Decimal Degrees to DMS Converter
Enter an angle in decimal degrees and get the equivalent in degrees, minutes, and seconds (DMS), the format used by GPS receivers, nautical charts, and classical surveying equipment. The calculator also shows degrees decimal minutes (DMM), total minutes, and total seconds, and can reverse-convert DMS back to decimal degrees. Switch modes with the Direction selector, and the full step-by-step arithmetic appears below the result.
Formula
Worked example
Converting 48.8583 degrees: degrees = trunc(48.8583) = 48. Remaining fraction = 0.8583; minutes = trunc(0.8583 x 60) = trunc(51.498) = 51. Remaining fraction = 0.498; seconds = 0.498 x 60 = 29.88. Result: 48 deg 51 min 29.88 sec.
What are degrees, minutes, and seconds?
A full circle is divided into 360 degrees. Each degree is further divided into 60 arc-minutes, and each arc-minute is divided into 60 arc-seconds. This sexagesimal system - base 60 - dates back to ancient Babylon and is still the standard for geographic coordinates in navigation, surveying, and astronomy. The notation 48 deg 51 min 29.88 sec means 48 degrees, 51 arc-minutes, and 29.88 arc-seconds. Decimal degrees express the same angle as a single number with a fractional part: 48.8583 degrees. Both formats describe exactly the same angle; they are just different ways of writing it.
How the DD to DMS conversion works
The conversion has three steps. First, strip the integer part of the decimal degree value to get whole degrees. Second, multiply the leftover fractional degrees by 60 and take the integer part of the result as the minutes. Third, multiply the remaining fractional minutes by 60 to get the seconds. For example, 48.8583 degrees: degrees = 48; fractional degrees = 0.8583; minutes = trunc(0.8583 x 60) = trunc(51.498) = 51; seconds = (51.498 - 51) x 60 = 0.498 x 60 = 29.88. Result: 48 deg 51 min 29.88 sec. Negative angles (south latitudes or west longitudes) are handled by applying the sign to the degrees component only - minutes and seconds are always non-negative.
Degrees decimal minutes (DMM): the third format
Many handheld GPS receivers and nautical chart plotters display coordinates in degrees decimal minutes (DDM or DMM) rather than full DMS. This format keeps the whole-number degrees and converts only the remaining fractional part into minutes with a decimal, skipping the separate seconds component. For example, 48.8583 degrees becomes 48 deg 51.498 min. This converter shows all three formats simultaneously so you can copy whichever one your device or software needs. Most modern web mapping APIs (Google Maps, OpenStreetMap, Leaflet) expect decimal degrees, so use that format when pasting into a URL or code.
Why precision matters: arc-seconds and GPS accuracy
One degree of latitude is approximately 111 kilometres. One arc-minute is therefore about 1.85 km, and one arc-second is about 31 metres. A fractional arc-second corresponds to sub-metre precision. This is why GPS coordinates are typically given with at least four or five decimal places in decimal degrees, or at least two or three decimal places in the seconds component of DMS. Rounding to the nearest whole arc-second gives roughly 31-metre accuracy - sufficient for city-level mapping but not for land surveying or precision agriculture. When entering coordinates manually, keep as many decimal places as your source provides.
Common applications: GPS, GIS, and astronomy
Geographic coordinates in DMS appear on topographic maps, nautical charts, aviation sectionals, and property boundary descriptions. GPS receivers historically displayed DMM or DMS because whole-number minutes and seconds are easier to read aloud on a radio or copy by hand than a string of decimal digits. Modern GIS software and web APIs almost always use decimal degrees internally, making the DD-to-DMS conversion a routine step when entering or exporting data. In astronomy, right ascension is traditionally expressed in hours-minutes-seconds (base 60 but scaled to 24 hours per full circle) and declination in DMS, so the same arithmetic applies with a different scale factor.
Coordinate notation formats compared
| Format | Example (latitude) | Common use |
|---|---|---|
| Decimal Degrees (DD) | 48.8583° | Web APIs, GIS, spreadsheets |
| Degrees Decimal Minutes (DMM) | 48° 51.498' | Handheld GPS, marine charts |
| Degrees Minutes Seconds (DMS) | 48° 51' 29.88" | Surveying, astronomy, topo maps |
| Signed DD (negative = S/W) | -33.8688° | GeoJSON, most programming SDKs |
The three main formats for expressing geographic coordinates, with a worked example using the Eiffel Tower (48.8583° N, 2.2945° E).
Frequently asked questions
How do I convert decimal degrees to degrees, minutes, seconds?
Take the integer part of the decimal degree value as whole degrees. Multiply the fractional remainder by 60 to get the total minutes, then take the integer part of that as whole minutes. Multiply the remaining fractional minutes by 60 to get the seconds. For example, 30.51 degrees: degrees = 30; minutes = trunc(0.51 x 60) = trunc(30.6) = 30; seconds = 0.6 x 60 = 36. Result: 30 deg 30 min 36 sec.
How do I convert DMS back to decimal degrees?
Divide the minutes by 60 and the seconds by 3600, then add them to the whole degrees. If the coordinate is south or west, apply a negative sign to the final result. For example, 48 deg 51 min 29.88 sec: 48 + 51/60 + 29.88/3600 = 48 + 0.85 + 0.0083 = 48.8583 degrees.
What do negative decimal degrees mean?
By convention, latitudes south of the equator and longitudes west of the prime meridian are negative. So -33.87 degrees latitude is 33.87 degrees S (Sydney, Australia), and -73.94 degrees longitude is 73.94 degrees W (New York). In DMS the sign is placed on the degrees component: -33 deg 52 min 12 sec.
What is the difference between DMS and DMM?
DMS (degrees-minutes-seconds) expresses the sub-degree portion as a whole number of minutes plus a seconds value. DMM (degrees decimal minutes) expresses the sub-degree portion as minutes with a decimal fraction. Many handheld GPS devices use DMM while paper charts and older equipment use DMS. Both carry the same information; the choice depends on your device or audience.
How accurate is one arc-second?
One arc-second of latitude corresponds to approximately 31 metres on the Earth's surface. One arc-second of longitude varies from 31 metres at the equator to zero at the poles, because meridians converge. For sub-metre GPS accuracy, you need coordinates expressed to at least two or three decimal places in the seconds component.
Can I use this converter for right ascension in astronomy?
Declination in astronomy uses the same DMS format as geographic latitude, so yes - the conversion arithmetic is identical. Right ascension is expressed in hours-minutes-seconds (0 to 24 h), not degrees, so multiply the hour value by 15 to convert to degrees first, then use this converter if you need a degree representation.