DMS and Decimal Degrees, Explained

By Udit Agarwal · Updated October 18, 2026

To convert degrees, minutes and seconds (DMS) to decimal degrees, add the degrees, the minutes divided by 60 and the seconds divided by 3,600, then add a minus sign for south or west. So 40°26'46"N is 40 + 26/60 + 46/3600 = 40.4461°. To go back, multiply the decimal part by 60 for the minutes, and the leftover decimal by 60 again for the seconds. Decimal degrees (DD), DMS and degrees with decimal minutes (DDM) all describe the same point; what matters is which one your map, receiver or form expects.

Three ways to write the same point

Latitude is the angle north or south of the equator, from -90° to 90°. Longitude is the angle east or west of the prime meridian through Greenwich, from -180° to 180°. Each angle can be written three ways:

• Decimal degrees (DD) use one number per axis, with a minus sign for south and west.
• Degrees, minutes and seconds (DMS) split a degree into 60 minutes and a minute into 60 seconds, like an hour on a clock, and use a letter for the hemisphere.
• Degrees and decimal minutes (DDM), also written DMM, keep whole degrees and give the minutes as a decimal.

Here is the Sydney Opera House, a preset in the ArrayKit converter, written each way:

Decimal degrees suit software: web maps, spreadsheets, databases and calculations such as the distance between two coordinates. DMS is traditional on paper maps and in surveying. DDM is the default on many handheld GPS receivers and the format geocaching uses, and receivers send it in NMEA 0183 sentences as ddmm.mmmm, which the NMEA Parser decodes.

Converting DMS to decimal degrees

The formula is DD = degrees + minutes ÷ 60 + seconds ÷ 3,600, made negative for S or W. For the Opera House latitude, 33°51'24.5"S:

1. 51 ÷ 60 = 0.85
2. 24.5 ÷ 3,600 = 0.0068056
3. 33 + 0.85 + 0.0068056 = 33.8568056
4. S makes it negative: -33.8568056

That is 0.6 m from the original -33.8568, a loss from rounding the seconds to one decimal. DDM works the same way without the seconds: 33°51.408'S is 33 + 51.408 ÷ 60 = 33.8568, made negative for south. In a spreadsheet with degrees, minutes and seconds in A2, B2 and C2, the formula is =A2+B2/60+C2/3600, multiplied by -1 for S or W.

Converting decimal degrees to DMS

Work with the number without its sign:

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 what is left after the decimal point by 60 again for the seconds.

For the Opera House longitude, 151.2153, the degrees are 151. Then 0.2153 × 60 = 12.918, so 12 minutes, and 0.918 × 60 = 55.08, so 55.1 seconds. The longitude is positive, so the letter is E: 151°12'55.1"E. Stopping after step 2 gives DDM: 151°12.918'E.

Two traps catch people out. Rounding can produce 60 seconds, as when 12°59'59.99996" rounds to 60.0"; write it as 13°0'0" instead. And the floor of -33.8568 is -34, as is a spreadsheet's INT(-33.8568), so strip the sign first or use TRUNC, which cuts toward zero.

Signs or letters: N, S, E and W

North latitudes and east longitudes are positive; south latitudes and west longitudes are negative. Use a sign or a letter, never both: -33.8568 and 33.8568° S are the same latitude, but a value with both, such as -33.8568 S, is ambiguous. The converter's four presets cover each combination:

How many decimal places do you need?

One degree of latitude is about 111 km everywhere, so each decimal place in a DD coordinate is worth a tenth of the one before:

Those are north–south distances. A degree of longitude shrinks toward the poles, from about 111.3 km at the equator to 85 km at 40° latitude and 55.8 km at 60°.

In DMS and DDM, a minute of latitude is about 1.85 km, which is where the 1,852 m nautical mile comes from. A second is about 31 m, a tenth of a second about 3 m, and a thousandth of a minute, the usual DDM precision, about 1.9 m.

GPS.gov puts the typical accuracy of a smartphone's GPS at about 4.9 m under open sky, and worse near buildings and trees. Five decimal places already resolve 1.1 m, so six is plenty for any phone or handheld reading. Extra digits describe a precision the measurement never had.

Which formats Google Maps and GPS devices accept

Google Maps accepts all three formats in its search box. Its help page on coordinates asks you to put latitude first, use a dot rather than a comma for decimals, and keep latitude between -90 and 90 and longitude between -180 and 180. To read coordinates out of Google Maps on a computer, right-click a spot: the latitude and longitude appear at the top of the menu in decimal degrees, and clicking them copies them.

Handheld and marine GPS units let you choose the position format in their settings. Garmin units, for example, offer hddd.ddddd° (DD), hddd°mm.mmm' (DDM, the default) and hddd°mm'ss.s" (DMS), alongside grid systems such as UTM and MGRS. Set the device to the format you have before typing a coordinate, and check that its map datum is WGS 84, the datum GPS uses. For grid formats, the UTM Converter, MGRS Converter and Plus Codes Converter translate to and from latitude and longitude.

