DMS to Decimal Degrees Converter

40°41′22″ N, 74°02′41″ W is 40.689444, −74.044722

To turn degrees, minutes and seconds into decimal degrees, add the degrees, the minutes divided by 60 and the seconds divided by 3,600, and put a minus sign in front of the whole sum for south and west. The Statue of Liberty is listed by UNESCO at N40 41 22, W74 2 41. For the latitude, 40 + 41 ÷ 60 + 22 ÷ 3,600 = 40.689444…, and for the longitude, −(74 + 2 ÷ 60 + 41 ÷ 3,600) = −74.044722…, so the pair is 40.689444, −74.044722.

The other direction works by multiplying the fraction by 60 twice. In 37.5665°, the whole number 37 is the degrees. Then 0.5665 × 60 = 33.99, so 33 is the minutes, and the remaining 0.99 × 60 = 59.4 is the seconds. That makes 37.5665° equal to 37°33′59.4″, or 37°33.99′ if you stop at decimal minutes.

The converter above shows decimal degrees (DD), degrees and decimal minutes (DDM) and degrees, minutes and seconds (DMS) for both latitude and longitude, six fields in all. Type into any field and the other five follow; a field that had to be rounded shows "≈". You can paste a whole pair such as "37.5665, 126.978", or type "37 33 59.4 N" without symbols. The magnifier below the fields narrows a world map down to a 1° cell, a 1′ cell and a 1″ cell, and draws how many kilometers or meters each of them covers on the ground at that latitude.

When you need to change the notation

• Moving a map-app coordinate into a document: map apps hand you decimals such as 40.689444, −74.044722, while survey records, legal descriptions and reports are often written as 40°41′22″ N. Both forms name the same point, so you only need to match the style the recipient expects.
• Searching a map for coordinates given in DMS: Google Maps Help says you can type decimal degrees (41.40338, 2.17403), degrees, minutes and seconds (41°24'12.2"N 2°10'26.5"E) or degrees and decimal minutes (41 24.2028, 2 10.4418) into the search box. One misplaced symbol can send you to the wrong place, so converting to decimals first is the safer habit.
• GPS units and marine charts: the degrees and decimal minutes format, such as 37°33.990′, looks a lot like DMS and is easy to misread. The 33.99′ in it is 33 minutes and 59.4 seconds, not 33 minutes and 99 seconds.
• Data files and spreadsheets: GeoJSON (RFC 7946) stores positions as longitude first, then latitude, while a map search box expects latitude first. If you move values between the two, swap them. For long lists, use "Many coordinates at once" or the spreadsheet formulas below.

How to use it

1. Type the value into the field that matches your format: DD for decimals, DDM when the minutes have a decimal part such as 37°33.99′, and DMS when degrees, minutes and seconds are all present. A value typed into a different format is still read correctly, and when you leave the field it is rewritten in that field's format.
2. If you have latitude and longitude as one pair, paste it into any field. Pairs separated by a comma, semicolon, tab or line break are read, and if N, S, E, W or the words north, south, east and west are present, they decide which value is the latitude and which is the longitude.
3. For south and west, put a minus sign in front in a decimal field. In the degrees-and-minutes and DMS fields, write S or W, or press the N|S or E|W button at the head of the column. A DMS value without a letter follows that button.
4. Under "Precision," choose how many decimals the seconds get. At 0.01″ the DMS field shows two decimals of a second, the DDM field four decimals of a minute and the decimal field six decimals of a degree. Under "Symbols," the ° ' " option gives the unspaced style used in the Google Maps help examples.
5. The copy button at the end of each row copies that format's latitude and longitude as one pair. The "Google Maps" and "OpenStreetMap" buttons open a map with a marker on that coordinate in a new tab.
6. On the magnifier, clicking the world map changes the degree, clicking the 1° cell changes the minute, clicking the 1′ cell changes the second and clicking the 1″ cell changes the fraction of a second. With a figure selected, the arrow keys move it by 1°, 1′, 1″ or 0.1″.

How the calculation works

Decimal degrees to DMS

Take the absolute value. Its whole part is the degrees. Multiply the remaining fraction by 60, and the whole part of that is the minutes. Multiply what is left by 60 again to get the seconds. The sign becomes a letter at the end: a negative latitude is S and a negative longitude is W.

1. For −33.8568, the whole part of 33.8568 gives 33 degrees.
2. 0.8568 × 60 = 51.408, so the minutes are 51.
3. 0.408 × 60 = 24.48 seconds. The latitude was negative, so the result is 33°51′24.48″ S.

