Coordinates Converter
Latitude and longitude can describe the same point in more than one notation. Decimal degrees are compact and easy for software: 40.748817, -73.985428. Degrees minutes seconds are more traditional and readable in field notes: 40° 44′ 55.74″ N, 73° 59′ 7.54″ W. This calculator converts between those formats for a latitude-longitude pair.
This is a geographic coordinate tool, not a generic angle converter. It uses the degree-minute-second subdivision of a degree, but it also keeps latitude and longitude roles separate. Latitude is the north-south angular coordinate, limited to -90 through 90 degrees. Longitude is the east-west angular coordinate, limited to -180 through 180 degrees. The signs and hemisphere letters are not decoration; they determine which side of the equator or prime meridian the location is on.
For a single angle, use the degrees minutes seconds calculator, degrees to minutes converter, or degrees to seconds converter. For projected UTM meter coordinates, use the lat long to UTM converter. For non-coordinate angle units such as radians and turns, use the angle converter.
What the calculation does
The converter starts in Decimal degrees mode. It reads a latitude and longitude, verifies both are finite, enforces latitude from -90 to 90, and enforces longitude from -180 to 180. Each value is converted to DMS separately. The sign chooses the direction: positive latitude becomes N, negative latitude becomes S, positive longitude becomes E, and negative longitude becomes W. The absolute value is split into whole degrees, whole minutes, and seconds. Seconds are displayed with two decimal places.
The decimal-to-DMS calculation splits entered value before rounding the display. If a coordinate lands extremely close to the next minute boundary, the two-decimal seconds display can round to 60.00″ without carrying into the minute field. The numeric location is still based on the entered decimal degrees, but formal DMS notation should carry that boundary value.
When the converter is switched to DMS mode, it reads positive numeric pieces for latitude and longitude plus direction menus. Latitude degrees must be 0 through 90, longitude degrees must be 0 through 180, and minutes and seconds must be at least 0 and less than 60. The direction controls the sign: S and W are negative, while N and E are positive. The primary result displays the signed latitude and longitude to six decimal places.
The calculation does not know which datum the coordinate came from. It does not transform WGS84 to NAD83 or any other reference frame. It simply rewrites the same latitude and longitude angle pair. If your field data, GPS receiver, GIS layer, or legal description uses a specific datum, keep that metadata with the coordinate.
Formula
Decimal degrees to DMS separates the absolute value:
DMS to decimal degrees applies the hemisphere sign:
A worked conversion
The default decimal coordinates are 40.748817° latitude and -73.985428° longitude. For latitude, the calculator keeps 40 whole degrees. The remaining 0.748817 degree is multiplied by 60, giving 44.92902 minutes. That leaves 44 whole minutes. The remaining 0.92902 minute is multiplied by 60, giving 55.7412 seconds, displayed as 55.74″. Because the latitude is positive, the direction is N.
For longitude, the calculator uses the absolute value 73.985428. It keeps 73 whole degrees. The remaining 0.985428 degree times 60 gives 59.12568 minutes, so the whole minutes are 59. The remaining 0.12568 minute times 60 gives 7.5408 seconds, displayed as 7.54″. Because the original longitude is negative, the direction is W.
The primary result is therefore 40° 44′ 55.74″ N, 73° 59′ 7.54″ W. If you switch to DMS mode and use the default pieces, the reverse calculation returns 40.748817, -73.985428 after six-decimal formatting.
Reference table
| Decimal degrees | DMS notation | Meaning |
|---|---|---|
| 40.748817, -73.985428 | 40° 44′ 55.74″ N, 73° 59′ 7.54″ W | New York example point |
| -33.856784, 151.215297 | 33° 51′ 24.42″ S, 151° 12′ 55.07″ E | Sydney example point |
| 0, 0 | 0° 0′ 0.00″ N, 0° 0′ 0.00″ E | Equator and Greenwich |
| 51.5007, -0.1246 | 51° 30′ 2.52″ N, 0° 7′ 28.56″ W | London example point |
Coordinate systems and domains
GPS receivers commonly report WGS84 latitude and longitude in decimal degrees, but many maps, signs, and field notes use DMS. Surveying records may preserve DMS because bearings and plats were historically written that way. Navigation also uses latitude and longitude, sometimes in degrees and decimal minutes rather than full DMS. Astronomy uses similar angular subdivisions, but celestial coordinates follow different reference systems and conventions.
A format conversion does not create a projected coordinate. UTM, State Plane, and other projected systems convert the curved Earth to a grid measured in meters or feet. That step needs a zone, projection parameters, and a datum. This page deliberately avoids that so it can do one thing accurately: keep the same latitude and longitude while changing the notation.
Common pitfalls
- Swapping longitude and latitude when copying into a map search box.
- Mixing signs with direction letters, such as writing a negative longitude and also marking it W in a system that expects one convention.
- Treating DMS as decimal notation. A coordinate with 30 minutes is half a degree, not a .30 decimal suffix.
- Forgetting that seconds and minutes must stay below 60.
- Assuming a coordinate becomes more accurate because it has more symbols. The original measurement precision still controls accuracy.
- Ignoring datum metadata when matching coordinates to GIS layers or survey documents.
Sources
- NIST, SP 330 section 4, Table 8 — exact angular identities
1′=(1/60)°and1″=(1/60)′, from which the DD↔DMS arithmetic is derived. - NOAA National Geodetic Survey, Datums — datum context for latitude and longitude; it is not cited as the arithmetic source.