Getting Ordnance Survey grid references to work in ArcGIS

How the 100 km squares work
Ordnance Survey (OS) divides Great Britain into 100 km by 100 km squares, each with a two-letter code. The two-letter codes can be found printed in faint-blue capitals on OS maps and are also given when using a GPS set to British National Grid. The first letter, for example ‘S’, denotes 500 km by 500 km squares and this is subdivided into 25 squares that are 100 km by 100 km within it, making ‘ST’, ‘SU’, ‘SO’ and so on. There are four main first letters: ‘S’, ‘T’, ‘N’ and ‘H’ covering Great Britain, plus an ‘O’ square covering a tiny part of North Yorkshire that is usually below tide. A unique National Grid reference should have this two-letter descriptor followed by the grid reference numbers within that square. ArcGIS, however, can’t cope with the two letter code, and instead divides Britain up into an xy coordinates grid in metres (a so called Cartesian coordinate system), starting in the bottom-left corner as shown below.

National Grid reference numbers
The numbers going across the map from left to right are called eastings, and go up in value eastwards, and the numbers going up the map from bottom to top are called northings, because they go up in a northward direction. In ArcGIS the eastings are the x-coordinates and northings the y-coordinates. Eastings are always given before northings, much as one gives x-coordinates before y-coordinates.

However, it is important to understand that grid references can be taken to varying precision (eastings and northings are invariably taken to the same precision). Ignoring the two letter code, a two-figure grid reference (one figure being an easting and one a northing) has a 10 km precision, a four-figure grid reference has 1 km precision and so forth. Typically, A GPS gives a 10-figure grid reference, which has a precision of 1 m (although it is not uncommon for modern differential GPSs to grid references with decimal places allowing sub-metre precision).

There is a step-by-step guide to reading and interpreting OS grid references here, but I'll explain briefly. First decide to what precision you want to take it and then you take it, then start by working out the two letter code, then take the eastings and then the northings. For example, look at the map below of the shores of Loch Fyne in Scotland. This actually encompasses four 100 km squares. The top-left, is in in square NM, the top-right in NN, the bottom-left in NR and the bottom-right in NS. The map is further divided into 1 km squares with a number system that begins at zero and goes to 99 and repeats in every 100 km square.

Click on the image to make it larger

If one wanted to work out the grid reference of most easterly building in the hamlet of Cumlodden Cott, then one first decides the precision. If to 1 km precision, then one simply needs the two letter code followed by a four figure grid number. The two letter code is NS, the eastings is quite close to the 01 line and the northings to the 99 line then the 00 line so the grid reference is NS 01 99. If you want to take it to 100 m precision, then divide (by eye or using a ruler) each one km square into 100 (10 x 10) little squares. The grid reference becomes NS 009 993. Often the grid reference are given without spaces so they would become NS0199 (1 km precision) or NS009993 (100m precision).

Converting National Grid references to numbers that can be used by ArcGIS

Here is a 3-step guide:
(1) Take the numbers of the grid references and split them down the middle. The first half are the eastings and the second half are the northings. In the example above (NS009993) the eastings are 009 and the northings are 993.

(2) Work out the precision based on the total number of figures given excluding the letters (2 figures = 10 km, 4 figures = 1 km, 6 figures = 100 m, 8 figures = 10m, 10 figures = 1m). NX009993 has six numbers, so the precision is 100. Then multiply the eastings and northings by the precision in metres. In the NS009993 example, the eastings (i.e. x-coordinates) become 00900 and the northings become 99300.

(3) Add the appropriate amount to take account of the two letter code. In the NS009993 example, you can see from the very top figure, that you need to add 200,000 to the eastings and 600,000 to the northings. In GIS ready format the eastings (x-cordinates) become 200,900 and the northings (y-coordinates) become 699,300.

Often you may need to convert a whole bunch of grid references at once, so I've included below some R-code and example datasets that should do the job for you here. The link is to a single zip file that includes the code, example datasets and a readme.txt file that gives instructions for use