DMS vs Decimal Degrees: How to Read and Convert GPS Coordinates

The same spot on Earth can be written as 37.422, -122.084, as 37° 25.32′ N, 122° 5.04′ W, or as 37° 25′ 19.20″ N, 122° 5′ 2.40″ W. All three describe one point. They are just different ways of splitting a degree into smaller pieces. This guide explains each format, shows how to convert between them by hand, and lists the mistakes that most often send a coordinate to the wrong field, the wrong country, or the wrong hemisphere.

The three formats

Latitude measures how far north or south of the equator a point is, from 0° to 90°. Longitude measures how far east or west of the prime meridian (through Greenwich) it is, from 0° to 180°. The formats differ only in how they write the fraction of a degree.

One degree is 60 minutes (′), and one minute is 60 seconds (″). These minutes and seconds are angles, not time. The system is base 60, the same as a clock face, which is why most conversion mistakes come from treating minutes as if they were a decimal fraction.

Decimal degrees are what most software, web maps, spreadsheets, and file formats use, because a single number is easy to store and calculate with. DMS is the traditional format found on older maps, deeds, survey plats, and nautical charts. DMM is common on handheld GPS units, in marine navigation, and in geocaching.

Signs and hemisphere letters

Each coordinate needs a direction. You can show it with a letter or with a sign:

• Latitude: N is positive, S is negative.
• Longitude: E is positive, W is negative.

So 33.8568° S, 151.2153° E and -33.8568, 151.2153 are the same point. Use one or the other, not both. A value like -37.5° N contradicts itself, and good software rejects it rather than guessing.

Converting decimal degrees to DMS

Work with the absolute value and put the hemisphere letter back at the end.

1. The whole number is the degrees.
2. Multiply the decimal part by 60. The whole number of the result is the minutes.
3. Multiply the remaining decimal by 60 again. That is the seconds.

Example: 37.422, −122.084

Latitude 37.422 is positive, so it is north.

• Degrees: 37
• 0.422 × 60 = 25.32, so minutes = 25
• 0.32 × 60 = 19.2, so seconds = 19.2
• Result: 37° 25′ 19.20″ N

Longitude −122.084 is negative, so it is west.

• Degrees: 122
• 0.084 × 60 = 5.04, so minutes = 5
• 0.04 × 60 = 2.4, so seconds = 2.4
• Result: 122° 5′ 2.40″ W

To get DMM instead, stop after step 2 and keep the decimals of the minutes: 37° 25.32′ N, 122° 5.04′ W.

Example in the southern and eastern hemispheres: −33.8568, 151.2153

• Latitude: 0.8568 × 60 = 51.408, so 51 minutes; 0.408 × 60 = 24.48 seconds. Result: 33° 51′ 24.48″ S (DMM: 33° 51.408′ S).
• Longitude: 0.2153 × 60 = 12.918, so 12 minutes; 0.918 × 60 = 55.08 seconds. Result: 151° 12′ 55.08″ E (DMM: 151° 12.918′ E).

When a calculator shows something like 59.9999 seconds, round the seconds and carry if needed. 59.99995″ rounded to two decimals is 60.00″, which should become one more minute and 0.00″. A value with 60 in the minutes or seconds is never correctly formatted.

Converting DMS or DMM to decimal degrees

Divide minutes by 60 and seconds by 3,600, then add them to the degrees:

decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3,600

Apply the sign last: negative for S or W.

Example: 40° 26′ 46″ N, 79° 58′ 56″ W

• Latitude: 40 + 26 ÷ 60 + 46 ÷ 3,600 = 40 + 0.433333 + 0.012778 = 40.446111
• Longitude: 79 + 58 ÷ 60 + 56 ÷ 3,600 = 79 + 0.966667 + 0.015556 = 79.982222, and west makes it −79.982222

Example from DMM: 40° 26.767′ N

• 40 + 26.767 ÷ 60 = 40 + 0.446117 = 40.446117

If you would rather not do this by hand, the coordinate converter converts a latitude and longitude between DD, DMM, and DMS in either direction.