DMS to decimal degrees

The size is degrees + minutes ÷ 60 + seconds ÷ 3,600. For south and west, apply the minus sign to the whole sum. South Korea's datum origin has the latitude 37°16′33.3659″, which gives 37 + 16 ÷ 60 + 33.3659 ÷ 3,600 = about 37.27593497°. Dividing seconds by 3,600 often gives a decimal that never ends, because 3,600 contains the prime factor 3. In that case the converter rounds at the precision you chose and marks the result with "≈".

Degrees and decimal minutes

Degrees and decimal minutes is degrees + minutes ÷ 60. So 37°33.99′ is 37 + 33.99 ÷ 60 = 37.5665°, and since 0.99′ × 60 = 59.4″ it is the same point as 37°33′59.4″. Never read the digits after the decimal point of the minutes as seconds.

Rounding and carrying

The converter keeps each coordinate as an exact whole number of seconds divided by a power of ten and rounds only once, at the last digit shown. That is why 37°59′59.996″ shown with two decimals of a second does not become 59.996″ rounded to 60.00″ but carries over to 38°00′00.00″. If you round degrees, minutes and seconds separately you can end up with "59′60″", so when working by hand it is safer to round the whole value first and split it afterward.

How far is 1°, 1′ and 1″ on the ground

One degree of latitude is about 111 km north to south everywhere. Because the Earth is flattened toward the poles, it is a little shorter at the equator (110.57 km) than near the poles (111.69 km). One degree of longitude shrinks as you move away from the equator: 111.32 km at the equator, 55.80 km at 60° latitude, roughly half, and zero at the pole. This is why the cells on the magnifier are not squares but rectangles that get narrower with latitude.

The table below uses the GRS80 ellipsoid (semi-major axis 6,378,137 m, inverse flattening 298.257222101) and gives the lengths at each latitude. The WGS 84 ellipsoid used by GPS differs only in the last digits of the inverse flattening (298.257223563), which makes no difference at the precision shown.

How many decimals do you need

The number of decimals in a decimal-degree coordinate sets the size of the cell it points to. Near latitude 40°, which passes close to New York and Madrid, four decimals (0.0001°) mark a cell about 11 m north-south and 8.5 m east-west, five decimals about 1.1 m and six about 11 cm. Five decimals are plenty for naming a building entrance or a parking spot, and more digits only mean something if the instrument that took the measurement is that accurate. Showing extra digits in the converter does not make the original position any more precise.

In DMS, 1″ is about 30.8 m north-south, one decimal of a second (0.1″) about 3.1 m and two decimals (0.01″) about 31 cm. The "Precision" buttons 1″, 0.1″, 0.01″ and 0.001″ correspond to these distances (hover over a button to see it), and the dashed box on the magnifier outlines the cell that the digits you entered point to, drawn at your latitude.

Latitude and longitude: order and sign

Google Maps Help tells you to enter latitude first and longitude second, and to use a period, not a comma, as the decimal separator. GeoJSON (RFC 7946) does the opposite and defines the first two values of a position as longitude and latitude "precisely in that order." So the same place can appear in a different order in a file and in a search box.

• Latitude runs from −90° to 90° and longitude from −180° to 180°. If the first value is above 90, the longitude must have come first, and the converter offers "Read swapped."
• When both values are 90 or below, the numbers alone cannot tell you the order. The world map on the magnifier also shows where the swapped reading would land as a dashed circle, so if your point falls in an odd stretch of ocean, suspect the order.
• If N, S, E and W are present, they are read as written regardless of order. "E 126.978 N 37.5665" is still latitude 37.5665 and longitude 126.978.
• In decimal form, north and east are positive and south and west are negative. The international standard for representing geographic point locations is ISO 6709:2022.

Excel and Google Sheets formulas

The "Excel and Google Sheets formulas" section of the converter builds the formulas with your chosen precision and symbols, and shows the result for your current coordinate. Both formulas use the same function names in Excel and Google Sheets. In locales where Excel expects a semicolon between arguments, replace the commas with semicolons.

• Four columns to decimal degrees: with degrees in B2, minutes in C2, seconds in D2 and N, S, E or W in E2, use =(B2+C2/60+D2/3600)*IF(OR(E2="S",E2="W"),-1,1). Only a direction of S or W multiplies the whole sum by −1.
• Decimal degrees to DMS text: first round the total seconds with ROUND(ABS(A2)*3600,2), then split that into degrees, minutes and seconds. Doing it in this order keeps the seconds from ever reaching 60. The sign becomes a letter with IF(A2<0,"S","N").
• Cutting a negative value directly with INT turns −33.8568 into −34, and the result of MOD has the same sign as the divisor, according to Microsoft, so minutes and seconds go wrong for negative coordinates. That is why the formula takes ABS first.

