GPS Coordinates Explained: Degrees-Minutes-Seconds vs Decimal Degrees
The Old Town Square in Prague can be written as 50°05′15″N 14°25′17″E or as 50.0875, 14.4214. Both describe exactly the same spot. The first format is how coordinates have been written on maps for centuries; the second is what Google Maps, phones and most software expect.
Mixing the two up is one of the most common ways to end up kilometres from where you meant to be. This guide explains both formats, the third format sailors and pilots use, how to convert by hand, and how much precision you really need.
Latitude and longitude in one minute
Every location on Earth is described by two angles:
- Latitude measures how far north or south of the equator you are, from 0° at the equator to 90° at the poles.
- Longitude measures how far east or west of the prime meridian (through Greenwich, London) you are, from 0° to 180°.
Because they are angles, they can be divided the same way as time on a clock: one degree has 60 minutes, and one minute has 60 seconds.
The three common formats
| Format | Example (Prague Old Town Square) | Where you see it |
|---|---|---|
| Degrees, minutes, seconds (DMS) | 50°05′15″N 14°25′17″E | Paper maps, surveying, Wikipedia |
| Degrees and decimal minutes (DDM) | 50°05.250′N 14°25.283′E | Marine and aviation GPS, geocaching |
| Decimal degrees (DD) | 50.0875, 14.4214 | Google Maps, phones, GIS software, databases |
In decimal degrees, the compass letters disappear. Instead, south latitudes and west longitudes are negative. New York is roughly 40.7128, −74.0060: the minus sign replaces the “W”.
Converting DMS to decimal degrees
Divide the minutes by 60 and the seconds by 3,600, then add everything together:
decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3600
For 50°05′15″N:
50 + 5 ÷ 60 + 15 ÷ 3600 = 50 + 0.08333 + 0.00417 = 50.0875
For 14°25′17″E:
14 + 25 ÷ 60 + 17 ÷ 3600 = 14 + 0.41667 + 0.00472 = 14.4214
If the coordinate is south or west, put a minus sign in front of the result. You can check your answer with the DMS to decimal degrees converter.
Converting decimal degrees to DMS
Work the other way, peeling off whole numbers at each step:
- The whole number is the degrees: 50.0875 → 50°.
- Multiply the remainder by 60 to get minutes: 0.0875 × 60 = 5.25 → 5′.
- Multiply the new remainder by 60 to get seconds: 0.25 × 60 = 15″.
Result: 50°05′15″. The decimal degrees to DMS converter handles negative values and adds the correct N/S/E/W letter automatically.
How many decimal places do you need?
One degree of latitude is about 111 km everywhere on Earth. Each extra decimal place makes the position ten times more precise:
| Decimal places | Example | Precision (approx.) | Good enough for |
|---|---|---|---|
| 1 | 50.1 | 11 km | A region |
| 2 | 50.09 | 1.1 km | A town or village |
| 3 | 50.088 | 110 m | A neighbourhood |
| 4 | 50.0875 | 11 m | A building |
| 5 | 50.08750 | 1.1 m | A doorway |
| 6 | 50.087500 | 0.11 m | Surveying, mapping |
For comparison, one arc-second in DMS is about 31 m of latitude, and a typical phone GPS is accurate to roughly 5 m outdoors. Five decimal places is therefore already more precise than most consumer devices can measure; anything beyond six decimals is usually false precision.
Longitude is slightly different: degrees of longitude get narrower as you move away from the equator, because the meridians meet at the poles. At Prague’s latitude, one degree of longitude is only about 71 km wide instead of 111 km.
The most common mistakes
Reading decimal minutes as seconds. 50°05.25′ (DDM) is not 50°05′25″. The “.25” is a quarter of a minute, which is 15 seconds. Confusing the two shifts the position by about 300 m.
Treating decimal degrees as minutes. 50.30 does not mean 50°30′. It means 50°18′. The difference is 22 km.
Forgetting the sign. Dropping the minus sign on a western longitude moves the point to the other side of the prime meridian. For a place in the Americas, that puts it somewhere in Asia or the Indian Ocean.
Swapping latitude and longitude. Most apps expect latitude first. A few file formats and programming libraries, including GeoJSON, expect longitude first. If your point appears in the ocean, try swapping the numbers.
Minutes or seconds of 60 or more. Valid minutes and seconds run from 0 to 59.999. A value like 50°65′ is invalid and usually means the coordinate was mistyped.
Which format should you use?
- Sharing a location with someone or pasting into an app: decimal degrees, with four or five decimal places.
- Reading or writing paper maps and official documents: DMS, as printed on the map.
- Marine or aviation navigation equipment: DDM, because that is what the devices display.
Whatever format you receive, convert it once and keep it in one format from then on. Most errors happen when formats are mixed in the same list or spreadsheet. The batch file converter can convert a whole column of coordinates in a CSV or Excel file at once, entirely in your browser.
Key takeaways
- DMS, DDM and decimal degrees are three ways to write the same angle; one degree = 60 minutes = 3,600 seconds.
- In decimal degrees, south and west are negative numbers.
- Four decimal places locate a building, five a doorway; more is rarely meaningful.
- Never mix decimal minutes, seconds and decimal degrees in the same dataset.