How this instrument works
GPS coordinates can be written in two common formats that mean exactly the same location: decimal degrees, like 40.6892, and degrees-minutes-seconds (DMS), like 40°41′21.120″. Every modern smartphone and most mapping software default to decimal degrees internally because they're easier to store and compute with, but nautical charts, aviation approach plates, land survey documents, and plenty of older or specialist GPS receivers still display and expect coordinates in DMS. Converting between them is routine work for anyone plotting a position across formats.
The conversion splits a decimal-degree coordinate into three parts. The whole number of degrees is taken first, and it alone carries the sign — negative for southern latitudes or western longitudes, positive for northern latitudes or eastern longitudes, matching the universal convention that south and west are negative in decimal notation. The fractional degree remaining is multiplied by 60 to get arcminutes, keeping only the whole number; whatever is left after that is multiplied by 60 again to get arcseconds, reported to three decimal places. Minutes and seconds are always positive — only the degrees field, or an appended N/S/E/W letter, tells you the hemisphere.
Precision matters more here than in most angle conversions, because one arcsecond of latitude corresponds to roughly 30.9 metres on the ground (a bit less for longitude away from the equator, since longitude lines converge toward the poles). A DMS coordinate rounded to the nearest whole arcsecond, as many paper charts and older GPS units do, pins a location to within about 30 metres — plenty for navigation, but coarser than the sub-metre precision a raw decimal-degree GPS fix can offer.
- Enter a single latitude or longitude value in decimal degrees into the Decimal degrees field — it starts at −73.985 as an example.
- Read the Degrees field for the whole-number coordinate, which carries the sign (negative for south or west).
- Read the Minutes field for the arcminutes remainder, always shown as a positive whole number.
- Read the Seconds field for the final remainder in arcseconds, shown to three decimal places.
- Combine all three fields as one coordinate, written 73° 59′ 6.000″ W, appending the correct hemisphere letter yourself since the calculator only outputs the signed number.
Worked example — a longitude of 73.985° W in Manhattan
A location-sharing app gives a longitude reading of −73.985 decimal degrees, close to Times Square in Manhattan, whose longitude is commonly published as about 73.9855° W — within roughly 50 metres of this value. Entering −73.985 into Decimal degrees gives the Degrees field its whole-number part with the original sign: floor(73.985) = 73, made negative, so Degrees reads −73.
The fractional part, 0.985 of a degree, is multiplied by 60 for arcminutes: 0.985 × 60 = 59.1, and Minutes keeps the whole number, 59. What remains, 0.1 of an arcminute, is multiplied by 60 again for arcseconds: 0.1 × 60 = 6.000. Read together, the three fields give −73° 59′ 6.000″, written on a chart as 73° 59′ 6.000″ W once the negative sign is translated into the westward direction letter.
Questions
Does the calculator tell me whether a coordinate is north/south or east/west?
No — it only converts the signed decimal-degree number you enter into a signed degrees-minutes-seconds triple. By universal GPS convention, a negative value is south (for a latitude) or west (for a longitude), and a positive value is north or east, so you supply that context yourself: enter a latitude and a longitude separately, once each, and label the DMS results N/S or E/W based on the sign you started with.
Why is the sign only ever on the Degrees field?
Because that's standard DMS convention: direction is expressed once, on the whole-degree part (or, equivalently, by an appended N/S/E/W letter with an unsigned degree), and minutes and seconds are always plain positive magnitudes. Writing a coordinate as 73° −59′ 6″ W, with a negative on the minutes, would be non-standard and confusing to read against a chart.
How much real-world distance does one arcsecond of latitude cover?
Roughly 30.9 metres (about 101 feet) anywhere on Earth, since a degree of latitude is close to constant at around 111 kilometres regardless of where you are. A degree of longitude varies instead, shrinking from about 111 km at the equator toward zero at the poles as the lines of longitude converge, so one arcsecond of longitude covers less ground the further you are from the equator.
Why do some GPS devices still show coordinates in DMS by default?
Largely for continuity with paper charts, survey monuments, and older aviation and maritime documentation, all of which were established in degrees-minutes-seconds long before consumer GPS existed. Pilots cross-referencing an approach plate, or sailors plotting a position against a nautical chart, need their receiver's display to match the format already printed on the chart in front of them.
What's the difference between DMS and the DDM (degrees-decimal-minutes) format some apps use?
DDM keeps the whole degrees and whole minutes but expresses the leftover as a decimal fraction of a minute instead of splitting it further into whole minutes plus seconds — for example, 73° 59.100′ instead of 73° 59′ 6.000″. Both represent the identical position; DDM is common on marine chartplotters because it matches how many GPS receivers historically reported a fix, while DMS is more traditional on printed charts and survey documents.
Can I convert two values at once to get a full latitude/longitude pair?
Enter the latitude's decimal-degree value once to get its DMS triple, then enter the longitude's value separately for its own triple, since the calculator converts a single decimal-degree number at a time. Combine the two results yourself into the familiar pair, such as 40° 45′ 29″ N, 73° 59′ 8″ W (Times Square's published coordinates), for a complete location.