Three formats for the same point, and why they all exist
A latitude and longitude is an angle measured at the centre of the Earth, and angles have been written down in three different ways for three different reasons. All three describe the same point; only the notation differs.
Degrees, minutes and seconds is the oldest, inherited from Babylonian sexagesimal arithmetic by way of every navigator since. It survives on topographic maps, in property descriptions, in survey reports and in older aviation publications. Degrees and decimal minutes is what almost every marine chart plotter, GPS receiver and aviation database uses, because a minute of latitude is a nautical mile, so keeping minutes visible keeps distance visible. Decimal degrees is what computers use — mapping URLs, GeoJSON files, spreadsheets and GIS software — because arithmetic on a single number is trivial and arithmetic on three sexagesimal fields is not.
The conversion is straightforward but the failure mode is not. Typing 40° 26.767′ into a field that expects 40.26767° puts you 10.7 nautical miles from where you meant to be, and both numbers look entirely plausible. That silent, self-consistent error is the reason a conversion tool earns its place in a navigation workflow, and the reason this page always shows all three forms side by side.
The arithmetic, and where the sign belongs
Going from sexagesimal to decimal is a single expression: divide the minutes by 60, divide the seconds by 3,600, and add both to the whole degrees. Then apply the hemisphere sign to the entire result, not to the degrees alone. That last point causes more errors than the division does. West longitude 79° 58′ 56″ is −79.982222, not −79 + 0.982222 = −78.017778. That is 1.9644° of longitude, which at this latitude is 1.9644 × 60 × cos(40.446°) = about 90 nautical miles away — a real place, and the wrong one.
Going the other way, take the absolute value, split off the whole degrees, and multiply the remainder by 60 to get minutes. If you want seconds as well, split off the whole minutes and multiply that remainder by 60 again. So 40.446111° gives 0.446111 × 60 = 26.76666′, and 0.76666 × 60 = 46.00″.
Precision is worth understanding numerically. One minute of latitude is one nautical mile — 1,852 metres — by definition, which is where the nautical mile came from. One second of latitude is therefore 1,852 ÷ 60 = 30.87 metres. In decimal degrees, the fourth decimal place is 11.1 metres and the sixth is 11 centimetres. On a chart plotter showing three decimal places of minutes, the last digit is 1.85 metres of latitude. Any digits beyond those are describing a precision the position itself does not have.
Longitude is different, and this is the part people forget. Meridians converge towards the poles, so a degree of longitude covers 60 nautical miles only at the equator and 60 × cos φ nautical miles at latitude φ. At 60° north that is exactly 30 NM; at 80° it is 10.4 NM. This is the classic departure relation of plane sailing, and it is why the great circle distance calculator cannot simply subtract coordinates, and why the same number of decimal places means something different for the two coordinates.
Worked example: converting 40° 26′ 46″ N, 79° 58′ 56″ W
This is a position in western Pennsylvania, written the way a topographic map would give it. Convert it to the decimal degrees a mapping link needs.
- Latitude minutes. 26 ÷ 60 = 0.433333°.
- Latitude seconds. 46 ÷ 3,600 = 0.012778°.
- Add to the degrees. 40 + 0.433333 + 0.012778 = 40.446111°. North, so positive.
- Longitude minutes. 58 ÷ 60 = 0.966667°.
- Longitude seconds. 56 ÷ 3,600 = 0.015556°.
- Add, then apply the sign. 79 + 0.966667 + 0.015556 = 79.982222, and west makes it −79.982222°.
Now go back the other way and produce the plotter format. Take 0.446111 × 60 = 26.7667′, so the latitude is 40° 26.767′ N. Take 0.982222 × 60 = 58.9333′, so the longitude is 79° 58.933′ W. Notice that the minutes figure has moved from 26 to 26.767 — the seconds have been folded into it, and anyone reading 26.767 as seconds would be nearly half a mile out.
