DMS ↔ Decimal Degrees Converter
Convert between the three angular coordinate formats — Decimal Degrees, Degrees-Minutes-Seconds, and Degrees-Decimal-Minutes. Format detected automatically; map and full geographic report below.
The three angular formats
Latitude and longitude are angles, and angles can be written three ways. Decimal Degrees (DD) is a single number with a decimal tail. Degrees-Minutes-Seconds (DMS) splits the fractional angle into base-60 minutes and base-60 seconds. Degrees-Decimal-Minutes (DDM) is the hybrid — whole degrees plus decimal minutes.
The three rows below show the same angle — the latitude of the Empire State Building's lobby — in all three notations. Blue is the whole-degree part (identical across all three); orange is the fractional angle re-expressed.
Use the converter below the diagram to round-trip in either direction. Paste DMS, get DD. Paste DD, get DMS. Paste DDM, get either of the other two.
Convert between DD, DMS, and DDM
Paste a coordinate in any of the three angular formats. The input format is detected automatically; pick the output format with the chips below.
Output format
See it on the map
Click anywhere on the map to set the input above to that point's decimal-degree coordinates — the conversion re-runs instantly.
How to use this tool
Paste your coordinate
Drop in DD, DMS, or DDM. The format is detected automatically — no need to identify it manually.
Pick your output format
Use the chip row to choose DD, DMS, DDM, or "All three" (the default). The result panel renders the conversion in whichever format you selected.
See and refine on the map
The map below the converter shows the resolved point. Click anywhere on the map to set the input to that point's decimal-degree coordinates; the conversion re-runs instantly.
How the conversion works (the math)
All three formats describe the same fractional angle in different bases. The full identity per ISO 6709:2022:
| From → To | Formula | Worked example |
|---|---|---|
| DMS → DD | DD = D + M/60 + S/3600 | 40° 44' 54.24" = 40 + 44/60 + 54.24/3600 = 40.7484° |
| DD → DMS | D = floor(DD); M = floor((DD − D)×60); S = ((DD − D)×60 − M)×60 | 40.7484° → D=40, (0.7484)×60 = 44.904 → M=44, (0.904)×60 = 54.24 → S=54.24 |
| DDM → DD | DD = D + M/60 | 40° 44.904' = 40 + 44.904/60 = 40.7484° |
| DD → DDM | D = floor(DD); M = (DD − D)×60 | 40.7484° → D=40, (0.7484)×60 = 44.904 → 40° 44.904' |
| DMS → DDM | D unchanged; M_decimal = M + S/60 | 40° 44' 54.24" → D=40, M=44 + 54.24/60 = 44.904 → 40° 44.904' |
The math is exact — no precision loss — provided the working precision is high enough. With JavaScript double-precision floats (15–17 significant decimal digits), round-trip DD → DMS → DD is exact to about 1 e-13 degrees ≈ 1 e-8 metres at the equator. Well below any practical use case.
The three angular formats by family and primary specification
All three describe the same angle; the table below groups them by which standard documents the notation.
| Format | Primary spec | Canonical use | Step size at default precision |
|---|---|---|---|
| DD | ISO 6709:2022 · W3C Geolocation API | Software, databases, APIs, web maps | 6 dp ≈ 11 cm at the equator |
| DMS | ISO 6709:2022 · USGS Snyder PP 1395 | Paper maps, surveying, historic deeds, celestial coordinates | 0.01" ≈ 31 cm |
| DDM | ICAO Annex 5 · IHO S-4 | Marine charts, aviation flight plans, geocaching listings | 0.001 min ≈ 1.85 m |
The precision chart includes UTM, MGRS, and Plus Code for context, but for this tool only the three angular rows matter. DD at 6 decimals is the most common default and lands at roughly the same precision as DMS at 0.01-second resolution — both around 30 cm.
Why each format exists
Three formats for the same angle isn't inefficiency — each one is the right format in its discipline.
DMS is the original, going back to Babylonian astronomers around 2,000 BCE and codified by Eratosthenes, Ptolemy, and the Islamic astronomers who refined the sexagesimal system. Paper maps, surveying records, celestial catalogues — every pre-computer geographic reference uses DMS. Modern surveying still uses it for backwards compatibility with historic plats.
DDM emerged in marine navigation and aviation. Chartwork is done by inspection — measuring with dividers — and a decimal-minute notation interpolates well between tick-marked latitude/longitude lines. The ICAO standard Annex 5 and the IHO chart standard S-4 both specify DDM as the standard for charts and flight plans.
DD became dominant with computers. A single float — one number — is easier to store, manipulate, and transmit than three separated values. Every modern web map, GPS receiver, and geospatial database speaks DD natively. W3C Geolocation API mandates DD for browser-reported positions.
Ten ways angular-format conversion gets used
The three angular formats meet at workflow boundaries — between paper and digital, between disciplines, between eras. The ten cases below are the most common in practice.
1. Hiking and outdoor recreation
Paper topographic maps use DMS; smartphone apps (AllTrails, Gaia GPS, CalTopo) report DD. Converting between them is the first step in transcribing a waypoint.
