The National Grid, Eastings and Northings

Yesterday I reported some nasty fly-tipping on one of the country lanes on the way to work.  I reported its location using the standard Ordnance Survey system of two letters and six digits, so SU 731189.  I copied it to the Hampshire police, who had to phone me to check the location as they "don't use that system".  "We use Eastings and Northings" said the copper.  But the OS system is Eastings and Northings: the 731 is Eastings in units of 100 metres and the 189 is Northings.  But the police mean something different.  They use two six-digit numbers which do the job of the letters and the numbers of the OS system. Their two numbers are measured in metres from the "false origin" of the national grid.  The true origin is at 2° west and 49° north.  The 2° is important - it's the "central meridian" going down the middle of the country, which makes it a good basis for the map projection they use.  But the trouble with the true origin is that you would have to have negative Eastings for everything west of the line.  So they have a "false origin" 400 km to the west, somewhere beyond the Isles of Scilly, so all the Eastings are positive.

Now, to keep the numbers manageable, they use letters to define 100 km grid squares.  The first letter chooses one of 25 500 km squares in a pattern like this:

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

with the false origin at the bottom left corner of the S (where I've put a dot).  They're not all needed - in fact H, N, O, S and T cover the whole of Great Britain.  Then the second letter selects a 100 km square using the same pattern, but within the 500 km square already chosen.

So now we can go from our OS grid reference to our eastings-and-northings numbers-only reference as used by the police.  In my example, the big square S places us at the false origin, and the U then takes us 400 km east and 100 km north.  That 4 and 1 give us the first digits of our eastings and northings.  So our map reference SU 731189 becomes 473100 118900.  The zeros are because the OS reference is only accurate to 100 metres, while the 12-digit one is accurate to one metre.  Actually, it should be a 13-digit reference - the northings really need an exrta digit to allow us to get up to square H which covers Orkney and Shetland.

Now finally here's a handy table matching two-letter grid squares to the first eastings digit and the first (two) northings digit(s).  I haven't found this table on the OS website, but it might be there somewhere.  Most of the other stuff is covered by a nice little presentation that starts here.


Second          First letter
letter    H     N     O     S     T
  A      0,14  0,9   5,9   0,4   5,4
  B      1,14  1,9   6,9   1,4   6,4
  C      2,14  2,9   7,9   2,4   7,4
  D      3,14  3,9   8,9   3,4   8,4
  E      4,14  4,9   9,9   4,4   9,4
  F      0,13  0,8   5,8   0,3   5,3
  G      1,13  1,8   6,8   1,3   6,3
  H      2,13  2,8   7,8   2,3   7,3
  J      3,13  3,8   8,8   3,3   8,3
  K      4,13  4,8   9,8   4,3   9,3
  L      0,12  0,7   5,7   0,2   5,2
  M      1,12  1,7   6,7   1,2   6,2
  N      2,12  2,7   7,7   2,2   7,2
  O      3,12  3,7   8,7   3,2   8,2
  P      4,12  4,7   9,7   4,2   9,2
  Q      0,11  0,6   5,6   0,1   5,1
  R      1,11  1,6   6,6   1,1   6,1
  S      2,11  2,6   7,6   2,1   7,1
  T      3,11  3,6   8,6   3,1   8,1
  U      4,11  4,6   9,6   4,1   9,1
  V      0,10  0,5   5,5   0,0   5,0
  W      1,10  1,5   6,5   1,0   6,0
  X      2,10  2,5   7,5   2,0   7,0
  Y      3,10  3,5   8,5   3,0   8,0
  Z      4,10  4,5   9,5   4,0   9,0