DMS to Decimal Degrees Converter (and DDM)
DMS to Decimal Degrees Converter (and DDM)
Convert coordinates between degrees-minutes-seconds, degrees and decimal minutes and decimal degrees, in every direction, for latitude and longitude — and see what each decimal place is actually worth in metres at your own latitude, computed on the WGS 84 ellipsoid.
DMS, DDM and decimal degrees
40.446195 ° N as decimal degrees, on the WGS 84 ellipsoid
The formats are arithmetic; the precision is geodesy
- a
- WGS 84 semi-major axis, 6 378 137 m exactly
- e squared
- first eccentricity squared, 6.694 379 990 14 × 10⁻³, derived from the defining flattening 1/298.257 223 563
- phi
- the latitude. For a latitude conversion it is the value itself; for a longitude you have to say where you are, which is why the page asks
- m lat
- metres per degree of latitude — the meridian arc. Varies by only 1% over the whole earth
- m lon
- metres per degree of longitude — an arc of the parallel. Falls to zero at the poles
Worked example
40.446195 ° N as decimal degrees, on the WGS 84 ellipsoid
North, so the sign is positive: 40.446195 °
The whole degrees are 40; the remainder 0.446195 × 60 = 26.7717 minutes, which is the DDM form 40° 26.7717′
Taking 26 whole minutes leaves 0.7717 of a minute, which is × 60 = 46.302 seconds — the DMS form 40° 26′ 46.302″
At this latitude the meridian radius of curvature is 6,362,308 m, so one degree of latitude is 111,043.2 m and one second is 30.85 m
A degree of LONGITUDE here is only 84,835.4 m, 76.4% of the latitude figure — which is why six decimal places do not buy the same precision on the two axes
What a decimal place is worth, in metres, at your latitude
| Latitude | km per degree of latitude | m per arcsecond of latitude | m in 0.001° of latitude | km per degree of longitude | m per arcsecond of longitude | m in 0.001° of longitude | Longitude / latitude |
|---|---|---|---|---|---|---|---|
| 0.0000 ° | 110.5743 | 30.715 | 110.57 | 111.3195 | 30.922 | 111.32 | 1.0067 |
| 15.0000 ° | 110.6487 | 30.736 | 110.65 | 107.5505 | 29.875 | 107.55 | 0.9720 |
| 30.0000 ° | 110.8524 | 30.792 | 110.85 | 96.4863 | 26.802 | 96.49 | 0.8704 |
| 45.0000 ° | 111.1318 | 30.870 | 111.13 | 78.8468 | 21.902 | 78.85 | 0.7095 |
| 51.4772 ° | 111.2574 | 30.905 | 111.26 | 69.4752 | 19.299 | 69.48 | 0.6245 |
| 60.0000 ° | 111.4123 | 30.948 | 111.41 | 55.8000 | 15.500 | 55.80 | 0.5008 |
| 75.0000 ° | 111.6184 | 31.005 | 111.62 | 28.9020 | 8.028 | 28.90 | 0.2589 |
Three formats for one point, and who uses which
| Format | The Empire State Building | Who uses it | What it implies |
|---|---|---|---|
| Decimal degrees (DD) | 40.748440, -73.985664 | Everything computational — GIS, GPS APIs, mapping libraries, GeoJSON | Six places is about 11 cm of latitude. Unambiguous, and the only format that arithmetic can be done in directly |
| Degrees, minutes, seconds (DMS) | 40° 44′ 54.38″ N, 73° 59′ 8.39″ W | Land survey, legal descriptions, older charts, anything printed before about 1990 | One whole second of latitude is about 31 m, so DMS rounded to the second locates you inside a box roughly 31 m by 24 m at this latitude |
| Degrees and decimal minutes (DDM) | 40° 44.7264′ N, 73° 59.1398′ W | Marine and aviation — chart plotters, AIS, VHF position reports, ICAO and IHO practice | Minutes are natural at sea because one minute of latitude is one nautical mile. Three decimal places of a minute is about 1.9 m |
| Hemisphere as a letter or as a sign | 40.748440 N is the same as +40.748440 | Both, interchangeably | S and W are negative. Losing the sign is the commonest single error in coordinate handling and puts you in the wrong hemisphere, not slightly off |
How many places to keep, and what each one costs you if you drop it
| Decimal places | Degrees | Latitude, metres | Longitude at 51.5° N, metres | Good enough for |
|---|---|---|---|---|
| 0 | 1 | 111,257.8 | 69,440.5 | Which country, roughly |
| 1 | 0.1 | 11,125.8 | 6,944.1 | Which town |
| 2 | 0.01 | 1,112.6 | 694.4 | Which neighbourhood |
| 3 | 0.001 | 111.3 | 69.4 | Which street, and the usual limit of a postcode-level geocode |
| 4 | 0.0001 | 11.126 | 6.944 | Which building |
| 5 | 0.00001 | 1.113 | 0.694 | Which part of the building — and about the limit of a consumer GNSS fix |
| 6 | 0.000001 | 0.111 | 0.069 | Sub-metre. Meaningful only with survey-grade or corrected GNSS |
| 7 | 0.0000001 | 0.011 | 0.007 | Nothing. This is noise dressed as precision |
Three formats, and the question nobody else answers
Three formats, one point, and three different implied precisions. Decimal degrees is what every mapping library, GPS API and GeoJSON file uses, because it is the only one you can do arithmetic in. Degrees, minutes and seconds is what land survey, legal descriptions and older charts use. Degrees and decimal minutes — 40° 26.7717′ — is what marine and aviation practice actually uses, and it is the one most converters forget, even though it is on the screen of every chart plotter afloat. The conversions between them are trivial and this page does them in every direction. The part that is not trivial, and that almost nothing else will tell you, is how many digits are worth writing down.