Worked example: Half Dome summit on the USGS topographic sheet: 37° 44' 46" N, 119° 31' 58" W. Converted for the app: 37.7461, -119.5328.
2. Aviation flight planning
ICAO Annex 5 specifies DDM for flight plans and air-traffic reporting; cockpit GPS receivers default to DD. Pre-flight preparation crosses both formats.
Worked example: JFK runway 22L threshold for the flight plan: 40° 38.3' N, 73° 47.1' W. Avionics DD: 40.6383, -73.7850.
3. Marine navigation
Paper nautical charts label coordinates in DDM. Chartplotters may report DD or DDM depending on the era; passages laid out on paper need conversion at export.
Worked example: A waypoint at the entrance to Boston Harbor on the chart: 42° 20.7' N, 70° 54.2' W. Loaded into the chartplotter as DD: 42.345, -70.9033.
4. Land surveying — historic deeds and plats
Property descriptions in deeds written before the 1990s use DMS in metes-and-bounds notation. Modern parcel GIS systems use DD. Title researchers and civil engineers convert as a routine step.
Worked example: A bearing from a 1922 deed: N 48° 12' 30" E at a point recorded as 40° 22' 15" N, 80° 04' 50" W. Converted to DD: 40.3708, -80.0806.
5. Geocaching
Geocaching.com lists caches in DDM by convention (a holdover from the early-2000s handheld GPS era). Phone apps prefer DD. The conversion is automatic in the app, manual in the planning spreadsheet.
Worked example: A cache at 40° 44.904' N, 73° 59.142' W on Geocaching.com. Converted to DD for the hiking app: 40.7484, -73.9857.
6. Astronomy — celestial coordinates
Right ascension and declination in star catalogues are historically in DMS (or its time-based equivalent for RA). Modern observatory control software speaks DD. Cross-walks are common when integrating older datasets.
Worked example:The bright star Vega's declination: +38° 47' 01". In DD: +38.7836. Telescope control system uses the latter.
7. Real estate listings — older property records
Older title records and tax-roll references use DMS. MLS feeds and modern listing platforms expect DD. Listing onboarding converts.
Worked example: Property recorded in 1968 as 34° 03' 45" N, 118° 14' 30" W. MLS DD: 34.0625, -118.2417.
8. Search and rescue cross-system communications
SAR operations involve multiple services with different format conventions — Coast Guard prefers DDM, civilian aircraft DD, military MGRS. Cross-system bridging is constant.
Worked example: Coast Guard reports last-known position 37° 48.5' N, 122° 27.0' W. Civilian aircraft asks for DD: 37.8083, -122.4500.
9. Archaeology and academic field records
Archaeological site records, especially pre-2000, use DMS in site logs and publication coordinates. Modern GIS overlay software uses DD. Researchers harmonising legacy datasets convert in bulk.
Worked example: A 1985 site report: 33° 30' 45" N, 90° 12' 30" W. Converted for site-distribution GIS: 33.5125, -90.2083.
10. Citizen science observation submissions
Platforms like iNaturalist and eBird ingest observations from both phone apps (DD) and older handheld GPS (DDM). The platform normalises to DD at ingest; researchers downloading datasets get DD.
Worked example: A birder submits an observation from an older Garmin GPS unit: 44° 58.2' N, 93° 16.5' W. iNaturalist stores it as DD 44.9700, -93.2750.
Choosing the right input
| Input shape | Right tool on Coordinately | Returns |
|---|---|---|
| DD, DMS, or DDM (this page) | This page | The same point in all three angular notations |
| UTM, MGRS, or Plus Code as well | /tools/coordinate-converter | All six common notations |
| Address or place name | /tools/address-to-coordinates | Forward geocoding with confidence bands |
| A Google / Apple / OSM Maps URL | /tools/google-maps-coordinates | Coordinate extracted from the URL |
| A click on a map | / | Click any point and read its coordinates |
Why a conversion might look wrong
- The 60-second carry bug. Writing
40° 44' 60"instead of40° 45' 0". The tool tolerates this on input but it's worth knowing for output validation. - Sign vs hemisphere letter.
40.7484Nis ambiguous shorthand. Use either signed numbers (40.7484, -73.9857) or full hemisphere indicators with units (40.7484° N, 73.9857° W). - Quotes vs primes.
44'(apostrophe) vs44′(proper prime) vs44"(double quote) vs44″(double prime). The parser tolerates ASCII punctuation; copied-from-Word text may have smart quotes that work too. - Old datum. The tool assumes WGS 84. If your coordinate is in NAD 27 (US legacy) the result will be offset by tens of metres. See /learn/wgs84-vs-nad83.
Privacy and data-flow notes
Conversion math runs entirely client-side. No service is called for the format conversion itself.
The optional nearest-place and elevation lookups in the report below the map hit server-side proxies (/api/geocode/reverse, /api/elevation) with Cache-Control: no-store. Browser geolocation is button-triggered only and never automatic.
