Coordinates Converter

Paste coordinates in any format, with degree signs or without, letters before or after, one coordinate or a lat long pair. This converts between decimal degrees, degrees minutes seconds, and the decimal-minutes format GPS units use, shows the arithmetic, and tells you what your precision is actually worth on the ground. Every coordinate is converted on your device and sent nowhere.

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You are reading a 4,000 year old number system

Every GPS coordinate on Earth is written in base 60, the counting system of ancient Mesopotamia. The Sumerians counted in sixties five thousand years ago, the Babylonians built their astronomy on it, and when Ptolemy divided each degree of a circle into 60 partes minutae primae (first small parts) and each of those into 60 partes minutae secundae (second small parts), he named our units for us. "Minute" is the first small part. A "second" is called a second because it is the second division by sixty. The phone in your pocket resolves your position using clay-tablet arithmetic, and this page does that arithmetic in the open.

The formula

decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3600
and back: whole degrees, then remainder × 60 for minutes, then remainder × 60 again for seconds

Worked example

40° 26′ 46″ N, 79° 58′ 56″ W converts as 40 + 26/60 + 46/3600 = 40.446111° latitude, and 79 + 58/60 + 56/3600 = 79.982222, written -79.982222° because west of Greenwich is negative.

Paste-ready for any mapping site: 40.446111, -79.982222

Same three numbers, three different places

Here is the trap that makes a converter worth having. The digits 40, 26, 46 are a different point on Earth in each of the three coordinate formats in daily use:

Read asWrittenIn decimal degrees
Degrees, minutes, seconds40° 26′ 46″40.446111°
Degrees and decimal minutes40° 26.46′40.441°
Decimal degrees40.2646°40.2646°

The first two are 568 meters apart. The third is 20.2 kilometers from the first, which is twelve and a half miles from the same three numbers. The middle format, degrees and decimal minutes, is what most GPS units and aviation charts use, and it is the one that causes the accidents: type 46 seconds into a box expecting decimal minutes as .46 and you have quietly moved yourself 568 meters. Geocachers call this the classic DNF. Pilots have less affectionate names for it. Nothing about the digits warns you; only the punctuation knows.

The nautical mile is a Babylonian minute

One minute of latitude is one nautical mile. That is not a coincidence, it is the original definition: sailors needed a distance unit that matched the coordinate grid, so they took the minute of arc itself. When the international nautical mile was fixed at exactly 1,852 meters in 1929, the planet's own mean minute of latitude came out at 1,852.2 meters, so the round number landed within 20 centimeters of the thing it was named for. It also means every ship's speed is sexagesimal: a knot is one Babylonian minute of planet per hour.

How many decimals do you actually need

Decimal degrees invite false precision, so here is what each decimal place of latitude is worth on the ground:

Decimal placesMoves you aboutEnough to find
111.1 kma city
21.1 kma neighborhood
3111 ma street
411 ma building
51.1 ma doorway
611 cma floor tile
71.1 cma coin
81.1 mma grain of sand

A phone GPS is accurate to roughly 3 to 5 meters, so the fifth decimal place is where its honesty ends. Coordinates get pasted around the internet with thirteen decimals, and the thirteenth decimal place of a degree is about 11 nanometers, which is smaller than a virus. The device is not wrong, it is just answering a question nobody asked, in a format that cannot say "roughly."

Why 360, and why the decimal replacement failed

Babylonian astronomers used a schematic year of 360 days, so the Sun moved about one degree a day along its circle, and 360 stuck because it is spectacularly divisible: halves, thirds, quarters, fifths, sixths, eighths, ninths, tenths and twelfths all come out even, with 24 divisors in total. The French Revolution tried to fix all of it, with a 400-degree circle (the gradian, still haunting a button on your calculator), 10-hour days and 100-minute hours. The decimal day lasted about 17 months. The Babylonian system is still here because being easy to divide turned out to matter more than being easy to write, and dividing is what navigators, surveyors and clockmakers actually do all day.

