GPS accuracy

So you think you've located a geohash with your GPS receiver? Just how sure can you be that the right spot really is here, and not somewhere else?

There are two elements of GPS accuracy. One is the precision to which the coordinates are written, and the other is the accuracy to which the receiver works.

Coordinate precision

Put simply, the more decimal places you use in your coordinates, the more precise they are.

A graticule is approximately 110km in the north-south direction, and up to 110km in the east-west direction. The actual figure for the east-west direction depends on your latitude -- taking 39,-84 (Cincinnati, Ohio) as an example, it's about 85km.

So using only the whole number of degrees of latitude and longitude -- N39° W84°, for example -- gives a precision of 110km north-south and 85km east-west. For each decimal place used, divide these figures by ten. A GPS receiver using five decimal digits -- N39.12345° W84.98765°, for example -- therefore has a precision of 1.1m north-south and 0.85m east-west.

Some GPS receivers use degrees and minutes instead of just degrees -- there are 60 minutes in each degree, so coordinates measured in minutes are 60 times more precise than coordinates measured in degrees. A GPS receiver using three decimal digits for its minutes -- N39° 12.345' W84° 54.321', for example -- has a precision of 1.8m north-south and 1.4m east-west.

Or you can use degrees, minutes and seconds -- again, there are 60 seconds in each minute, so these are 60 times more precise. A GPS receiver using one decimal degree for its seconds -- N39° 12' 34.5" W84° 54' 32.1", for example -- has a precision of 3.1m north-south and 2.4m east-west.

	Precision north-south
Decimal places	degrees	minutes	seconds
1	11 km	180 m	3.1 m
2	1.1 km	18 m	0.31 m
3	110 m	1.8 m	3.1 cm
4	11 m	0.18 m	3.1 mm
5	1.1 m	1.8 cm	0.31 mm

As you can see, the usual precision of GPS receivers is plenty for the purposes of geohashing.

GPS system accuracy

Before May 2000, GPS signals were subject to Selective Availability (SA), which meant that for ordinary users, the signals were only accurate to approximately 50 metres. Since then, SA has been removed and GPS signals are generally now accurate to a few metres. See [1] for further information.

With a clear view of the whole sky, GPS receivers are able to receive signals from multiple satellites, enabling them to calculate very accurately where they are. However, in woodland, cities or other areas where the view of the sky is limited, the receiver may not be able to calculate so accurately. Generally your GPS receiver will quote a figure to which its navigation is accurate -- usually between three and ten metres.

Overall accuracy

With both types of error, then, your GPS may say you are in exactly the right place, but you may actually be a small distance away. A simple rule of thumb is to add together the possible errors in precision and accuracy, and halve the total. This will give you the radius of a circle, centred on you, within which your destination lies.

A more accurate way to calculate the radius of the error circle is to sum the north-south errors and the east-west errors, halve each of them, then square both totals, add them, and take the square root of the sum. This final number is the circle's radius.

For example, if your GPSr uses four decimal digits of degrees, and is quoting a signal accuracy of 5 metres, the simple rule of thumb gives an error circle of radius 10.5-metres. The more accurate calculation has a N-S error of 10.5 metres and an E-W error of 9.25 metres, for an overall error circle of radius 14 metres.