SQL function to convert UK OS coordinates from easting/northing to longitude and latitude - sql

Question

Please can someone post a SQL function to convert easting/northing to longitude/latitude. I know it's incredibly complicated but I haven't found anyone who has documented it in T-SQL.
This javascript code works but I'm having trouble converting it to SQL.
I have 16,000 coordinates and need them all converted to lat/long.
This is what I have so far but it's not getting past the while loop.
DECLARE #east real = 482353,
#north real = 213371
DECLARE #a real = 6377563.396,
#b real = 6356256.910,
#F0 real = 0.9996012717,
#lat0 real = 49*PI()/180,
#lon0 real = -2*PI()/180
DECLARE #N0 real = -100000,
#E0 real = 400000,
#e2 real = 1 - (#b*#b)/(#a*#a),
#n real = (#a-#b)/(#a+#b)
DECLARE #n2 real = #n*#n,
#n3 real = #n*#n*#n
DECLARE #lat real = #lat0,
#M real = 0
WHILE (#north-#N0-#M >= 0.00001)
BEGIN
SET #lat = ((#north-#N0-#M)/(#a*#F0)) + #lat
DECLARE #Ma real = (1 + #n + (5/4)*#n2 + (5/4)*#n3) * (#lat-#lat0),
#Mb real = (3*#n + 3*#n*#n + (21/8)*#n3) * SIN(#lat-#lat0) * COS(#lat+#lat0),
#Mc real = ((15/8)*#n2 + (15/8)*#n3) * SIN(2*(#lat-#lat0)) * COS(2*(#lat+#lat0)),
#Md real = (35/24)*#n3 * SIN(3*(#lat-#lat0)) * COS(3*(#lat+#lat0))
SET #M = #b * #F0 * (#Ma - #Mb + #Mc - #Md)
END
DECLARE #cosLat real = COS(#lat),
#sinLat real = SIN(#lat)
DECLARE #nu real = #a*#F0/sqrt(1-#e2*#sinLat*#sinLat)
DECLARE #rho real = #a*#F0*(1-#e2)/POWER(1-#e2*#sinLat*#sinLat, 1.5)
DECLARE #eta2 real = #nu/#rho-1
DECLARE #tanLat real = tan(#lat)
DECLARE #tan2lat real = #tanLat*#tanLat
DECLARE #tan4lat real = #tan2lat*#tan2lat
DECLARE #tan6lat real = #tan4lat*#tan2lat
DECLARE #secLat real = 1/#cosLat
DECLARE #nu3 real = #nu*#nu*#nu
DECLARE #nu5 real = #nu3*#nu*#nu
DECLARE #nu7 real = #nu5*#nu*#nu
DECLARE #VII real = #tanLat/(2*#rho*#nu)
DECLARE #VIII real = #tanLat/(24*#rho*#nu3)*(5+3*#tan2lat+#eta2-9*#tan2lat*#eta2)
DECLARE #IX real = #tanLat/(720*#rho*#nu5)*(61+90*#tan2lat+45*#tan4lat)
DECLARE #X real = #secLat/#nu
DECLARE #XI real = #secLat/(6*#nu3)*(#nu/#rho+2*#tan2lat)
DECLARE #XII real = #secLat/(120*#nu5)*(5+28*#tan2lat+24*#tan4lat)
DECLARE #XIIA real = #secLat/(5040*#nu7)*(61+662*#tan2lat+1320*#tan4lat+720*#tan6lat)
DECLARE #dE real = (#east-#E0)
DECLARE #dE2 real = #dE*#dE
DECLARE #dE3 real = #dE2*#dE
DECLARE #dE4 real = #dE2*#dE2,
#dE5 real = #dE3*#dE2
DECLARE #dE6 real = #dE4*#dE2,
#dE7 real = #dE5*#dE2
SET #lat = #lat - #VII*#dE2 + #VIII*#dE4 - #IX*#dE6
DECLARE #lon real = #lon0 + #X*#dE - #XI*#dE3 + #XII*#dE5 - #XIIA*#dE7
SELECT #lon, #lat

