# Why does a coordinate system transformation warp distances?

I have two points in `NAD_1983_UTM_Zone_8N`:

``````A: 520474.065771355,7146471.63532946
B: 523398.322298721,7146491.17961279,1056.79350172838
Distance A-B: 2925.739824m
``````

When I convert them to `NAD_1983_UTM_Zone_10N` I get the points:

``````A: -54764.4762031343,7197193.19405588
B: -51878.0632641406,7196659.83388472
Distance A-B: 2936.689978m
``````

Both coordinate systems are using the same spheroid and datum. What is causing the 11 m discrepancy between the A-B distances?

• UTM Zone projection precision degenerates outside of their defined bounds, with distortion increasing exponentially with distance to the reference meridian. Commented May 22, 2020 at 22:07
• How did you convert coordinates from `Zone8` to `Zone10`? Commented May 23, 2020 at 11:34

In UTM projection, distortion is small near central meridian, when you move away it increases. `A` and `B` are near central meridian in `UTM Zone 8`. When you convert them to `UTM Zone 10`, coordinates of `A` and `B` are calculated based on central meridian of `UTM Zone 10`.

After transformation, points are still in the same location on earth, but far from central meridian of `Zone 10` in comparison with `Zone 8`'s. Therefore, distortion of `A-B` distance is bigger. This is nature of UTM.

Near the equator 1 degree N-S is the same length as 1 degree E-W.

UTM zones rotate the coordinate system to have an "equator" that runs through the poles [1]. The different zones set this "equator" at different longitudes, or meridians.

So at that longitude, in UTM, one unit of distance (metres) N-S is the same E-W. Whether that's on the real equator at that longitude or on the poles or anywhere on a line between.

The distortion you see is because your points are further from that "equator" meridian in one of the UTM zones. Its like if the points were on the equator in a lat-long system or positioned a bit north of the equator.

If you want a precise distance, transform to lat-long and do a proper ellipsoid or spherical distance. This should be much closer than with two UTM systems.

[1] its also not a lat-long spherical coordinate system but a cylindrical projection, but near the UTM meridian that's not that relevant to this.