Common mistakes

Swapped latitude and longitude. Sometimes a swap is caught, because Sydney's longitude, 151.2153, is not a valid latitude. Often it is not: swap Pittsburgh's 40.446195, -79.982195 and you get a valid point on the Antarctic ice sheet. Swaps often happen when data from a GeoJSON file (RFC 7946) or a KML file, both of which put longitude first, meets a tool that expects latitude first.

Minutes or seconds of 60 or more. Both run from 0 to 59.999…, so 40°70'10" is not a valid coordinate. It usually means the decimal part of a DD value was copied as minutes: 40.75° is 40°45', not 40°75'. The reverse mistake does more damage: reading 40°26' as 40.26° moves the point about 19 km, because 26 minutes is 0.4333 of a degree.

A missing minus sign. Drop the minus from Pittsburgh's longitude and 79.982195° E puts the point in western China. When you copy coordinates between programs, check the sign on every southern latitude and western longitude, or keep the letter.

Decimal commas. Many countries write decimals with a comma, but coordinate tools expect a dot. Google's help page marks comma decimals as incorrect. The ArrayKit converter reads a comma as the decimal point only when it is the only separator, as in 40,446195, and shows an error for anything it could read two ways, such as 40,446,195 or a value that mixes commas and dots.

The wrong datum. Coordinates are measured against a datum, a model of the Earth's shape. GPS and web maps use WGS 84, but older paper maps often use a local datum such as NAD27 in North America or OSGB36 in Great Britain, and the same numbers on a different datum can mark a spot tens or even hundreds of metres away.

Converting with the Coordinate Converter

The Coordinate Converter converts one latitude and longitude pair at a time. Pick the input notation (Decimal, DMS or DDM) and type each axis in its own box. It shows the other two notations for each axis with copy buttons, a signed decimal pair such as -33.8568, 151.2153 for pasting into Google Maps, and a link to the point in the Coordinate Map Viewer. Switching notation rewrites your values in the new format, and four presets load the places used in this guide.

• Flexible input. It reads ° ′ ″, plain ' and ", the units d, m and s, or just spaces, as in 33 51 24.5 S. One hemisphere letter can go before or after the number and must suit the box: N or S for latitude, E or W for longitude. A minus sign that contradicts the letter, as in -33.8568 N, is an error. In 40d26m46.3s the s is the seconds unit, so that value is north; 40d26m46.3s S is south.
• Range checks. Latitude must be between -90 and 90, longitude between -180 and 180, and minutes and seconds below 60. Each box takes one value, so a latitude and longitude pasted together are rejected. Anything else it can't read shows an error instead of a result.
• Output precision. Decimal degrees are shown to six places (about 11 cm), DMS to a tenth of a second (about 3 m) and DDM to a thousandth of a minute (about 1.9 m). A rounded 60 carries into the next minute or degree.
• Match the notation to your input. DMS mode also accepts decimal degrees and decimal minutes. Decimal mode takes exactly one number per box and DDM mode at most two, so a DMS value typed there shows an error rather than losing its minutes or seconds; switch to DMS instead.

The conversion is plain arithmetic in your browser, and nothing you type is uploaded. It changes notation only: it assumes WGS 84 and does not convert between datums.

Frequently asked questions

How do I convert DMS to decimal degrees? Add the degrees, the minutes divided by 60 and the seconds divided by 3,600, then make the result negative for S or W. For example, 40°26'46"N is 40 + 26/60 + 46/3600 = 40.446111.

How do I convert decimal degrees to DMS? Keep the whole degrees, multiply the decimal part by 60 for the minutes, then multiply the remaining decimal by 60 for the seconds. So 151.2153 becomes 151° and 12.918 minutes, which is 151°12'55.1"E.

Does latitude or longitude come first? Latitude comes first in everyday use, in Google Maps and on most forms. GeoJSON and KML put longitude first, so check the order whenever data moves between a file and a map.

What does a negative latitude or longitude mean? A negative latitude is south of the equator, and a negative longitude is west of the prime meridian. In DMS and DDM the minus sign becomes an S or a W, so -79.982195 is written 79°58'55.9"W.

What is the difference between DMS and DDM? Both start with whole degrees. DMS adds whole minutes and seconds, as in 33°51'24.5", while DDM gives minutes with a decimal fraction and no seconds, as in 33°51.408'. DDM is common on GPS receivers and in geocaching, and DMS on maps and in surveying.

Keep going

• Coordinate Converter — convert latitude and longitude between DD, DMS and DDM.
• Coordinate Map Viewer — plot a coordinate on a map, or click the map to read one.
• Distance Between Coordinates — how far apart two points are.
• UTM Converter — convert latitude and longitude to UTM and back.
• Geo Tools — every map and coordinate tool on ArrayKit.
• Ohm's Law and Electrical Power, Explained — another formula guide, for voltage, current and resistance.

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