How many decimal places you need

More digits are not automatically better. A coordinate only needs enough precision to match how well the point was actually measured. On a sphere with the mean Earth radius of 6,371 km, one degree of latitude is about 111.2 km. On the real, slightly flattened Earth it varies a little with latitude, but the rough figures below hold everywhere.

A step in longitude is shorter away from the equator, because the meridians converge toward the poles. It shrinks by the cosine of the latitude: at 37° N, 0.00001° of longitude is about 0.88 m, and at 60° it is about 0.56 m.

For the other formats, the equivalent steps in latitude are:

• DMS: 1″ is about 31 m, 0.1″ is about 3.1 m, and 0.01″ is about 0.31 m.
• DMM: 0.001′ is about 1.85 m, and 0.0001′ is about 0.19 m.

Typical phone GPS under open sky is good to a few meters. Five decimal places in DD, one or two decimals of seconds in DMS, or three to four decimals of minutes in DMM are therefore plenty for fieldwork with a phone. Writing more digits does not make a phone fix more accurate. It only hides how accurate the fix really was.

Common mistakes

Treating minutes as decimals

37° 25′ 19″ is not 37.2519. The minutes and seconds are sixtieths, so the correct value is 37.421944. Reading it as 37.2519 moves the point about 18.9 km south. This is the most common conversion error, and it often happens when someone types DMS into a spreadsheet cell as one number.

Minutes or seconds of 60 or more

Minutes and seconds both run from 0 up to, but not including, 60. A value like 37° 61′ is invalid. It usually comes from a typo or from the rounding problem described above.

Decimals in more than one place

In DMM, only the minutes have decimals. In DMS, only the seconds should. 37.5° 30′ mixes formats and has no clear meaning.

Dropping the minus sign

Longitudes in the Americas are negative and latitudes in the southern hemisphere are negative. Lose the sign on −122.084 and a point in California lands near the eastern tip of China’s Shandong Peninsula, about 9,400 km away. If a point appears on the wrong continent, check the signs first.

Swapping latitude and longitude

Most people write “latitude, longitude”, and most coordinate entry forms expect it. Many data formats store it the other way round. GeoJSON and KML both put longitude first, as [-122.084, 37.422] or -122.084,37.422. A swapped pair is easy to catch when one value is above 90, because no latitude can be. When both values are small, a swap quietly moves the point somewhere else. Our guide to KML, GPX, and GeoJSON covers the order each format uses.

Decimal commas

Many countries write 37,422 instead of 37.422. That is fine in a field that holds a single number, but it collides with the comma that separates latitude from longitude. In 37,422, -122,084 it is no longer clear where one number ends. When you paste a pair onto one line, or save a CSV file, use decimal points.

Mixing datums

GPS, web maps, GeoJSON, and GPX all use the WGS 84 datum. Old paper maps and some national grids use other datums, and the same printed numbers can then point to a spot tens or even hundreds of meters away. If coordinates come from an old survey or deed, check which datum they use before you compare them with GPS readings.

What Land Measure and this site accept

The coordinate converter on this site and the Land Measure app use the same parsing rules, so a coordinate that works in one works in the other:

• Decimal degrees, such as 37.422 or -122.084
• Degrees and decimal minutes, such as 37 25.32 N or 37° 25.32′ N
• Degrees, minutes, seconds, such as 37 25 19.2 N, 37°25'19.2"N, or 37:25:19.2
• A hemisphere letter at the start or the end (N 37 25 19.2 or 37 25 19.2 N), or a sign instead
• A decimal comma in a single value, such as 37,422

Some inputs are rejected on purpose instead of guessed at: minutes or seconds of 60 or more, decimal degrees combined with minutes, a minus sign together with N or E, and values beyond 90° of latitude or 180° of longitude. Output always uses a decimal point. In the app, typing coordinates is one of the ways to build a measurement, and it works offline with no map at all, which is handy when the corner coordinates come from a survey document.

Quick reference

Once your coordinates are in a consistent format, you can measure between them with the distance and bearing tool, or paste a list of corners into the coordinates area calculator to get the area of a parcel.