Coordinate converter

Three spellings of the same place

A position on the earth is two numbers, and there are three conventional ways of writing them down. Nothing is gained or lost between them; they differ only in where the decimal point falls and how much of the value has been split off into smaller units.

Decimal degrees keeps it as one number per axis, with a minus sign for south and west. It is what mapping software, spreadsheets and nearly every published dataset use, because a single signed number is the easiest thing to compute with.

Degrees and decimal minutes splits off the whole degrees and expresses the remainder in minutes, of which there are sixty to a degree. This is what geocaching uses, on every mainstream listing service, in every listing you will read.

Degrees, minutes and seconds splits it once more, into sixty seconds to the minute. It is the oldest of the three; it is what you find on printed charts and in older writing, and it is the one most likely to appear in a source published before about 1990.

Why geocaching settled on the middle one

Degrees and decimal minutes is a compromise, and a sensible one for the job.

Seconds are awkward to read aloud and awkward to type, and a hobby built on people copying coordinates from a screen into a device does not want a third unit. Plain decimal degrees, on the other hand, gives no useful sense of scale: the difference between 51.4687 and 51.4692 does not announce itself as roughly fifty metres to anybody glancing at it.

Minutes sit in a range people develop a feel for. A minute of latitude is about 1,852 metres everywhere, and a tenth of a minute is about 185. After a season of caching, the gap between 28.123 and 28.140 reads as a distance rather than as arithmetic, which is exactly what you want when you are deciding whether two caches are worth doing on one walk.

The mistake that puts you a mile away

Nearly every serious coordinate error in this hobby is the same one: decimal minutes read as decimal degrees, or the reverse.

The two formats look alike. Both are a number, a point and some digits. But in N 51° 28.123 the part after the degree symbol is minutes, and in N 51.28123 it is a fraction of a degree. Twenty-eight minutes is a little under half a degree; 0.28 of a degree is nearly seventeen minutes. Confuse them and you are perhaps twenty kilometres from where you meant to be: far enough to be badly wrong, close enough to look plausible on a map.

Two checks catch it every time, and both are quick.

Minutes never reach 60. If the number after the degrees is 60 or more, it is not minutes, whatever the punctuation suggests. This is the check the tool above applies before it will accept anything.

Look at the shape of the degrees. A coordinate in decimal degrees has one number per axis and nothing after it. A coordinate in decimal minutes has two. If you are holding three numbers per axis, you have seconds.

How much precision is real

It is worth knowing where the useful digits stop, because tools will happily print more.

Three decimal places of a minute (the geocaching convention) is about 1.8 metres of latitude. Five decimal places of a degree is about the same. Both are already finer than a consumer receiver manages on a good day, and finer than the coordinates printed on the listing, which were taken by somebody standing in the same imperfect conditions you will be standing in.

Longitude behaves differently and this catches people out: a degree of longitude is widest at the equator and narrows to nothing at the poles. At British or German latitudes a minute of longitude is roughly 1.1 kilometres rather than 1.85, so the same number of decimals buys you more precision east to west than north to south.

None of which matters much in practice, because the last ten metres of any find are done by eye. Carrying six decimal places into a device that reports a five-metre error is arithmetic rather than accuracy.

There is one place the extra digits do earn their keep, and it is not navigation. If you are working a multi-stage cache or a puzzle whose final coordinates come out of a calculation, keep the full precision through every intermediate step and round only at the end. Rounding early and then adding offsets compounds the error, and a stage that is thirty metres out sends everybody behind you to the wrong tree.

Datum, briefly

A coordinate means nothing without knowing which model of the earth it was measured against. Geocaching uses WGS 84 throughout, which is also what satellite positioning natively produces, so for ordinary caching the question never arises.

It arises when you take a coordinate from an old map. National grid systems and older national datums can differ from WGS 84 by a couple of hundred metres, and no amount of reformatting fixes that, converting between DDM, DD and DMS re-spells the number and leaves the datum exactly where it was. If a source predates satellite survey, find out what it was measured against before trusting it to the metre.