The OS grid reference system

To convert a grid reference into Cartesian coordinates an explanation of the system is necessary. For full details refer to OS publications such as `Ordnance Survey Maps - A Descriptive Manual', J.B.Harley, HMSO, 1975.

Grid references are given in the form ABeenn where A and B are letters and e and n are digits. This is best decoded by an example. The city of Coventry is at SP3683, i.e. it has coordinates (36,83) in square SP. The units used are kilometres, so it is 36km East and 83km North of the bottom left hand corner (origin) of square SP. The first letter, the S, identifies which 500km square the reference occurs in. The squares are laid out as follows, over an area covering 2500km x 2500km:

A	B	C	D	E
F	G	H	J	K
L	M	N	O	P
Q	R	S	T	U
V	W	X	Y	Z

Adding coordinates
4	A	B	C	D	E
3	F	G	H	J	K
2	L	M	N	O	P
1	Q	R	S	T	U
0	V	W	X	Y	Z
	0	1	2	3	4

(Note I is missing)

So major square S has the 500km coordinates (2,1), or in kilometres, (1000,500).

The second letter, `P', identifies a square of 100km side within that major square. These 100km squares have the same layout, so P has the 100km co-ordinates (4,2) - i.e. (400,200) in kilometres. So square SP has the coordinates (1400,700) = (1000,500) + (400,200).

Adding in the coordinates within the SP square (36,83) gives the coordinates of SP3683 as (1436,783) = (1400,700) + (36,83).

OS grid references are sometimes encountered in that purely numeric form, but with (1000,500) subtracted so they are relative to (1000,500) or SV0000,
which is known as the `False Origin' of the National Grid. So our example SP3683, coordinates (1436,783), might also be called 436 283.