Converting OS Coodinates into Longitude & Latitude

Preface: Geolocating Postcode Solution

• The Post Office: "PostZon" [ accuracy ~100m, cost ~£250 ]
  The British Post office does provide a list of every postcode ( >1.5Million ) with the geographical relationship of every code. However, these locations are rounded to the nearest 100 metres which, for the exacting user is simply not good enough.
  
  The reseller who seems to dominate associated adwords sells the data for £250 - not bad if you consider that's 60 postcodes for every penny!
  
  - The Post Office PostZon File
  
• The Ordinance Survey: "Code-Point" [1m, £750+]
  The Ordinance Survey ( in association with a number of other UK Gov. Depts. it seems ) provides an alternate database of 1.7Million postcodes with a 'resolution' of 1metre.
  
  My understanding is that the figure given is the location of the property closest to the centre of the scatter of all the properties in the code, which seems about as good as it's going to get, short of giving you the locations of every one of the 26M properties. This also ensures that the code-point will be within the boundries of the scatter, whatever it's shape.
  
  This is a little more pricey, but worth it for the extra resolution. There are also some interesting extras; as well as things like NHS wards and such you get a number of business versus residential versus PO-Box delivery points within the code. Licenses start at £750 and range to ~£5.5k for 101+ users.
  
  - The Ordinance Survey Code-Point

The Catch! : Both provide "Northing" and "Easting"

The only catch is that both the OS and the PO provide their locations in what is known as Eastings and Northings. I shalln't go into a great deal of detail about these here as a number of sites/articles cited here explain it better than I can but in short this co-ordinating system stems from the UK Ordinance Survey maps of the country.

Use of Easting & Northing does not in of itself bring inaccuracy to mapping postcodes on something like Google Maps - these coordinates are exceedinly accurate - but translating between the two systems is not increadably simple.

There are two things you need to do here:

1. Convert Easting & Northing to Longitude & Latitude
   
   This is the process of translating OS Coordinates like "264046", "192487", which as a GridRef looks like SN26401924 to their Lat/Long equivalents : 051°50′40″N, 004°31′13″W or, in decimal 51.61430, -3.96382
   
   There are a number of great online tools for demonstrating this; Chris Veness has published some javaScript here which shows how intricate just this little bit of maths is!
   
2. Converting between Airy1830/OSGB36 and WGS84/GRS80
   
   What? Ok, so you have your latitude & longitude but when you compare these to Google's estimation of where a postcode lies you'll realise that you're a few blocks out!
   
   As I understand it it goes like this: The OS coordinates are based on a model of the shape of the Earth called the "Airy 1830 ellipsoid".
   
   Google Maps ( and GPS systems etc ) are based on a different model of the curvature of the Earth, developed - to be fair to George Airy - some 150 years later. This model - or "Datum" is called called WGS84
   
   It is this difference between the Datum used within the OS Coordinates and the Datum used by Google that causes the lats and longs to be out.
   
   According to Wikipedia longitude lines are our byt around 70 metres in Cornwall, rising to ~120metres on the east coast of East Anglia.

Fitting the square peg through the round hole.

I have therefore been trawling around looking for a solution for the next problem: how do we convert our Eastings and Northings into Longitude and Latitude that work with Google Maps?

First we need to convert East/North to Lat/Long.

Then we convert OSGB/Airy1830 to WGS84

Putting all this together

I think this is probably far more easily explained on a map! .. so here it is:

• A = Before transformation;
• B = After transformation;
• C = phpcoord, jcoord, jscoord's transformed answer ( which is so similar it's obscured by B );
• X = Google's opinion of "SA1 4LS"

So.. is that it?

Well... yes... that's it: some solutions for turning Easting/Northing into Lat/Longs that can be used with Google Maps.

.. I just spent a long time banging my head against this so I thought it might help someone else if it were all in one place... or in yet another place!

( Incidentally, if anyone can explain why all the methods above agree on the position but Google's own estimate is different I'd be interested to hear. It seems ( having looked up the postcode in question ) that Marker "C" is in exactly the right spot so I'd be interested in understanding the discrepancy. )