The numerical management answer above is all very well for working with the received data but takes no accoount of errors in the signal as received.
The mathematics is based on the travelling-time differences in the signals from several satellites that your GPS unit may be a able to receive signals from in a particular location.
It is assumed that the signals are travelling through a standard atmosphere which has specified pressure density gradients, and compensations are made for the various angles at which the signals arrive, and in some units, for the temperature and measured air pressure for which a thermometer and barometer has to be built into the unit or manual inputs are made from external measurements.
Radio waves are electromagnetic waves just as light is, and when the density of the medium they travel through changes the speed of the wave changes.
Light only has a constant velocity in a vaccuum.
Light passing through a lens is slowed more by denser glass and by the thicker parts of the curved lens elements than the thinner parts. Slowing the light by having smoothly changing thicknesses of glass, that is, by having smoothly polished curved lens surfaces, is what makes the light bend and form an image through the lens.
In the atmosphere the effect causes stars to twinkle amongst other causes, and mirages to form by the bending of light through thicker and thinner layers of air, and the Sun to appear to be setting when it has already set. That effect, called astronomical refraction, is allowed for in precise tables of sunrise and sunset times, and the actual altitude of stars also varies from their observed altitude and must be corrected for from tables calculated for it or these days by a convenient computer algorithm as on here
http://www.google.com/search?q=observed+altitude+of+star+actual+altitude&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-GB:official&client=firefox-a . . . .
The number of factors involved can be seen here...quite a lot.
http://aa.usno.navy.mil/data/docs/celnavtable.php . . . . . . . .
You can be 120 miles out easily by ignoring it, a fact known well before the twentieth century.
http://books.google.com/books?id=8InOAAAAMAAJ&pg=PT203&lpg=PT203&dq=observed+altitude+of+star+actual+altitude&source=bl&ots=mtSqkIbge4&sig=Geu_1k9hWW-0AxQAF0_R2yZPTS0&hl=en&ei=xgCTS47-NdW7jAfpvqmACw&sa=X&oi=book_result&ct=result&resnum=8&ved=0CBkQ6AEwBzgK
All that of course applies equally to very high frequency radio waves, which behave very much like light.
Low frequency radio waves behave differently than very high frequency ones as far as radio reception is concerned, which is why FM broadcasting on VHF is a short range signal but MW and LW signals can go round the world easily.
Long range VHF is possible during solar storms. South African TV has been picked up in England.
Expensive FM tuners like my Kenwood 6005 and 8005 have a multipath output and using it means you can detect signals reflected from buliding etc arriving slightly later than the direct signal, introducing phase distortions and spoiling the quality of sound, and you move the aerial until no multipath distortion is detected.
Now the upshott of that is that there is no point manipulating figures to twelve places of decimals if the signal is no more accurate than six places of decimals and it also means there is there is no such thing as a particular accuracy of a particular GPS unit.
The posh approach is to give confidence limits to your results at the time you get them.
95% confident the result is accurate to within 10 meters
70% confident the result is accurate to within 5 meters
10% confident the result is accurate to within 1 meter
and so on
The limits vary with weather, (density and depth of cloud cover, rain etc ), your particular location compared to the positions of the satellites observable, your altitude above sea level, the stabilty of the circuitry in your own GPS unit,(whether it has automatic compensation for temperature and pressure differences for the signals, temperature drift compensation for the circuits etc), the software algorithms used to reduce the time data to positional data, and probably more I've never even heard of.
Scroll down to navigation error sources on here
http://www.agi.com/downloads/support/productSupport/literature/pdfs/whitePapers/Long%20term%20prediction%20of%20GPS%20accuracy%20-%20Understanding%20the%20Fundamentals.pdf . . . . . .
You can only know the truth of your unit's accuracy on any day by having a standard to compare your readings to and that standard can only be by dead reckoning ....except for one line on Earth for longitude and one place on Earth for latitude.
At Greenwich is the meridian line. It is known to within a foot for many places due north and south of Greenwich.
Everywhere else on Earth has to be measured to find out where it is in relation to that line....that is, what longitude it has.
In Equador is the equator mark. That's where it was measured by Charles de la Condomine and his team, now known poor soul not for his explorations and the huge scientifc haul he got through but for condoms. He sent the first samples of rubber to Paris from Equador after completing the measurement of where the equator is and the length of one degree of it.
https://answersrip.com/question/index?qid=20091030140108AArpC5q . . . . . . .
On Ordance survey maps you will find trig points marked. They are very accurately measured and the corordinates can be read from the map on the lat/long scales.
Even they are now surpassed by the best GPS sytems and control data for them is no longer charged for.
http://benchmarks.ordnancesurvey.co.uk/
Here is a calculator and a method for converting lat/long differences to feet or meters
http://bytes.com/topic/visual-basic-net/answers/368097-distance-formula-long-lat-coord . . . . . .
http://bytes.com/forum/thread368097.html . . . . . .
Find a place to measure on Google Earth, measure it with your GPS, and do the conversions.
Measuring my garden at the four corners using Google Earth showed a total inccauracy of less than 0.5" of arc from the four measurements, getting to within twenty inches in forty three feet which means any pair of corner points must have been identified to better than 0.13 seconds of arc in accuracy for the distances to have tied up so well with reality.
I make astronomical telescopes and measure variable stars and double star position angles etc. Getting 0.1" accuracy in a telescopic observation using very good equipment is a dream. We do a dozen measurements and average them to get near that.That is pretty good.
http://www.maps-gps-info.com/gps-accuracy.html . . . . . . .