A digit is a distance, and the distance depends on where you are. One whole second of latitude is about 31 m — 30.72 m at the equator, 31.03 m at the poles, so nearly constant. One thousandth of a degree is about 111 m. That is the whole basis for choosing a precision, and it means a DMS reading given to the nearest second is less precise than five decimal places of a degree, despite looking more official.
Longitude is the one that moves, and it moves a lot. A degree of longitude is an arc of a parallel of latitude, and the parallels shrink to nothing at the poles: their radius goes as the cosine of the latitude. So a degree of longitude is 111.32 km at the equator, 78.85 km at 45°, 69.44 km at the latitude of London and 55.80 km at 60° — exactly half the equatorial figure, because the cosine of 60° is exactly a half. Which means that six decimal places of latitude and six of longitude are not the same amount of precision anywhere except on the equator, and that a rule of thumb quoting “111 km per degree” is wrong for every longitude in the temperate world. This page asks for your latitude when you are converting a longitude for exactly that reason, and computes the figure for the latitude you give it.
Why a degree of latitude changes at all. On a sphere it would not. On WGS 84 — the ellipsoid GPS actually uses — the meridian is an ellipse, and the radius of curvature of an ellipse is smallest where it is most sharply curved. The earth is flattened at the poles, so the meridian is less curved there and a degree along it is longer: 110.574 km at the equator against 111.694 km at the pole, a spread of one per cent, which is the flattening. Both radii of curvature are on this page as outputs, computed from the two WGS 84 defining constants — a = 6 378 137 m and 1/f = 298.257 223 563 — and nothing else. They reproduce the published degree-length table to better than a metre.
The nautical mile is hiding in here. One minute of latitude comes out at 1,852.2 m at 45° latitude against the nautical mile’s defined 1 852 m, which is not a coincidence: the mile was chosen to be a minute of arc and then fixed at a round metric figure in 1929 so that everybody could agree on it. That is why marine positions are quoted in decimal minutes — a difference in minutes of latitude is a distance in nautical miles, with no arithmetic in between.
And the sign. South and west are negative. The hemisphere letter and the sign carry the same information, and losing one of them is the commonest single failure in coordinate handling — it does not put you slightly out, it puts you in the wrong hemisphere. This page takes the hemisphere as an explicit choice and shows the sign it corresponds to, so that the thing you paste into a mapping library is the thing you meant.
For the angle arithmetic itself — degrees, gradians, radians and the rest — and for the slope side of the same subject, the slope and grade converter handles the five different ways the trades write a gradient down.
Frequently asked questions
How do I convert DMS to decimal degrees?
Degrees plus minutes over sixty plus seconds over three thousand six hundred, and then make it negative if it is south or west. So 40° 26′ 46.302″ N is 40 + 26/60 + 46.302/3600 = 40.446195. The only place this goes wrong is the sign: south and west are negative, and dropping the letter is how a point ends up in the wrong hemisphere rather than slightly out of place.
What is DDM, and why do boats and aircraft use it?
