Coordinates Converter — Decimal Degrees and DMS

Background.

Copy a location out of a phone's map app and you get something like −1.286389, 36.817222. Read the same spot off an older topographic sheet, a nautical chart or a climbing guide and it is more likely to be printed 1° 17′ 11″ S, 36° 49′ 2″ E. Both describe the same two angles. Decimal degrees put each angle into one signed number; degrees, minutes and seconds (DMS) break it into sixtieths, the way a clock breaks an hour into minutes and seconds, and swap the minus sign for a compass letter.

The arithmetic between them is short, yet three mistakes keep turning up. One is reading the digits after a decimal point as minutes: 1.17° is not 1° 17′, and confusing the two moves a point about 12.6 km. Another is keeping a minus sign and a hemisphere letter together, so that −1° 17′ S gets read as north of the equator. The third is swapping latitude and longitude, because different software lists the pair in different orders.

To keep those errors out, the converter handles one labelled component at a time: you say whether the angle is a latitude or a longitude, and it attaches the matching letter, N or S for latitude and E or W for longitude. It also holds each to its geographic range. Latitude ends at 90° at either pole and longitude at 180° on the antimeridian in the Pacific, so a latitude of 120° is refused even though 120° is an ordinary angle in geometry.

What no notation change can do is move a point onto a different datum. A position surveyed on Kenya's older Arc 1960 datum, or on NAD27 in North America, is still on that datum after you rewrite its digits, and it will not line up exactly with the WGS 84 coordinates a GPS receiver reports. Nor can extra decimal places make a position more accurate than the receiver or map that produced it.

What is coordinates converter?

Latitude is the angle north or south of the equator, from 0° on the equator to 90° at each pole. Longitude is the angle east or west of the prime meridian through Greenwich, running to 180° in each direction until the two halves meet on the antimeridian. Each is a single angle, and a coordinate pair is two of them.

In decimal degrees the angle is one number with a sign: positive for north and east, negative for south and west. In DMS the same angle is split into whole degrees, arcminutes (each 1⁄60 of a degree) and arcseconds (each 1⁄60 of a minute, so 1⁄3,600 of a degree), and the direction moves into a letter. Degrees and minutes are whole numbers; only the seconds carry decimals. A hybrid form, degrees and decimal minutes such as 1° 17.1833′ S, is common on handheld GPS units and marine electronics and converts by the same sixties.

A value of exactly zero sits on the dividing line itself. The converter labels 0° of latitude N and 0° of longitude E, since zero has no negative direction to report.

How to use this calculator.

1. 01Choose the direction: decimal degrees to DMS if you are starting from a phone, a web map or a spreadsheet; DMS to decimal if you are starting from a chart, a printed guide or a survey listing.
2. 02Set the component to latitude or longitude before typing. It decides the allowed range, ±90° or ±180°, and which pair of letters can appear.
3. 03For decimal input, type the number with its sign exactly as given, for example −1.286389. If your source writes 1.286389 S instead, enter it as negative. When converting a latitude, make sure the whole-degrees box below is not holding a leftover value above 90, because those boxes are still checked in this mode.
4. 04For DMS input, enter whole degrees with no sign, whole minutes from 0 to 59, seconds below 60 with any decimals you have, and the letter. If your source gives decimal minutes such as 17.1833′, enter 17 as the minutes and multiply 0.1833 by 60 to get the seconds, 10.998 here.
5. 05Read the result, then cut digits to suit the source. Six decimals of a degree, or two decimals of a second, already resolve finer than a phone can locate you.

The formula.

DMS to decimal is a weighted sum: decimal = sign × (D + M ÷ 60 + S ÷ 3,600), where D is whole degrees, M arcminutes and S arcseconds, and the sign is +1 for N or E and −1 for S or W. Thirty minutes add 0.5°; thirty seconds add only 0.008333°.

Decimal to DMS runs the same steps backwards on the absolute value. Keep the whole part as degrees. Multiply what is left by 60 and keep the whole part of that as minutes. Multiply the remaining fraction by 60 again for the seconds. The letter comes from the original sign and the component you chose: a negative latitude becomes S, a negative longitude W.

Two boundary rules keep the output well formed. Seconds are carried to ten decimal places, and if a value sitting a hair below a whole minute rounds to 60 seconds, the seconds become 0 and the minutes go up by one; 60 minutes roll into the next degree in the same way, so a result never reads 59′ 60″. At the extremes, 90° of latitude and 180° of longitude, nothing can be added on: a pole is a single point and anything beyond 180° would be past the antimeridian, so minutes and seconds must both be zero there.

What the units mean on the ground explains why the digits matter. On a sphere of the Earth's mean radius, 6,371 km, one degree of latitude spans about 111.2 km, one arcminute about 1,853 m, close to the 1,852 m nautical mile that was originally defined as a minute of latitude, and one arcsecond about 30.9 m. A degree of longitude covers that full distance only on the equator; it shrinks with the cosine of the latitude, to about 55.6 km at 60° north or south.

A worked example.

Frequently asked questions.

References& sources.

1. [1]USGS/NASA Technical Methods 11-E1 §§2.33–2.35 publishes decimal-degree and DMS conversion procedures.
2. [2]FCC Degrees, Minutes, Seconds to/from Decimal Degrees independently gives D + M/60 + S/3600.
3. [3]NGA coordinate-system reference documents sexagesimal coordinate notation and hemispheres.
4. [4]ISO 6709:2022 defines standard representation of geographic point locations by coordinates.
5. [5]EPSG Guidance Note 7 explains that datum, coordinate reference system and axis order are separate from numeric notation.