# Calculating lat/long coordinates from DLS (Dominion Land Survey) Location

I am trying to calculate the legal subdivision center of a DLS location and even when I try the simplest calculation my numbers are always off from other calculators.

Take for example DLS location 1-1-1-1 W2. From what I understand being adjacent to the 102W meridian and adjacent to 49N as well it should be relatively easy to calculate This is also simple since I do not believe road allowances come into effect on this section as they begin on the top and left sides only AFAIK, and this section and LSD is the very bottom right side of the grid.

That said, even when I dumb down the calculations to go straight to the LSD level my numbers are off. An LSD is known to be 1/4 mile, and being in the bottom right section and bottom right legal division grid, it should be 1/4 mi west and 1/4 north north for the top left boundary from 49N/102W.

I used the rhumb line calculator here (http://www.movable-type.co.uk/scripts/latlong.html) to calculate .25 miles west (bearing 270), then .25 miles north (bearing 0) to get the the top left point of the polygon square.

I get the following top left corner coordinate: 49.0036182946, -102.0055151967

When I average that and 49, -102 I get: 49.0018091473, -102.0027575983

Yet the calculators I see are all extremely close to: 49.000976, -102.009228

So I must be missing something here because I cannot see how everyone else gets a number the same but not my calculation. Does anyone know what I am missing here?

• I'm not familiar with the DLS; I work with the PLSS to the south. However one thing that stands out is you're going directly north to get a corner. Apparently in the DLS range lines converge to the north (see section on townships). The townships aren't square. Also at play may be the idea of a projected vs geographic coordinate. Projected is flat plane, geographic is spherical or ellipsoidal - can't use the same math in both cases. Commented Feb 23, 2015 at 21:49
• Going directly north should work as far as I know, i.e. 49,-102 and 49,-101 are 73 km apart. Going north 10 degrees in latitude with same longitude would result in 57km so it seems like my calculations fit the converging (as meridians do). Also I checked into the fact that other calculators might be using a projected center, but my results are still too far off).
– m1g
Commented Feb 25, 2015 at 18:36