to DMS" or "DMS to Decimal" using the toggle buttons at the top.
  2. Enter coordinates: For Decimal to DMS, enter the latitude (-90 to 90) and longitude (-180 to 180) as decimal numbers. For DMS to Decimal, enter the degrees, minutes, seconds, and direction (N/S for latitude, E/W for longitude) in the respective fields.
  3. Read the result: The converted coordinates appear instantly in the result panel. For Decimal to DMS, you see both the DMS format and the degrees-decimal minutes format. For DMS to Decimal, you see the decimal degree representation.
  4. Explore famous locations: The reference panel below the calculator shows coordinates for iconic landmarks to help you verify the conversion is working correctly.

Real-World Applications

Coordinate conversion is essential in GPS navigation. Handheld GPS receivers and smartphone mapping apps typically display coordinates in decimal degrees, but compass bearings and nautical charts often use DMS. Hikers, geocachers, and field researchers frequently need to convert between formats when transferring coordinates between devices or referencing published geographic data.

Geographic Information Systems (GIS) professionals routinely convert coordinate formats when integrating datasets from different sources. A cadastral survey might record property boundaries in DMS, while the GIS database stores locations in decimal degrees. Automated coordinate conversion ensures data consistency across heterogeneous spatial datasets.

Aviation and maritime navigation rely heavily on DMS coordinates. Flight plans, vessel tracking systems, and search-and-rescue operations reference positions in degrees, minutes, and seconds. Pilots and mariners must be able to convert between formats when cross-referencing coordinates from different sources such as flight management systems, charts, and communication with air traffic control or port authorities.

Worked Examples

Converting New York City to DMS

Problem:

Convert New York City's coordinates (40.7128° N, -74.0060° W) to DMS format.

Solution Steps:

  1. 1Latitude degrees: floor(40.7128) = 40°
  2. 2Latitude minutes: floor((40.7128 - 40) × 60) = floor(42.768) = 42'
  3. 3Latitude seconds: (40.7128 - 40 - 42/60) × 3600 = 46.08" ≈ 46"
  4. 4Direction: positive latitude = N, negative longitude = W
  5. 5Result: 40° 42' 46" N, 74° 0' 22" W

Result:

40.7128° N, -74.0060° W converts to 40° 42' 46" N, 74° 0' 22" W

Converting DMS to Decimal

Problem:

Convert the Eiffel Tower's DMS coordinates (48° 51' 29.6" N, 2° 17' 40.2" E) to decimal degrees.

Solution Steps:

  1. 1Latitude decimal: 48 + 51/60 + 29.6/3600 = 48 + 0.85 + 0.00822 = 48.8582
  2. 2Longitude decimal: 2 + 17/60 + 40.2/3600 = 2 + 0.28333 + 0.01117 = 2.2945
  3. 3Direction check: N and E are positive, so no negation needed

Result:

48° 51' 29.6" N, 2° 17' 40.2" E converts to 48.8582° N, 2.2945° E

Converting Southern Hemisphere Coordinates

Problem:

Convert the Sydney Opera House coordinates (-33.8568°, 151.2153°) to DMS format.

Solution Steps:

  1. 1Latitude degrees: floor(33.8568) = 33°
  2. 2Latitude minutes: floor((33.8568 - 33) × 60) = floor(51.408) = 51'
  3. 3Latitude seconds: (33.8568 - 33 - 51/60) × 3600 = 24.48" ≈ 24"
  4. 4Direction: negative latitude = S, positive longitude = E
  5. 5Result: 33° 51' 24" S, 151° 12' 55" E

Result:

-33.8568°, 151.2153° converts to 33° 51' 24" S, 151° 12' 55" E

Tips & Best Practices

  • Use decimal degrees for entering coordinates into databases, APIs, and mapping software.
  • Use DMS when referencing coordinates from maps, nautical charts, or land surveys.
  • Remember: N and E are positive, S and W are negative in decimal degree format.
  • One second of latitude equals approximately 30.87 meters, useful for estimating precision.
  • Always verify latitude is between -90 and 90 and longitude between -180 and 180.
  • When copying coordinates from Google Maps, right-click and select coordinates to get decimal degrees.

Frequently Asked Questions

Decimal degrees express coordinates as a single number with a decimal fraction, such as 40.7128°. DMS breaks the coordinate into three components: degrees, minutes, and seconds, such as 40° 42' 46". Decimal degrees are preferred in software and databases, while DMS is traditional in cartography and navigation. Both formats represent the same geographic location.
Latitude measures angular distance north or south of the Equator. The North Pole is at +90° and the South Pole is at -90°, spanning the full 180 degrees from pole to pole. Latitude cannot exceed these bounds because the Equator serves as the reference plane, and angles measured beyond the poles have no meaningful geographic definition.
The direction letter indicates which hemisphere the coordinate falls in. N (North) and S (South) apply to latitude, indicating positions north or south of the Equator. E (East) and W (West) apply to longitude, indicating positions east or west of the Prime Meridian in Greenwich, England. In decimal format, north and east are positive while south and west are negative.
DMS precision depends on the smallest unit used. One second of latitude equals approximately 30.87 meters (101.3 feet), so coordinates given to the nearest second are accurate to about 30 meters. For greater precision, fractional seconds are used. Modern GPS receivers typically provide coordinates accurate to within a few meters, which requires several decimal places in seconds.
Most modern GPS receivers and smartphone mapping applications use decimal degrees as the default display format because it is simpler to read, store, and transmit. However, many devices allow you to switch to DMS display in settings. Professional surveying equipment and marine navigation systems frequently default to DMS format.

Sources & References

Last updated: 2026-06-06

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Editorial Note

MyCalcBuddy Editorial Team

This page is maintained as an educational calculator reference.

Source

Formula Source: NIST Guide to SI Units

by National Institute of Standards

UpdatedLast reviewed: May 2026
CheckedFormula checks are based on standard references and internal QA review.