Answer 1

I've been struggling with this one for a while.
I had a lot of northing/easting points in OSGB36 that have to be converted on the fly on a regular basis.
Please note that the UDF below converts northings/eastings in OSGB36 (Ordnance Survey) projection to latitude/longitude in WGS84 projection so they can be used in Google Maps.
/****** Object: UserDefinedFunction [dbo].[NEtoLL] Script Date: 09/06/2012 17:06:39 ******/
SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
CREATE FUNCTION [dbo].[NEtoLL] (#East INT, #North INT, #LatOrLng VARCHAR(3)) RETURNS FLOAT AS
BEGIN
--Author: Sandy Motteram
--Date: 06 September 2012
--UDF adapted from javascript at http://www.bdcc.co.uk/LatLngToOSGB.js
--found on page http://mapki.com/wiki/Tools:Snippets
--Instructions:
--Latitude and Longitude are calculated based on BOTH the easting and northing values from the OSGB36
--This UDF takes both easting and northing values in OSGB36 projection and you must specify if a latitude or longitude co-ordinate should be returned.
--IT first converts E/N values to lat and long in OSGB36 projection, then converts those values to lat/lng in WGS84 projection
--Sample values below
--DECLARE #East INT, #North INT, #LatOrLng VARCHAR(3)
--SELECT #East = 529000, #North = 183650 --that combo should be the corner of Camden High St and Delancey St
DECLARE #Pi FLOAT
, #K0 FLOAT
, #OriginLat FLOAT
, #OriginLong FLOAT
, #OriginX FLOAT
, #OriginY FLOAT
, #a FLOAT
, #b FLOAT
, #e2 FLOAT
, #ex FLOAT
, #n1 FLOAT
, #n2 FLOAT
, #n3 FLOAT
, #OriginNorthings FLOAT
, #lat FLOAT
, #lon FLOAT
, #Northing FLOAT
, #Easting FLOAT
SELECT #Pi = 3.14159265358979323846
, #K0 = 0.9996012717 -- grid scale factor on central meridean
, #OriginLat = 49.0
, #OriginLong = -2.0
, #OriginX = 400000 -- 400 kM
, #OriginY = -100000 -- 100 kM
, #a = 6377563.396 -- Airy Spheroid
, #b = 6356256.910
/* , #e2
, #ex
, #n1
, #n2
, #n3
, #OriginNorthings*/
-- compute interim values
SELECT #a = #a * #K0
, #b = #b * #K0
SET #n1 = (#a - #b) / (#a + #b)
SET #n2 = #n1 * #n1
SET #n3 = #n2 * #n1
SET #lat = #OriginLat * #Pi / 180.0 -- to radians
SELECT #e2 = (#a * #a - #b * #b) / (#a * #a) -- first eccentricity
, #ex = (#a * #a - #b * #b) / (#b * #b) -- second eccentricity
SET #OriginNorthings = #b * #lat + #b * (#n1 * (1.0 + 5.0 * #n1 * (1.0 + #n1) / 4.0) * #lat
- 3.0 * #n1 * (1.0 + #n1 * (1.0 + 7.0 * #n1 / 8.0)) * SIN(#lat) * COS(#lat)
+ (15.0 * #n1 * (#n1 + #n2) / 8.0) * SIN(2.0 * #lat) * COS(2.0 * #lat)
- (35.0 * #n3 / 24.0) * SIN(3.0 * #lat) * COS(3.0 * #lat))
SELECT #northing = #north - #OriginY
, #easting = #east - #OriginX
DECLARE #nu FLOAT
, #phid FLOAT
, #phid2 FLOAT
, #t2 FLOAT
, #t FLOAT
, #q2 FLOAT
, #c FLOAT
, #s FLOAT
, #nphid FLOAT
, #dnphid FLOAT
, #nu2 FLOAT
, #nudivrho FLOAT
, #invnurho FLOAT
, #rho FLOAT
, #eta2 FLOAT
/* Evaluate M term: latitude of the northing on the centre meridian */
SET #northing = #northing + #OriginNorthings
SET #phid = #northing / (#b*(1.0 + #n1 + 5.0 * (#n2 + #n3) / 4.0)) - 1.0
SET #phid2 = #phid + 1.0
WHILE (ABS(#phid2 - #phid) > 0.000001)
BEGIN
SET #phid = #phid2;
SET #nphid = #b * #phid + #b * (#n1 * (1.0 + 5.0 * #n1 * (1.0 + #n1) / 4.0) * #phid
- 3.0 * #n1 * (1.0 + #n1 * (1.0 + 7.0 * #n1 / 8.0)) * SIN(#phid) * COS(#phid)
+ (15.0 * #n1 * (#n1 + #n2) / 8.0) * SIN(2.0 * #phid) * COS(2.0 * #phid)
- (35.0 * #n3 / 24.0) * SIN(3.0 * #phid) * COS(3.0 * #phid))
