The three formats, and who uses which
A coordinate is written three ways and all three say the same thing:
- Decimal degrees: 40.4168. What phone maps and databases use, because it is a number and can be sorted and subtracted.
- Degrees and decimal minutes: 40° 25.008′. The format of navigation and aviation, and not by whim: one minute of latitude is exactly one nautical mile, so distance can be read straight off the chart.
- Degrees, minutes and seconds: 40° 25′ 0.48″. The one on land registries, old maps and survey markers.
Converting between them is sexagesimal arithmetic: sixty minutes to a degree and sixty seconds to a minute, the same as a clock. This page accepts all three as input and returns all three, so it does not matter how the coordinate arrives.
The sign, the letter and the 28-kilometre mistake
The hemisphere is marked two ways and you can only use one: with a letter (N, S, E, W) or with a sign, where north and east are positive. «3° W» and «−3°» are identical; «−3° W» is a point in the opposite hemisphere to the one you wanted.
The most expensive mistake is a different one, and it has nothing to do with the sign: reading 40 25 00 as though it were 40.25 degrees. It is not. Twenty-five minutes is 0.4167 degrees, not 0.25, so the gap is 0.1667 degrees of latitude — about eighteen and a half kilometres. With seconds involved the drift reaches twenty-eight. It is why a point pasted into a spreadsheet sometimes lands in the middle of a field.
Converting by hand
From decimal to degrees, minutes and seconds:
- The degrees are the whole part: in 40.4168, that is 40.
- The decimal part times 60 gives the minutes: 0.4168 × 60 = 25.008 → 25.
- What is left times 60 gives the seconds: 0.008 × 60 = 0.48.
And back the other way by dividing: 25 minutes by 60 and 0.48 seconds by 3,600, added to the 40 degrees.
What is worth knowing
Latitude always goes first. It is the cartographic convention, what search engines expect and what GPS units use, and swapping them produces no error at all: it produces a perfectly valid point somewhere else. Madrid with its coordinates reversed lands in the Alboran Sea.
On decimals: one degree of latitude is about 111 kilometres anywhere on the planet, so three decimals locate a block, five a doorway and six a metre. In longitude it depends on latitude, because the meridians converge towards the poles: a degree is 111 kilometres at the equator and under eighty in Madrid. Copying more decimals than the original measurement had adds no precision, only the appearance of it.