Finally, the UTM zone. Zones are six degrees of longitude wide, numbered from 1 starting at 180° W, so the zone is ⌊(longitude + 180) ÷ 6⌋ + 1 = ⌊(−79.982222 + 180) ÷ 6⌋ + 1 = ⌊16.67⌋ + 1 = zone 17. At this latitude, one degree of longitude covers 60 × cos(40.446°) = 45.66 NM, against a full 60 NM for a degree of latitude.
Checking a converted position before you trust it
Run three checks on any coordinate you have converted, and they will catch nearly every real-world mistake.
Check the hemisphere. The most damaging errors are sign errors, because they move you to the wrong continent while leaving the digits looking right. A negative latitude is southern; a negative longitude is western. If you are working in North America, longitude should be negative and between about −52 and −168.
Check the magnitude of the minutes. Minutes and seconds are always less than 60. A value of 71.5 minutes means someone has mixed a decimal fraction into a sexagesimal field, or has typed seconds where minutes belong. This calculator flags it rather than silently accepting the arithmetic.
Check the decimal against the sexagesimal. The fractional part of a decimal degree is always the minutes divided by 60, so a position at 26 minutes has a fractional part near 0.43, and one at 45 minutes has a fractional part near 0.75. If a converted decimal ends in the same digits as the original minutes — 40.26 for 40° 26′ — the conversion has not happened at all. That single check catches the most common format confusion there is.
One caution about datums. All of these formats express the same angle, but an angle is only a position once you say which reference ellipsoid and datum it is measured against. Modern GPS output, aviation charts and most web mapping use WGS 84, and the conversions on this page are datum-neutral: they change notation, not the reference frame. Older surveys quoted on NAD 27, OSGB36 or a local datum can differ from WGS 84 by tens or even hundreds of metres for the same written coordinate, and that shift is a separate transformation this calculator does not perform.
What each digit of precision is worth on the ground
| Unit | In degrees | Latitude distance | Where you see it |
|---|---|---|---|
| 1 degree | 1 | 60 NM / 111.1 km | Chart grid lines |
| 1 minute | 0.016667 | 1 NM / 1,852 m | Definition of the nautical mile |
| 0.1 minute | 0.001667 | 185.2 m | Older GPS displays |
| 0.001 minute | 0.0000167 | 1.85 m | Modern chart plotters |
| 1 second | 0.000278 | 30.87 m | Topographic maps, surveys |
| 0.0001 degree | 0.0001 | 11.1 m | Four-decimal web coordinates |
| 0.00001 degree | 0.00001 | 1.11 m | Five-decimal web coordinates |
| 0.000001 degree | 0.000001 | 0.111 m | Six-decimal GIS output |
Distances follow from one minute of latitude being one nautical mile, 1,852 m, by definition. A degree of latitude is 60 NM, which is 111.12 km.
How far a degree of longitude reaches, by latitude
| Latitude | cos φ | Nautical miles per degree | Kilometres per degree |
|---|---|---|---|
| 0° (equator) | 1.000 | 60.0 | 111.1 |
| 15° | 0.966 | 58.0 | 107.3 |
| 30° | 0.866 | 52.0 | 96.2 |
| 40° | 0.766 | 46.0 | 85.1 |
| 45° | 0.707 | 42.4 | 78.6 |
| 51.5° | 0.623 | 37.4 | 69.2 |
| 60° | 0.500 | 30.0 | 55.6 |
| 70° | 0.342 | 20.5 | 38.0 |
| 80° | 0.174 | 10.4 | 19.3 |
| 90° (pole) | 0.000 | 0.0 | 0.0 |
Kilometre figures use 1 NM = 1.852 km. This spherical relation is what navigators use; on the WGS 84 ellipsoid a degree of longitude at the equator is about 60.1 NM, a difference of two parts in a thousand.
