Coordinates Converter
Convert geographic coordinates between decimal degrees, DMS, DDM, and UTM formats. Supports both hemispheres.
Coordinates Converter
Calculator
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Formula: DD = D + M/60 + S/3600
Worked example โ 40 degrees 42 minutes 46.08 seconds N, 74 degrees 0 minutes 21.6 seconds W
Formula
DD = D + M/60 + S/3600
Coordinates are converted through decimal degrees as the base format. DMS is broken into degrees plus minutes divided by 60 plus seconds divided by 3600. UTM conversion uses the Transverse Mercator projection with zone calculations based on longitude bands.
Worked Examples
Example 1: New York City Conversion
Problem:Convert 40.7128 N, 74.006 W from decimal degrees to DMS and UTM.
Solution:DMS: 40 + 0.7128 x 60 = 42.768 min -> 42 min + 0.768 x 60 = 46.08 sec Latitude: 40 degrees 42 min 46.08 sec N Longitude: 74 degrees 0 min 21.6 sec W UTM Zone: 18N, Easting: ~583960 m, Northing: ~4507523 m
Result:40 degrees 42 minutes 46.08 seconds N, 74 degrees 0 minutes 21.6 seconds W
Example 2: Southern Hemisphere
Problem:Convert DMS coordinates 33 degrees 51 min 31.68 sec S, 151 degrees 12 min 33.48 sec E to decimal.
Solution:Lat DD = -(33 + 51/60 + 31.68/3600) = -33.8588 Lon DD = 151 + 12/60 + 33.48/3600 = 151.2093 This is Sydney, Australia.
Result:-33.8588, 151.2093
Frequently Asked Questions
What is the difference between DD, DMS, and DDM coordinate formats?
DD (Decimal Degrees) expresses coordinates as simple decimal numbers like 40.7128, -74.0060. DMS (Degrees Minutes Seconds) breaks each coordinate into degrees, minutes (1/60th of a degree), and seconds (1/60th of a minute), such as 40 degrees 42 minutes 46.08 seconds N. DDM (Degrees Decimal Minutes) is a hybrid that uses degrees and decimal minutes without seconds, like 40 degrees 42.768 minutes N. All three formats represent the same location; the choice depends on the application and convention.
How do I convert DMS coordinates to decimal degrees?
To convert DMS to decimal degrees, take the degrees value and add the minutes divided by 60, plus the seconds divided by 3600. The formula is DD = D + M/60 + S/3600. If the direction is South or West, make the result negative. For example, 40 degrees 42 minutes 46.08 seconds N becomes 40 + 42/60 + 46.08/3600 = 40.7128 degrees. West longitude 74 degrees 0 minutes 21.6 seconds becomes -74.006 degrees.
What is UTM and when should I use it?
UTM (Universal Transverse Mercator) is a map projection system that divides Earth into 60 zones, each 6 degrees of longitude wide. It gives coordinates in meters (easting and northing) relative to the zone origin, making it ideal for measuring distances and areas on flat maps. UTM is widely used in military mapping, topographic maps, land surveying, and GIS applications because meter-based coordinates are easier to work with for distance calculations than angular degrees.
Why are some coordinates negative?
In decimal degree notation, negative latitude values indicate positions south of the equator, and negative longitude values indicate positions west of the prime meridian (Greenwich). This convention eliminates the need for N/S/E/W direction letters. For example, New York at 40.7128 N, 74.006 W becomes 40.7128, -74.006 in decimal degrees. Sydney at 33.8688 S, 151.2093 E becomes -33.8688, 151.2093. The sign convention is universal in GPS devices and digital mapping.
What do easting and northing mean, and why does easting start near 500,000?
Easting is the distance in metres across the zone and northing the distance up it. Each zone's central meridian is assigned a false easting of exactly 500,000 metres so that everything west of it still gets a positive number instead of a negative one. Since a zone reaches three degrees either side of that meridian, roughly 334 kilometres at the equator, eastings in practice run from about 166,000 to 834,000 metres. An easting far outside that band is the quickest sign that the point has been assigned to the wrong zone.
Why is the UTM scale factor 0.9996 rather than 1?
Transverse Mercator is a cylindrical projection, and if the cylinder touched the central meridian exactly, distortion would be zero there and would grow steadily to its maximum at the zone edges. Shrinking the projection by a factor of 0.9996 makes the cylinder secant instead, so it cuts the ellipsoid along two lines either side of the meridian. Scale is then 0.04 percent short at the centre, about 40 centimetres per kilometre, correct along the two secant lines, and slightly long at the edges, which roughly halves the worst-case distortion across the zone.
Why does a southern-hemisphere northing start at 10,000,000?
Northings are measured from the equator, so a point south of it would otherwise carry a negative value. UTM avoids that by giving southern-hemisphere zones a false northing of 10,000,000 metres, a value chosen to exceed any northing that actually occurs inside UTM's 80 degrees south limit, roughly 8,880 kilometres from the equator, so the equator reads 10,000,000 and values decrease going south. The consequence is that a northing alone is ambiguous: 4,500,000 could be northern or southern. The hemisphere designator or the MGRS band letter must always travel with the pair.
What is the difference between grid north and true north in UTM?
True north follows the meridian through your point, while grid north follows the vertical lines of the UTM grid, which are parallel to the zone's central meridian. The angle between them is the meridian convergence, and it grows with both distance from the central meridian and latitude, reaching a couple of degrees near a zone edge at high latitude. A bearing plotted from grid eastings and northings is therefore a grid bearing, and it must be corrected by the convergence before being compared with a geodetic azimuth or a compass bearing.
Which places break the simple six-degree zone rule?
Two well-known exceptions. Zone 32 is widened over southwestern Norway so the mainland is not split, and the zones around Svalbard are rearranged, leaving 31, 33, 35 and 37 covering twelve degrees each. There is also a hard latitude limit: UTM is defined only between 80 degrees south and 84 degrees north, because Transverse Mercator distortion becomes unusable near the poles. Polar regions use the Universal Polar Stereographic grid instead, so a polar position simply has no valid UTM easting and northing.
Which ellipsoid do these UTM figures assume?
The WGS84 ellipsoid, with a semi-major axis of 6,378,137 metres and the corresponding first eccentricity, is built into the projection formulas used here. That matters because the projection converts angles on a specific reference surface into metres on a grid. Feeding in latitude and longitude recorded on an older datum such as NAD27 or a national ellipsoid produces a grid position that can be tens or hundreds of metres from the truth. Transform the coordinates onto WGS84 first, then project them.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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