The 20-kilometre typo
This is the coordinate mistake that actually happens, and it is invisible at every stage after it is made.
40° 26′ 46″ N in decimal degrees is 40.4461. Read the digits straight across and you get 40.2646. Those two points are about 20 kilometres apart.
The reason nothing catches it is that 40.2646 is a perfectly valid latitude. It plots. It passes every range check. A mapping tool will happily show you a place, and it will be the wrong place, twenty kilometres from where you meant.
The mistake is easy because the two notations look similar in a hurry: one has the same digits with different punctuation. It is common in copied addresses, in data entered from a photograph of a sign or a document, and in spreadsheets where the degree symbols have been stripped somewhere upstream.
The tool computes that distance for whatever coordinate you enter, rather than quoting the 20 km figure as a general claim — because how far the error puts you depends on the coordinate, and seeing it for your own numbers is more useful than reading about someone else’s.
Minutes are sixtieths, not tenths
The whole misreading comes from one structural fact: this is a sexagesimal notation. A degree is 60 minutes and a minute is 60 seconds, inherited from Babylonian arithmetic by way of astronomy — the same structure as hours, minutes and seconds of time, for the same historical reason.
So the decimal fraction is not the minutes. 40.5° is 40° 30′, because half a degree is thirty minutes. 40.5° is not 40° 50′, and 40° 50′ is 40.8333°.
To convert by hand, divide and add: degrees + minutes/60 + seconds/3600. For 40° 26′ 46″ that is 40 + 0.4333 + 0.0128 = 40.4461. Going the other way, take the whole degrees, multiply the remainder by 60 for the minutes, and repeat for the seconds.
One arithmetic detail the tool handles and hand conversion often does not: rounding can push the seconds to exactly 60, which is not a legal value. It has to carry into the minutes, and if the minutes then reach 60 they carry into the degrees. A coordinate printed as 40° 59′ 60″ is a rounding bug rather than a place.
Latitude 118 is a longitude
Latitude runs from −90 at the south pole to +90 at the north. Longitude runs from −180 to +180, meeting itself at the antimeridian. Those ranges are different, and the difference is a useful error check.
A latitude of 118 is not a coordinate at all — it is almost always a longitude that has landed in the wrong field, which happens whenever a pair is pasted in the opposite order to the one expected. It is worth knowing that some systems write latitude first and others longitude first, and that the two conventions are both common: geographic notation and most APIs use lat-lon, while GeoJSON and several mapping libraries use lon-lat.
This tool refuses a latitude above 90 and says what it probably is, rather than rejecting it as merely invalid — because knowing which mistake you made is more useful than knowing that you made one.
The transposition is only detectable when the longitude exceeds 90. A pair like (40, 30) is valid in either order and silently plots somewhere else entirely, which is the same class of failure as the digits-run-together typo and has the same defence: check against a map before trusting it.
How many decimals you need
Decimal places on a coordinate correspond to real distances, and knowing the scale stops both over- and under-quoting.
At the equator, one degree of latitude is about 111 km. So:
- 2 decimals (40.45) — about 1.1 km. A town.
- 3 decimals (40.446) — about 110 m. A city block.
- 4 decimals (40.4461) — about 11 m. A building.
- 5 decimals (40.44611) — about 1.1 m. A doorway.
- 6 decimals — about 11 cm, which is finer than consumer GPS can measure.
Longitude is different: a degree of longitude shrinks as you move away from the equator, from 111 km down to nothing at the poles. At 50° north it is about 71 km, so the same number of decimals buys more precision there.
Quoting more than six decimals is quoting precision the measurement does not have. A phone GPS is typically accurate to a few metres at best, so anything past five decimals is describing noise — and it looks authoritative, which is worse than being obviously rough.
Doing it in a spreadsheet
With degrees, minutes and seconds in three columns, decimal degrees is =D+M/60+S/3600, then multiplied by −1 for south or west. Going back from a decimal in A1: =INT(A1) for the degrees, =INT((A1-INT(A1))*60) for the minutes, and =((A1-INT(A1))*60-INT((A1-INT(A1))*60))*60 for the seconds.
Two things bite in practice. Store coordinates as text or as numbers with enough decimals — a default cell format showing two places will round 40.4461 to 40.45 on screen while keeping the full value, and someone will eventually copy what they see rather than what is stored.
And watch the degree symbol. A coordinate pasted as 40° 26' 46" N is text, not a number, and any arithmetic on it silently returns zero or an error. Splitting it needs a formula over the symbols, and the apostrophe and quote marks are frequently smart-quoted, so a naive split on ' misses them.
Sources and methodology
Nothing here is fetched and there is no data feed. The conversion is exact arithmetic on sixtieths. What the sources settle is what the numbers mean: the representation and sign conventions from ISO 6709, and the point this page cannot help with — that a coordinate pair is meaningless without a datum, and the same physical point has different coordinates in different ones.