# Conversion of 3 degree UTM zone Easting Northing to WGS-84

In Nepal we use 3 degrees width zone UTM with 3 central meridians 81 E, 84 E and 87 E and datum: Everest-1830. I am trying to convert the Everest-projected coordinates to WGS-84's Latitude and Longitude. I applied reverse of projection for conversion of Everest projected Easting and Northing to Everest's Latitude and Longitude and then transformed to WGS-84's Latitude and Longitude

I used the formula in ogp publications 373-7-2 geomatics guidance note number 7 page number 50 and 54 to calculate latitude and longitude from Easting and Northing Projected coordinates and created code to do so.

But whenever I tested the conversion and input Easting, Northing and height values 617000, 3038250, 1230 respectively of zone 88 (Central meridian 84 degree E, datum : Everest-1830). I get output latitude 27.461834699447184 and longitude 83.86573999170062 (Datum: Wgs-84). But the expected output is latitude: 27.732 and longitude: 85.417.

I guess you stumbled over this note on page 53:

subsequent civilian adoption of the systems usually ignores the zone prefix to easting. Where this is the case the formulas below do not apply: use the standard TM formula separately for each zone

The formulas on page 54 should only be used if the zone number is written before the false Easting, which is not the case here. So I took only the formulas from p 50ff into Libre Office and got these results:

``````M0  0
e1  0.0016649922
mue1    0.4772587465
M1  3038553.85538554
T1  0.2701106629
C1  0.0059292372
esq 0.0066822021
D   0.0183352698
phi1    0.4793002154
nue1    6381782.36093598
rho1    6348382.77011411
``````

which returns the same lat and lon on the Everest ellipsoid as

``````cs2cs +proj=tmerc +lon_0=84 +lat_0=0 +k=0.9999 +a=6377276.345 +b=6356075.41314024 +x_0=500000 +units=m +towgs84=282,726,254 +no_defs +to +proj=longlat +a=6377276.345 +b=6356075.41314024 +towgs84=282,726,254 +no_defs -f "%%.6f"<MUTM88.txt >WGS84out.txt

85.183840   27.456849 1230.000000
``````

Transforming to WGS84 returns:

``````85.181615   27.457128 1188.383496
``````

which is still not exactly what you expected, but more close than your result.

• Thanks @AndreJ I think you are right, the note on page 53 is useful. But instead of doing everything on my own i choose to use library proj4js which makes work very easy. Jul 23 '15 at 7:21