Mistakes that put a position in the wrong place
- Reading decimal minutes as decimal degrees. 40° 26.767′ is not 40.26767°. The error is 0.178 degrees of latitude, which is 10.7 nautical miles, and both numbers look entirely reasonable on screen.
- Applying the hemisphere sign to the degrees only. West 79° 58′ is −79.9667, not −78.0333. Negate the whole value after adding the minutes and seconds.
- Mixing minutes and seconds in one field. Entering 26.767 into a minutes field alongside 46 in a seconds field counts the same arc twice.
- Assuming the source is WGS 84. A coordinate on a local datum can be tens or hundreds of metres from the same written coordinate on WGS 84, and no notation conversion will reveal it.
- Quoting more digits than the fix supports. Six decimal places implies 11 cm. A handheld GPS receiver is doing well to give you three metres, so the extra digits are noise dressed as precision.
- Forgetting that longitude gets narrower. Two positions a tenth of a degree apart in longitude are 6 NM apart at the equator and 3 NM apart at 60° latitude. Use the great circle distance calculator rather than subtracting coordinates.
- Dropping the leading zero on longitude. Aviation and marine practice writes longitude with three digits — 007° 25′ E, not 7° 25′ E — precisely so that a truncated field is obvious.
Why a minute of latitude is a nautical mile
The nautical mile was defined as the length of one minute of arc along a meridian, which is what makes a latitude scale on a chart also a distance scale — the reason navigators measure distance from the side of the chart and never from the top or bottom. Because the Earth is slightly flattened, that arc length is not quite constant, running from about 1,843 m near the equator to about 1,862 m near the poles, so in 1929 the international nautical mile was fixed at exactly 1,852 metres. The practical rule survives intact: one minute of latitude is one nautical mile, everywhere, near enough for navigation.
Coordinates in a wider navigation workflow
A converted coordinate is usually the input to something else. Once a position is in decimal degrees it feeds distance and bearing calculations directly — see the great circle distance calculator for the spherical trigonometry, and the dead reckoning position calculator for advancing a position by a course and distance run. Both need signed decimal degrees, which is exactly why the conversion matters.
Grid systems sit alongside geographic coordinates rather than replacing them. UTM divides the world into 60 zones of six degrees of longitude and expresses position in metres east and north within a zone, which suits ground survey and military use because distances are computed with ordinary arithmetic. The zone number this calculator reports is the first thing you need for that conversion; the eastings and northings require a projection calculation. Aviation adds its own shorthand in the ARINC 424 five-character identifiers used in flight management systems, which encode a coordinate in a form that fits a database field.
For work near land, remember that a coordinate is only as good as the chart it is plotted on. Many charts of remote areas still carry survey data from the nineteenth century, and their datum shifts can exceed the size of the hazards they show — which is why chart notes about datum are worth reading before trusting a GPS position plotted on paper. Practical seamanship problems that depend on position, such as working out how much rode to lay with the anchor scope calculator or how far you can see with the distance to horizon calculator, are downstream of getting the position itself right.
Key terms
- Latitude (φ)
- Angular distance north or south of the equator, from 0° to 90°. One minute of latitude is one nautical mile everywhere.
- Longitude (λ)
- Angular distance east or west of the prime meridian, from 0° to 180°. The ground distance it represents shrinks as the cosine of the latitude.
- Degrees and decimal minutes (DDM)
- The format used by nearly all marine chart plotters and GPS receivers, written as 40° 26.767′ N. Keeps minutes visible so that distance stays readable.
- Datum
- The reference ellipsoid and its orientation to the Earth. WGS 84 is the datum GPS uses; the same written coordinate on another datum can be a different physical place.
- UTM zone
- One of 60 six-degree bands of longitude used by the Universal Transverse Mercator grid, numbered eastwards from the 180th meridian.
- Departure
- The east-west distance corresponding to a change of longitude, equal to the longitude difference in minutes multiplied by the cosine of the latitude.