Coordinates written in law: national datum origins

Some countries fix the starting point of their survey in a statute. In South Korea, the Enforcement Decree of the Act on the Establishment and Management of Spatial Data, Article 7, gives the national datum origin as 127°03′14.8913″ E, 37°16′33.3659″ N, which is about 127.05413647°, 37.27593497° in decimals. The converter's example list includes this point, and the seconds are given to four decimals because the figure is the reference for surveying; everyday map coordinates need far fewer digits.

Japan does the same in Article 2 of the Survey Act Enforcement Order: 139°44′28.8869″ E, 35°39′29.1572″ N, about 139.74135747°, 35.65809922°. Four decimals of a second is about 3 mm on the ground.

Common mistakes

• Reading 37.5° as 37°50′: the fraction 0.5 is 0.5 × 60 = 30 minutes, not 50.
• Putting the minus sign on the degrees only: for 12°30′ S, −12 + 30 ÷ 60 = −11.5 is wrong. The sign goes on the whole sum: −(12 + 0.5) = −12.5°.
• Forgetting west of 0°: with 0°30′ W there seems to be no degree to carry a minus sign. The value is −0.5°, and dropping the letter turns it into 0.5° east.
• Reading degrees and decimal minutes as DMS: in 37°33.99′, the .99 is 0.99 of a minute (59.4 seconds), not 99 seconds.
• Using a comma as the decimal point: written as 37,5665, 126,978, a map search reads four numbers. In coordinates, the decimal separator is a period.
• Swapping latitude and longitude: GeoJSON and some data files put longitude first. Check the column names (lat, lon, latitude, longitude).

Limits

• It only changes how an angle is written. It does not convert between datums (an older national datum and WGS 84, for example) or to projected coordinates such as X and Y in meters.
• It does not find a coordinate from an address or an address from a coordinate. The "Google Maps" and "OpenStreetMap" buttons open that service at the point.
• The world map on the magnifier is the Natural Earth 1:110m outline, so coastlines are simplified. The 1°, 1′ and 1″ cells show the length at that latitude and do not draw the small differences across a cell.
• Input is read up to 15 decimal places. The number of digits shown says nothing about how accurate the measurement was.
• Coordinates are calculated in your browser on this device and are not sent to a server. "Copy link" puts the coordinates after the # in the address, and opening that link removes them from the address bar right away.

Basis: the relation between angle units (1° = 60′ = 3,600″) is a definition and does not change. The Korean Enforcement Decree, Article 7 and the Japanese Survey Act Enforcement Order, Article 2 were checked on October 21, 2026 and are the current text. The Google Maps Help page, RFC 7946, ISO 6709 and the UNESCO World Heritage List coordinates were checked against the originals on the same day.

Sources

• 01Google Maps Help: Search by latitude & longitude in Google MapsDMS 41°24'12.2"N 2°10'26.5"E, DDM 41 24.2028, 2 10.4418, decimal 41.40338, 2.17403, latitude first, period as decimal point
• 02RFC 7946 The GeoJSON Format, 3.1.1 PositionThe first two values are longitude and latitude, "precisely in that order"
• 03ISO 6709:2022 Standard representation of geographic point location by coordinatesInternational standard for geographic point locations (3rd edition, 2022)
• 04Google Maps URLssearch action https://www.google.com/maps/search/?api=1&query=latitude,longitude
• 05OpenStreetMap Wiki: Browsingmlat and mlon parameters place a red marker
• 06Microsoft Support: MOD functionThe result has the same sign as the divisor
• 07EPSG:7019 Ellipsoid GRS 1980Semi-major axis 6,378,137 m, inverse flattening 298.257222101
• 08EPSG:7030 Ellipsoid WGS 84Inverse flattening 298.257223563
• 09Korea Law Information Center: Enforcement Decree of the Act on the Establishment and Management of Spatial Data, Article 7Ellipsoid figures and the national datum origin 127°03′14.8913″ E, 37°16′33.3659″ N (in force 2026-07-01; text in Korean)
• 10e-Gov Laws: Survey Act Enforcement Order, Article 2Japan's datum origin 139°44′28.8869″ E, 35°39′29.1572″ N (text in Japanese)
• 11UNESCO World Heritage List: Statue of LibertyN40 41 22 W74 2 41
• 12UNESCO World Heritage List: Sydney Opera HouseS33 51 24 E151 12 55
• 13UNESCO World Heritage List: Historic Sanctuary of Machu PicchuS13 11 5.762 W72 32 0.395
• 14Natural Earth: Terms of UseWorld outline on the magnifier (1:110m land), public domain

Frequently asked questions

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