What this page does with your paste

It reads all three formats in either direction, with degree signs or without, letters before or after the numbers, commas or spaces, and it applies the rules that catch real mistakes: minutes and seconds must be under 60 (they are clock digits, and for the same reason your clock never shows 10:75), latitude cannot pass 90, longitude cannot pass 180, and south and west are negative. If you paste longitude first with the letters to prove it, it swaps them politely and says so. Everything is converted on your device; no coordinate you type here is sent anywhere, which seems like the least a page can offer people pasting in the location of their own house.

Frequently asked questions

How do I convert degrees minutes seconds to decimal degrees?

Degrees plus minutes divided by 60 plus seconds divided by 3600. So 40 degrees 26 minutes 46 seconds is 40 + 26/60 + 46/3600 = 40.446111. South latitudes and west longitudes take a minus sign. Going the other way, keep the whole degrees, multiply the remainder by 60 for minutes, and multiply that remainder by 60 again for seconds. It is base-60 arithmetic, unchanged since Babylonian astronomers invented it.

What are the three coordinate formats?

Decimal degrees (40.446111), which mapping sites and programmers use; degrees minutes seconds (40 deg 26 min 46 sec), the traditional form on charts and monuments; and degrees with decimal minutes (40 deg 26.767 min), which most GPS units, geocaching listings and aviation use. The same digits mean different places in each format, which is why mixing them up is the classic navigation error, and why this page accepts all three and always shows all three.

Why are coordinates in base 60?

Because Babylonian astronomers worked in base 60 and divided the circle into 360 degrees, and Ptolemy divided each degree into 60 first small parts, partes minutae primae, and each of those into 60 second small parts, partes minutae secundae. Those Latin names are literally where the words minute and second come from: a second is the second division by sixty. The system survived because 60 and 360 divide evenly by almost everything, which mattered enormously before decimal fractions existed.

Why is west longitude negative?

By convention, coordinates are signed from the two zero lines: north of the equator and east of the Greenwich meridian are positive, south and west are negative. So a minus sign and a W mean the same thing, and this converter treats them identically. The order convention matters too: latitude first, longitude second, which is why pasting a US location with the longitude first produces an impossible latitude over 90 and a polite correction rather than a wrong answer.

How accurate is a GPS coordinate?

A phone GPS is typically accurate to 3 to 5 meters in the open, and the fifth decimal place of a decimal degree is about 1.1 meters, so five decimals captures everything a phone honestly knows. One second of arc is about 31 meters of latitude, one minute is about 1.85 kilometers, and a whole degree is about 111. Digits past the fifth decimal describe the file format rather than your position; the thirteenth decimal, which pasted coordinates sometimes carry, is 11 nanometers.

Is a nautical mile really a minute of latitude?

Yes, that is its original definition, and it is why the unit exists at all: sailors wanted distance and position on the same grid. The modern international nautical mile is exactly 1,852 meters, fixed in 1929, and the planet's actual mean minute of latitude works out to 1,852.2 meters, so the round definition landed within 20 centimeters of the real thing. A knot, one nautical mile per hour, is therefore one Babylonian minute of arc per hour.

Does this converter send my coordinates anywhere?

No. The conversion runs entirely in your browser and nothing you type is transmitted, logged or stored by us. That is worth saying plainly because coordinates are often somebody's home. It is also why this page deliberately has no map preview: showing a map would mean sending your coordinates to a map provider, and the arithmetic does not need one.

What is the most common coordinate conversion mistake?

Format confusion, and it is worth real distance. Reading 40 deg 26.46 min (decimal minutes) as 40 deg 26 min 46 sec moves you 568 meters, since 46 seconds is 0.767 minutes, not 0.46. And reading the bare digits 40.2646 as degrees-minutes-seconds moves you about 20 kilometers. The digits carry no warning; only the punctuation says which system you are in, which is exactly the kind of thing a 4,000 year old convention gets to do.

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