Degrees and decimal minutes — 40° 26.7717′ rather than 40° 26′ 46.30″. It is what chart plotters, AIS and VHF position reports use, and the reason is that one minute of latitude is one nautical mile by construction. A position in decimal minutes can be read as a distance without any arithmetic, which matters when you are navigating rather than computing. The ellipsoidal figure for a minute of latitude at 45° comes out at 1,852.2 m against the nautical mile’s defined 1 852 m.
How many decimal places of latitude and longitude do I need?
It depends what you are doing and where you are standing, which is why almost no converter will tell you. At the latitude of London one thousandth of a degree is 111 m of latitude and 69 m of longitude; one hundred-thousandth is about a metre and 0.7 m. Five places is the honest limit of a consumer GNSS fix. Six is sub-metre and needs corrected or survey-grade equipment to mean anything. Seven is noise.
How many metres is one second of latitude?
About 31 m, and very nearly the same everywhere: 30.72 m at the equator and 31.03 m at the poles, because the meridian’s radius of curvature grows slightly as the earth flattens towards the poles. Longitude is the one that moves: an arcsecond of longitude is 30.92 m at the equator, 19.29 m at London and 8.03 m at 75° N.
Why does a degree of longitude change size but a degree of latitude not?
Because they are measured along different curves. A degree of longitude is an arc of a parallel of latitude, and the parallels are circles that shrink to nothing at the poles — their radius goes as the cosine of the latitude, so a degree of longitude at 60° is half what it is at the equator, exactly. A degree of latitude is an arc of the meridian, which is a full ellipse from pole to pole and always has roughly the same radius of curvature: it varies only by one per cent, from 110.574 to 111.694 km, and that one per cent is the flattening of the earth.
Are these figures for a sphere or an ellipsoid?
An ellipsoid — WGS 84, the one GPS uses. A degree of latitude on a sphere would be the same everywhere; on WGS 84 it runs from 110.574 km at the equator to 111.694 km at the poles. This page computes the meridional radius of curvature and the radius in the prime vertical from the two WGS 84 defining constants and shows both, and the answers match the published degree-length table to better than a metre.
Can I just put a decimal point in the minutes to get DDM?
You can go from DMS to DDM by dividing the seconds by sixty and adding them to the minutes, yes — 26′ 46.302″ becomes 26.7717′. What you cannot do is treat 40° 26.77′ as though the 26.77 were seconds, or as though it were 40.2677°, and both mistakes are common enough to have sunk boats. If a number after the degree symbol is between 0 and 60 it is minutes; if it is a fraction of a degree it belongs after the decimal point in the degrees.
Related calculators
References
- National Geospatial-Intelligence Agency. Department of Defense World Geodetic System 1984, NGA.STND.0036_1.0.0_WGS84. The defining parameters used here are the semi-major axis a = 6 378 137 m exactly and the flattening 1/f = 298.257 223 563 exactly, from which the first eccentricity squared is 6.694 379 990 14 × 10⁻³. Every metres-per-degree figure on this page is computed from those two numbers and nothing else.
- The meridional and prime-vertical radii of curvature used here are the standard ellipsoidal expressions M = a(1−e²)/(1−e²sin²φ)^{3/2} and N = a/√(1−e²sin²φ); see Snyder JP, Map Projections: A Working Manual, USGS Professional Paper 1395 (1987), § Ellipsoidal parameters. A US Government work. The figures this page computes reproduce the published table of longitudinal degree lengths — 111.3195 km at the equator, 96.4863 at 30°, 78.8468 at 45°, 69.4752 at Greenwich’s latitude and 55.8000 at 60° — to four decimal places of a kilometre.
- International Hydrographic Organization, First International Extraordinary Hydrographic Conference, Monaco 1929: the international nautical mile is 1 852 m exactly. This page’s ellipsoidal figure for one minute of latitude at 45° is 1,852.2 m, which is the historical origin of that definition.
- ISO 6709, Standard representation of geographic point location by coordinates, cited by number only: it is a copyrighted standard and its text and tables are not reproduced here. It is the reference for the ordering (latitude before longitude) and for the sign convention that this page follows.
- International Civil Aviation Organization, Annex 4 and Annex 15, and IHO S-4 chart specifications, for the practice of quoting positions in degrees and decimal minutes in aviation and at sea rather than in degrees-minutes-seconds. Cited as practice; the documents themselves were not fetched for this batch and the statement rests on the published conventions of chart plotters and AIS message formats, which use decimal minutes.
- National Institute of Standards and Technology. NIST Handbook 44, Appendix C, General Tables of Units of Measurement. The US liquid gallon is 231 cubic inches exactly and the international inch is 25.4 mm exactly; every volume on this page descends from those two definitions.