Related tools
- Full six-format converter— Same point in DD, DMS, DDM, UTM, MGRS, and Plus Code
- Find lat/lon of any point on a map— Click the map; read the coordinates
- Coordinates to address— Reverse-geocode the converted point
- Address to coordinates— The inverse — start from an address
- Extract coordinates from a maps URL— Paste a Google / Apple / OSM URL
Related articles
- Decimal degrees vs DMS— The conversion math + the 60-second carry bug in detail
- Coordinate formats explained— Pillar article on all six formats
- How to read coordinates— Visual fingerprints and decoding rules
- How to write coordinates— Choosing format, precision, and convention
- Positive and negative coordinates— Signed numbers vs hemisphere letters, sign-loss bugs
Frequently asked questions
Which formats does the tool recognise?
Decimal Degrees (DD), Degrees-Minutes-Seconds (DMS), and Degrees-Decimal-Minutes (DDM) — the three angular notations. For UTM, MGRS, or Plus Codes, use /tools/coordinate-converter (the six-format superset).
How does the auto-detection work?
The parser checks for degree symbol (°), prime ('), or double-prime (") to distinguish DMS / DDM from plain DD. If the input contains a single quote followed by digits (the decimal-minute pattern), it's DDM. If it contains both prime and double-prime, it's DMS. Otherwise it's DD.
How accurate is the conversion?
Exact to about 1e-13 degrees (≈ 10 nanometres at the equator) per round-trip in JavaScript double-precision floats. Far below any practical use case. Input precision is the limit — if you paste DMS with the seconds rounded to whole numbers, the DD output reflects that rounding.
What is the 60-second carry bug?
Forgetting that 60 seconds = 1 minute (and 60 minutes = 1 degree). Writing 40° 44' 60" is malformed; the correct value is 40° 45' 0". The converter tolerates this on input — it parses 40° 44' 60" as the next whole minute — but generating DMS by hand can produce it. See /learn/decimal-degrees-vs-dms for the underlying sexagesimal math.
Why does DMS use base-60 (60 minutes per degree)?
Historical — the Babylonian sexagesimal system, 4,000 years old. 60 has many divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) which makes integer arithmetic with fractional angles convenient. The same logic gives us 60 seconds per minute, 60 minutes per hour, and 360 degrees per circle.
Why doesn't 40.7484 always equal 40°44'54.24"?
It does, exactly. The arithmetic: 40.7484 − 40 = 0.7484; 0.7484 × 60 = 44.904; 44 minutes + 0.904 × 60 = 54.24 seconds. So 40° 44' 54.24" = 40.7484° exactly. Any apparent disagreement is a rounding choice — DD at 4 decimal places vs DMS at 0.01-second precision lands at very close numbers but not bit-identical floats.
Can I enter an address instead?
Not on this page — this tool is focused on the three angular notations. For address input use /tools/address-to-coordinates; the result there will be in DD which you can paste back into this converter to see DMS and DDM.
Why are smart quotes like " and ′ tolerated?
Because copy-pasting from Word, Google Docs, or a PDF often includes typographic punctuation rather than ASCII quotes. The parser normalises these — both the ASCII apostrophe (') and the typographic prime (′) are treated as the minute marker; both ASCII double quote (") and the typographic double prime (″) are treated as the second marker.
Sources
- ISO 6709:2022 — ISO 6709:2022 — Standard representation of geographic point location by coordinates (the standard that defines DD, DMS, DDM conversion) · https://www.iso.org/standard/75147.html · Accessed .
- ICAO Annex 5 — ICAO Annex 5 — Units of Measurement to be Used in Air and Ground Operations (DDM as aviation standard) · https://www.icao.int/Pages/default.aspx · Accessed .
- IHO S-4 — International Hydrographic Organization S-4 — Regulations of the IHO for International (INT) Charts (DDM as marine chart standard) · https://iho.int/uploads/user/pubs/standards/s-4/S-4_eEd4.9.0_EN.pdf · Accessed .
- NGS NCAT — NGS Coordinate Conversion and Transformation Tool — US government format conversion utility · https://geodesy.noaa.gov/NCAT/ · Accessed .
- NIMA TR 8350.2 (WGS 84) — NIMA Technical Report 8350.2 — Department of Defense World Geodetic System 1984 (the reference frame the conversion assumes) · https://earth-info.nga.mil/php/download.php?file=coord-wgs84 · Accessed .
- W3C Geolocation API — W3C Geolocation API Level 2 — defines DD as the format browsers return · https://www.w3.org/TR/geolocation/ · Accessed .
- Bowditch — American Practical Navigator — NGA Publication 9 (Bowditch), the American Practical Navigator — chapter on marine coordinate notation · https://msi.nga.mil/Publications/APN · Accessed .
- USGS Snyder PP 1395 — J. P. Snyder, "Map Projections — A Working Manual", USGS Professional Paper 1395 (1987) · https://pubs.usgs.gov/pp/1395/report.pdf · Accessed .
- IAU astronomical coordinates — IAU SOFA — Standards of Fundamental Astronomy. Defines celestial coordinate conventions (RA in time units, Dec in DMS) · https://www.iausofa.org/ · Accessed .
- Mapbox Geocoding API v6 — Mapbox Geocoding v6 — used by the nearest-place lookup in the report · https://docs.mapbox.com/api/search/geocoding-v6/ · Accessed .