GPS Coordinates Explained: Decimal Degrees, DMS, and the Sign That Trips Everyone Up

A coordinate looks simple until you copy one out of Wikipedia, paste it into a map, and land in the wrong ocean. The number was fine. The format was not. GPS coordinates travel between charts, phone apps, spreadsheets, and code, and each of those wants a slightly different notation. If you have ever stared at 40°26′46″N next to 40.446111 and wondered whether they are the same place, this guide is for you.

The short answer: they are the exact same point. The longer answer is worth ten minutes, because once the two formats click, you stop second-guessing every coordinate you handle.

The two formats that describe the same point

There are two notations you will meet almost everywhere.

Degrees-minutes-seconds (DMS) writes a coordinate the old nautical way: 40°26′46″N. You read it as 40 degrees, 26 minutes, 46 seconds, north. Minutes and seconds here have nothing to do with time. A minute is one-sixtieth of a degree, and a second is one-sixtieth of a minute, which makes it one thirty-six-hundredth of a degree. DMS reads cleanly on a paper chart and in aviation, where people have quoted positions this way for centuries.

Decimal degrees (DD) writes the same place as a single number: 40.446111. No symbols, no hemisphere word, just a signed value. This is what software wants. Google Maps, GeoJSON, Leaflet, PostGIS, and basically every GPS library you will touch consume decimal degrees and nothing else.

Both describe the same latitude. The only difference is whether you break the fractional part into minutes and seconds or leave it as a decimal tail. Converting between them is arithmetic, not magic.

How minutes and seconds become a decimal

Here is the one rule that makes everything fall into place: minutes are the fractional degree multiplied by 60, and seconds are the fractional minute multiplied by 60. Going the other direction, you divide.

So to turn DMS into decimal degrees, you add the degrees, the minutes over 60, and the seconds over 3600:

decimal = degrees + minutes/60 + seconds/3600

Take 40°26′46″:

40 + 26/60 + 46/3600
= 40 + 0.433333 + 0.012778
= 40.446111

That is it. The N keeps the result positive, and you have decimal degrees ready to paste anywhere. To go back from decimal to DMS, you reverse the process: the whole part is the degrees, you multiply the remainder by 60 to get minutes, take the whole minutes, then multiply that remainder by 60 for the seconds.

If you would rather not do this by hand every time, the coordinate converter does both directions at once and shows all three notations side by side, including degrees-decimal-minutes, the in-between format that GPS devices love.

A worked example: New York City to DMS

Let's convert a familiar pair of decimal coordinates into DMS. Lower Manhattan sits at roughly 40.7128, -74.0060.

Start with the latitude, 40.7128:

Degrees: the whole part is 40.
Minutes: take the remainder 0.7128, multiply by 60: 0.7128 × 60 = 42.768, so 42 minutes.
Seconds: take the new remainder 0.768, multiply by 60: 0.768 × 60 = 46.08, so about 46 seconds.
The value is positive, so the hemisphere is N.

Latitude in DMS: 40°42′46″N.

Now the longitude, -74.0060. Work with the absolute value 74.0060 and remember the sign at the end:

Degrees: 74.
Minutes: 0.0060 × 60 = 0.36, so 0 minutes.
Seconds: 0.36 × 60 = 21.6, so about 22 seconds.
The original value was negative, so the hemisphere is W.

Longitude in DMS: 74°00′22″W.

Put together, 40.7128, -74.0060 is 40°42′46″N 74°00′22″W. Same rooftop, two outfits.

Where the minus sign comes from: N/S/E/W vs the sign

This is the part that flips more pins than anything else. In DMS, the hemisphere is a letter. In decimal degrees, the hemisphere is a sign.

North latitude and East longitude are positive.
South latitude and West longitude are negative.

So 33°51′54″S is not 33.865, it is −33.865. And 79°58′56″W is not 79.982, it is −79.982. The letter and the sign carry the same information; you just cannot keep both. When you strip the S or the W and forget to add the minus, your coordinate quietly jumps to the opposite hemisphere. A spot meant for Sydney ends up near the Arctic, and the map looks broken when really the sign was dropped.

This is also why a bare decimal like 79.982 is ambiguous on its own. Without context, it could be east or west of Greenwich. Decimal degrees only work because the sign is part of the number. If you ever import a dataset where every Western Hemisphere point lands in Asia, check whether someone wrote the longitudes as positive.

Reading coordinates off a map versus an app

The format you see depends on where you are looking.

Paper charts, surveying plats, and aviation documents almost always use DMS, sometimes degrees-decimal-minutes (40°26.767′N), which is degrees and minutes with a decimal tail but no seconds. Marine GPS units favor decimal minutes too. Phone apps and web maps lean the other way: long-press a spot in Google Maps and it hands you decimal degrees, 40.446111, -73.9819, latitude first, comma separated.

Two ordering rules save you most of the grief. Latitude always comes first, and latitude is bounded to ±90 while longitude runs ±180. If you see a value above 90 sitting in the latitude slot, the pair is almost certainly reversed. The equator is 0 latitude; the prime meridian through Greenwich is 0 longitude; the antimeridian out in the Pacific is ±180.

When you paste into Maps, the decimal pair is the most reliable input. DMS works too, but the decimal pair never gets misread.

A mistake I keep making

I will be honest: the format I get wrong most often is degrees-decimal-minutes. A GPS handheld once gave me 40°26.767′N and I typed 40.767 into my plotting tool without thinking, because the .767 looked like a decimal degree. That dropped me about 35 kilometers from where I meant to be, far enough that the route made no sense and I spent twenty minutes blaming the software. The .767 was minutes, not degrees. The fix is to convert the minutes properly: 26.767 / 60 = 0.4461, giving 40.4461°. Now I match the format before I touch the number, and I let a converter split the minutes for me instead of eyeballing it.

Precision, datums, and what conversion does not fix

Six decimal places of decimal degrees resolves to roughly 0.11 metre at the equator, which is plenty for map pins, geocaching, route planning, and marine or aviation plotting. Rounding seconds to one decimal place keeps DMS just as tight.

One thing format conversion does not do is shift datums. A WGS84 coordinate stays WGS84 whether you write it as DMS or decimal degrees; converting notation never moves the point on the Earth. If your source uses a national datum like OSGB36 or NAD27, you need a separate datum transformation, which is a different operation entirely. Changing the clothes is not the same as moving the body.

If you work with numbers in other systems too, the same "same value, different notation" idea shows up everywhere: a unit converter does it for length and mass the way a coordinate converter does it for latitude and longitude. Once you trust that the number is preserved and only the presentation changes, conversion stops feeling risky.

Coordinates are not hard. They are just written two ways, and the sign hides inside a letter. Keep latitude first, keep south and west negative, and remember that minutes and seconds are sixtieths, and you will never land in the wrong ocean again.

Made by Toolora · Updated 2026-06-13