User:Tim Zukas/example

Example: OSGB36 grid to lat-lon
On the OSGB36 grid the Topcroft churchtower is 626575.127 meters East, 292894.813 meters North; what's its OSGB36 lat-lon?

The British grid uses the Airy spheroid, with a = 6377563.39603 meters rounded and r being 20923713 divided by 69903, or 299.32496 45938; $$ \epsilon $$ comes out 0.00671 53349 10257.

The OS Grid sets Easting at 400000 meters at the central meridian of 2 degrees West longitude; $$ k_0$$ is 0.99960 12717 75 rounded. Northing is set at minus-100000 meters at latitude 49 degrees on the central meridian; on the Airy spheroid 49 deg latitude is meters from the equator, so it's 5427063.8153 meters from the equator along the central meridian of the OS Grid. So on the OS Grid, Northing at any point has to be increased by 5527063.8153 meters to get grid distance from the equator.