Coordinate Format Converter
Free Coordinate format Converter for geography & distance units. Enter a value to see equivalent measurements across systems.
Coordinate Format Converter
Calculator
Adjust values & calculateEnter your values below. Every result is computed in your browser โ no data is sent to any server.
Formula: DD = Degrees + Minutes/60 + Seconds/3600
Worked example โ 40.6892, -74.0444
Formula
DD = Degrees + Minutes/60 + Seconds/3600
Geographic coordinates use a sexagesimal (base-60) system inherited from Babylonian mathematics. One degree contains 60 arc-minutes, and one arc-minute contains 60 arc-seconds, for a total of 3600 arc-seconds per degree. Converting to decimal degrees simply expresses this relationship as a single decimal number, making computation straightforward.
Worked Examples
Example 1: Statue of Liberty Coordinates
Problem:Convert 40d 41m 21s N, 74d 2m 40s W to decimal degrees.
Solution:Latitude: 40 + 41/60 + 21/3600 = 40 + 0.6833 + 0.00583 = 40.6892 N Longitude: -(74 + 2/60 + 40/3600) = -(74 + 0.0333 + 0.0111) = -74.0444 W
Result:40.6892, -74.0444
Example 2: Tokyo Tower
Problem:Convert 35.6586 N, 139.7454 E to DMS format.
Solution:Latitude: 35 + 0.6586 * 60 = 35d 39.516m = 35d 39m 30.96s N Longitude: 139 + 0.7454 * 60 = 139d 44.724m = 139d 44m 43.44s E
Result:35d 39m 30.96s N, 139d 44m 43.44s E
Frequently Asked Questions
What are the main coordinate formats used in mapping?
The three main geographic coordinate formats are Decimal Degrees (DD), Degrees Minutes Seconds (DMS), and Degrees Decimal Minutes (DDM). Decimal Degrees like 40.7128, -74.006 are the standard for GPS devices and digital mapping APIs including Google Maps. DMS format like 40d 42m 46s N uses the traditional sexagesimal system from ancient Babylon. DDM like 40d 42.768m N is commonly used in marine navigation and older GPS units. All three represent the same location, just expressed differently.
How do I convert DMS (Degrees Minutes Seconds) to Decimal Degrees?
To convert DMS to Decimal Degrees, use the formula: DD = Degrees + Minutes/60 + Seconds/3600. For example, 40 degrees 42 minutes 46.08 seconds North becomes 40 + 42/60 + 46.08/3600 = 40.7128 degrees. For southern latitudes or western longitudes, make the result negative. This works because there are 60 minutes in a degree and 60 seconds in a minute, so 3600 seconds in a degree. The conversion is purely mathematical with no approximation involved.
Why do different mapping systems use different coordinate formats?
Different formats evolved for different use cases. DMS was the original format from celestial navigation, easy to read on graduated instruments like sextants. DDM became standard in marine GPS units because minutes of latitude directly correspond to nautical miles, making distance estimation intuitive. Decimal Degrees became dominant with digital computing because they simplify mathematical calculations, database storage, and API interfaces. UTM coordinates are preferred for military and land surveying because they provide flat-plane measurements in meters.
What is the precision of each coordinate format?
In Decimal Degrees, 4 decimal places give about 11 meter precision, 5 decimal places about 1.1 meters, and 6 decimal places about 0.11 meters. In DMS format, whole seconds give about 31 meter precision, tenths of seconds about 3.1 meters, and hundredths about 0.31 meters. In DDM, 3 decimal places of minutes give about 1.9 meters, and 4 decimal places about 0.19 meters. For most consumer navigation, 5-6 decimal places in DD or hundredths of seconds in DMS provide sufficient accuracy.
How do hemisphere letters map onto positive and negative signs?
Decimal degrees replace the hemisphere letter with a sign: north and east are positive, south and west negative, so 74 degrees west becomes minus 74, and 74 degrees 0 minutes 21.6 seconds west becomes minus 74.006. In degrees-minutes-seconds the sign belongs to the degrees field only and the minutes and seconds are always entered as positive magnitudes. Writing a western longitude as minus 74 degrees, minus 2 minutes double-counts the direction and lands you in the wrong hemisphere. Convert the absolute value first, then apply the sign to the finished decimal figure.
Should the pair be written latitude first or longitude first?
It depends on the consumer, and the mismatch is one of the most common mapping bugs. Consumer mapping services, GPS receivers and most web APIs expect latitude then longitude. GeoJSON, well-known text and many spatial databases follow the mathematical x then y ordering, which means longitude then latitude. A swapped pair is often silently valid, since 40.71 and 74.01 are both legal in either slot, so the point simply appears somewhere unexpected. Latitude beyond plus or minus 90 degrees is the one reliable clue that the pair is reversed.
Why do navigators care that one arc-minute equals a nautical mile?
The nautical mile was defined as one minute of arc along a meridian and is now fixed at exactly 1,852 metres, which is why a chart's latitude scale doubles as a distance ruler. That equivalence holds for latitude everywhere, but not for longitude: meridians converge towards the poles, so a minute of longitude spans 1,852 metres times the cosine of the latitude. At 60 degrees north the cosine is 0.5 and a minute of longitude covers only about half a nautical mile. This is exactly why marine receivers display degrees and decimal minutes.
Does converting the format also change the datum?
No, and assuming it does causes real positional errors. Format conversion is pure arithmetic between notations for the same angle, while the datum defines the reference ellipsoid and origin those angles are measured against. The same physical point carries different coordinates on WGS84, NAD27 or a national grid, with discrepancies ranging from a few metres to well over a hundred depending on the region. Before converting an old map coordinate, find out which datum it was recorded on and transform the datum separately.
How is the UTM zone number derived from longitude?
Universal Transverse Mercator divides the globe into 60 zones, each six degrees of longitude wide, numbered eastwards from the antimeridian. The zone is therefore the whole part of (longitude plus 180) divided by 6, plus one, so a longitude of minus 74 degrees falls in zone 18. The letter shown here simply flags the northern or southern hemisphere, which selects the false northing applied to the easting and northing pair. It is not the same as an MGRS latitude band letter, which encodes eight-degree bands of latitude instead.
Why can converting to DMS produce 60 seconds or 60 minutes?
Because the seconds field is rounded after being extracted. A decimal fraction that leaves 59.9997 seconds displays as 60.00 once rounded to two places, which is not a valid reading. The fix is to carry: 60 seconds becomes zero seconds and one extra minute, and 60 minutes becomes zero minutes and one extra degree. Round the decimal degrees to your target precision before splitting them, rather than rounding each field independently, and the carry problem disappears along with the odd off-by-one-second mismatch between tools.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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