SET #dnphid = #b * ((1.0 + #n1 + 5.0 * (#n2 + #n3) / 4.0) - 3.0 * (#n1 + #n2 + 7.0 * #n3 / 8.0) * COS(2.0 * #phid)
+ (15.0 * (#n2 + #n3) / 4.0) * COS(4 * #phid) - (35.0 * #n3 / 8.0) * COS(6.0 * #phid))
SET #phid2 = #phid - (#nphid - #northing) / #dnphid
END
SELECT #c = COS(#phid)
, #s = SIN(#phid)
, #t = TAN(#phid)
SELECT #t2 = #t * #t
, #q2 = #easting * #easting
SET #nu2 = (#a * #a) / (1.0 - #e2 * #s * #s)
SET #nu = SQRT(#nu2)
SET #nudivrho = #a * #a * #c * #c / (#b * #b) - #c * #c + 1.0
SET #eta2 = #nudivrho - 1
SET #rho = #nu / #nudivrho;
SET #invnurho = ((1.0 - #e2 * #s * #s) * (1.0 - #e2 * #s * #s)) / (#a * #a * (1.0 - #e2))
SET #lat = #phid - #t * #q2 * #invnurho / 2.0 + (#q2 * #q2 * (#t / (24 * #rho * #nu2 * #nu) * (5 + (3 * #t2) + #eta2 - (9 * #t2 * #eta2))))
SET #lon = (#easting / (#c * #nu))
- (#easting * #q2 * ((#nudivrho + 2.0 * #t2) / (6.0 * #nu2)) / (#c * #nu))
+ (#q2 * #q2 * #easting * (5 + (28 * #t2) + (24 * #t2 * #t2)) / (120 * #nu2 * #nu2 * #nu * #c))
SELECT #lat = #lat * 180.0 / #Pi
, #lon = #lon * 180.0 / #Pi + #OriginLong
--Now convert the lat and long from OSGB36 to WGS84
DECLARE #OGlat FLOAT
, #OGlon FLOAT
, #height FLOAT
SELECT #OGlat = #lat
, #OGlon = #lon
, #height = 24 --London's mean height above sea level is 24 metres. Adjust for other locations.
DECLARE #deg2rad FLOAT
, #rad2deg FLOAT
, #radOGlat FLOAT
, #radOGlon FLOAT
SELECT #deg2rad = #Pi / 180
, #rad2deg = 180 / #Pi
--first off convert to radians
SELECT #radOGlat = #OGlat * #deg2rad
, #radOGlon = #OGlon * #deg2rad
--these are the values for WGS84(GRS80) to OSGB36(Airy)
DECLARE #a2 FLOAT
, #h FLOAT
, #xp FLOAT
, #yp FLOAT
, #zp FLOAT
, #xr FLOAT
, #yr FLOAT
, #zr FLOAT
, #sf FLOAT
, #e FLOAT
, #v FLOAT
, #x FLOAT
, #y FLOAT
, #z FLOAT
, #xrot FLOAT
, #yrot FLOAT
, #zrot FLOAT
, #hx FLOAT
, #hy FLOAT
, #hz FLOAT
, #newLon FLOAT
, #newLat FLOAT
, #p FLOAT
, #errvalue FLOAT
, #lat0 FLOAT
SELECT #a2 = 6378137 -- WGS84_AXIS
, #e2 = 0.00669438037928458 -- WGS84_ECCENTRIC
, #h = #height -- height above datum (from $GPGGA sentence)
, #a = 6377563.396 -- OSGB_AXIS
, #e = 0.0066705397616 -- OSGB_ECCENTRIC
, #xp = 446.448
, #yp = -125.157
, #zp = 542.06
, #xr = 0.1502
, #yr = 0.247
, #zr = 0.8421
, #s = -20.4894
-- convert to cartesian; lat, lon are in radians
SET #sf = #s * 0.000001
SET #v = #a / (sqrt(1 - (#e * (SIN(#radOGlat) * SIN(#radOGlat)))))
SET #x = (#v + #h) * COS(#radOGlat) * COS(#radOGlon)
SET #y = (#v + #h) * COS(#radOGlat) * SIN(#radOGlon)
SET #z = ((1 - #e) * #v + #h) * SIN(#radOGlat)
-- transform cartesian
SET #xrot = (#xr / 3600) * #deg2rad
SET #yrot = (#yr / 3600) * #deg2rad
SET #zrot = (#zr / 3600) * #deg2rad
SET #hx = #x + (#x * #sf) - (#y * #zrot) + (#z * #yrot) + #xp
SET #hy = (#x * #zrot) + #y + (#y * #sf) - (#z * #xrot) + #yp
SET #hz = (-1 * #x * #yrot) + (#y * #xrot) + #z + (#z * #sf) + #zp
-- Convert back to lat, lon
SET #newLon = ATAN(#hy / #hx)
SET #p = SQRT((#hx * #hx) + (#hy * #hy))
SET #newLat = ATAN(#hz / (#p * (1 - #e2)))
SET #v = #a2 / (SQRT(1 - #e2 * (SIN(#newLat) * SIN(#newLat))))
SET #errvalue = 1.0;
SET #lat0 = 0
WHILE (#errvalue > 0.001)
BEGIN
SET #lat0 = ATAN((#hz + #e2 * #v * SIN(#newLat)) / #p)
SET #errvalue = ABS(#lat0 - #newLat)
SET #newLat = #lat0
END
--convert back to degrees
SET #newLat = #newLat * #rad2deg
SET #newLon = #newLon * #rad2deg
DECLARE #ReturnMe FLOAT
SET #ReturnMe = 0
IF #LatOrLng = 'Lat'
SET #ReturnMe = #newLat
IF #LatOrLng = 'Lng'
SET #ReturnMe = #newLon
RETURN #ReturnMe
END
GO

