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
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 as | Written | In decimal degrees |
|---|---|---|
| Degrees, minutes, seconds | 40° 26′ 46″ | 40.446111° |
| Degrees and decimal minutes | 40° 26.46′ | 40.441° |
| Decimal degrees | 40.2646° | 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 places | Moves you about | Enough to find |
|---|---|---|
| 1 | 11.1 km | a city |
| 2 | 1.1 km | a neighborhood |
| 3 | 111 m | a street |
| 4 | 11 m | a building |
| 5 | 1.1 m | a doorway |
| 6 | 11 cm | a floor tile |
| 7 | 1.1 cm | a coin |
| 8 | 1.1 mm | a 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.