Answer 2

I ended up using the following javascript functions to convert the values. I know it's not a SQL solution but it did the job for me.
function OSGridToLatLong(E, N) {
var a = 6377563.396, b = 6356256.910; // Airy 1830 major & minor semi-axes
var F0 = 0.9996012717; // NatGrid scale factor on central meridian
var lat0 = 49*Math.PI/180, lon0 = -2*Math.PI/180; // NatGrid true origin
var N0 = -100000, E0 = 400000; // northing & easting of true origin, metres
var e2 = 1 - (b*b)/(a*a); // eccentricity squared
var n = (a-b)/(a+b), n2 = n*n, n3 = n*n*n;
var lat=lat0, M=0;
do {
lat = (N-N0-M)/(a*F0) + lat;
var Ma = (1 + n + (5/4)*n2 + (5/4)*n3) * (lat-lat0);
var Mb = (3*n + 3*n*n + (21/8)*n3) * Math.sin(lat-lat0) * Math.cos(lat+lat0);
var Mc = ((15/8)*n2 + (15/8)*n3) * Math.sin(2*(lat-lat0)) * Math.cos(2*(lat+lat0));
var Md = (35/24)*n3 * Math.sin(3*(lat-lat0)) * Math.cos(3*(lat+lat0));
M = b * F0 * (Ma - Mb + Mc - Md); // meridional arc
} while (N-N0-M >= 0.00001); // ie until < 0.01mm
var cosLat = Math.cos(lat), sinLat = Math.sin(lat);
var nu = a*F0/Math.sqrt(1-e2*sinLat*sinLat); // transverse radius of curvature
var rho = a*F0*(1-e2)/Math.pow(1-e2*sinLat*sinLat, 1.5); // meridional radius of curvature
var eta2 = nu/rho-1;
var tanLat = Math.tan(lat);
var tan2lat = tanLat*tanLat, tan4lat = tan2lat*tan2lat, tan6lat = tan4lat*tan2lat;
var secLat = 1/cosLat;
var nu3 = nu*nu*nu, nu5 = nu3*nu*nu, nu7 = nu5*nu*nu;
var VII = tanLat/(2*rho*nu);
var VIII = tanLat/(24*rho*nu3)*(5+3*tan2lat+eta2-9*tan2lat*eta2);
var IX = tanLat/(720*rho*nu5)*(61+90*tan2lat+45*tan4lat);
var X = secLat/nu;
var XI = secLat/(6*nu3)*(nu/rho+2*tan2lat);
var XII = secLat/(120*nu5)*(5+28*tan2lat+24*tan4lat);
var XIIA = secLat/(5040*nu7)*(61+662*tan2lat+1320*tan4lat+720*tan6lat);
var dE = (E-E0), dE2 = dE*dE, dE3 = dE2*dE, dE4 = dE2*dE2, dE5 = dE3*dE2, dE6 = dE4*dE2, dE7 = dE5*dE2;
lat = lat - VII*dE2 + VIII*dE4 - IX*dE6;
var lon = lon0 + X*dE - XI*dE3 + XII*dE5 - XIIA*dE7;
return {
longitude: lon.toDeg(),
latitude: lat.toDeg()
};
}
Number.prototype.toRad = function() { // convert degrees to radians
return this * Math.PI / 180;
}
Number.prototype.toDeg = function() { // convert radians to degrees (signed)
return this * 180 / Math.PI;
}
Number.prototype.padLZ = function(w) {
var n = this.toString();
for (var i=0; i<w-n.length; i++) n = '0' + n;
return n;
}

Answer 3

I needed the same function, and javascript made it difficult to interact with the DB. I have converted your JS to PHP and this could be more useful when updating your database - ie: query table, loop through result set, call function, update table.
function OSGridToLatLong($E, $N) {
$a = 6377563.396;
$b = 6356256.910; // Airy 1830 major & minor semi-axes
$F0 = 0.9996012717; // NatGrid scale factor on central meridian
$lat0 = 49*M_PI/180;
$lon0 = -2*M_PI/180; // NatGrid true origin
$N0 = -100000;
$E0 = 400000; // northing & easting of true origin, metres
$e2 = 1 - ($b*$b)/($a*$a); // eccentricity squared
$n = ($a-$b)/($a+$b);
$n2 = $n*$n;
$n3 = $n*$n*$n;
$lat=$lat0;
$M=0;
do {
$lat = ($N-$N0-$M)/($a*$F0) + $lat;
$Ma = (1 + $n + (5/4)*$n2 + (5/4)*$n3) * ($lat-$lat0);
$Mb = (3*$n + 3*$n*$n + (21/8)*$n3) * sin($lat-$lat0) * cos($lat+$lat0);
$Mc = ((15/8)*$n2 + (15/8)*$n3) * sin(2*($lat-$lat0)) * cos(2*($lat+$lat0));
$Md = (35/24)*$n3 * sin(3*($lat-$lat0)) * cos(3*($lat+$lat0));
$M = $b * $F0 * ($Ma - $Mb + $Mc - $Md); // meridional arc
} while ($N-$N0-$M >= 0.00001); // ie until < 0.01mm
$cosLat = cos($lat);
$sinLat = sin($lat);
$nu = $a*$F0/sqrt(1-$e2*$sinLat*$sinLat); // transverse radius of curvature
$rho = $a*$F0*(1-$e2)/pow(1-$e2*$sinLat*$sinLat, 1.5); // meridional radius of curvature
$eta2 = $nu/$rho-1;
$tanLat = tan($lat);
$tan2lat = $tanLat*$tanLat;
$tan4lat = $tan2lat*$tan2lat;
$tan6lat = $tan4lat*$tan2lat;
$secLat = 1/$cosLat;
$nu3 = $nu*$nu*$nu;
$nu5 = $nu3*$nu*$nu;
$nu7 = $nu5*$nu*$nu;
$VII = $tanLat/(2*$rho*$nu);
$VIII = $tanLat/(24*$rho*$nu3)*(5+3*$tan2lat+$eta2-9*$tan2lat*$eta2);
$IX = $tanLat/(720*$rho*$nu5)*(61+90*$tan2lat+45*$tan4lat);
$X = $secLat/$nu;
$XI = $secLat/(6*$nu3)*($nu/$rho+2*$tan2lat);
$XII = $secLat/(120*$nu5)*(5+28*$tan2lat+24*$tan4lat);
$XIIA = $secLat/(5040*$nu7)*(61+662*$tan2lat+1320*$tan4lat+720*$tan6lat);
$dE = ($E-$E0);
$dE2 = $dE*$dE;
$dE3 = $dE2*$dE;
$dE4 = $dE2*$dE2;
$dE5 = $dE3*$dE2;
$dE6 = $dE4*$dE2;
$dE7 = $dE5*$dE2;
$lat = $lat - $VII*$dE2 + $VIII*$dE4 - $IX*$dE6;
$lon = $lon0 + $X*$dE - $XI*$dE3 + $XII*$dE5 - $XIIA*$dE7;
return array(
'longitude' => $lon * 180 / M_PI,
'latitude' => $lat * 180 / M_PI
);
}

Answer 4

If anyone's interested in non-SQL solution I strongly recommend using this http://www.howtocreate.co.uk/php/gridref.php PHP/JavaScript class.
One important thing to mention here is the library supports Helmert transformation.
PHP
$grutoolbox = Grid_Ref_Utils::toolbox();
$source_coords = Array(54.607720,-6.411990);
//get the ellipsoids that will be used
$Airy_1830 = $grutoolbox->get_ellipsoid('Airy_1830');
$WGS84 = $grutoolbox->get_ellipsoid('WGS84');
$Airy_1830_mod = $grutoolbox->get_ellipsoid('Airy_1830_mod');
//get the transform parameters that will be used
$UK_to_GPS = $grutoolbox->get_transformation('OSGB36_to_WGS84');
$GPS_to_Ireland = $grutoolbox->get_transformation('WGS84_to_Ireland65');
//convert to GPS coordinates
$gps_coords = $grutoolbox->Helmert_transform($source_coords,$Airy_1830,$UK_to_GPS,$WGS84);
//convert to destination coordinates
print $grutoolbox->Helmert_transform($source_coords,$WGS84,$GPS_to_Ireland,$Airy_1830_mod,$grutoolbox->HTML);
JavaScript
var grutoolbox = gridRefUtilsToolbox();
var sourceCoords = [54.607720,-6.411990];
//get the ellipsoids that will be used
var Airy1830 = grutoolbox.getEllipsoid('Airy_1830');
var WGS84 = grutoolbox.getEllipsoid('WGS84');
var Airy1830Mod = grutoolbox.getEllipsoid('Airy_1830_mod');
//get the transform parameters that will be used
var UKToGPS = grutoolbox.getTransformation('OSGB36_to_WGS84');
var GPSToIreland = grutoolbox.getTransformation('WGS84_to_Ireland65');
//convert to GPS coordinates
var gpsCoords = grutoolbox.HelmertTransform(sourceCoords,Airy1830,UKToGPS,WGS84);
//convert to destination coordinates
element.innerHTML = grutoolbox.HelmertTransform(sourceCoords,WGS84,GPSToIreland,Airy1830Mod,grutoolbox.HTML);

Answer 5

I have developed a library in .NET to be called from transact sql Converts WGS84/UTM coordinates to Latitude and Longitude
It does just the opposite, but as it uses CoordinateSharp you can download the code and change it easily to convert from lat/long to wgs84 instead.
You can download it from github:
https://github.com/j-v-garcia/UTM2LATITUDE
usage:
SELECT dbo.UTM2LATITUDE(723399.51,4373328.5,'S',30) AS Latitude, dbo.UTM2LONGITUDE(723399.51,4373328.5,'S',30) AS Longitude
result:
39,4805657453054 -0,402592727245112
<param name="XUTM">pos UTM X</param>
<param name="YUTM">pos UTM Y</param>
<param name="LatBand">Latitude band grid zone designation letter (see http://www.dmap.co.uk/utmworld.htm) </param>
<param name="LongBand">Longitude band grid zone designation number (see http://www.dmap.co.uk/utmworld.htm) </param>