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There's something I don't understand: I have a map in ArcMap in Lambert RGF93 projection (conic projection system for France) at scale 1:10000 then I change the coordinate system to WGS84 WebMercator map, I get a map at 1:10000 but data are zoomed in.

Here's my map in RGF93/Lambert-93: enter image description here

And here's the WebMercator one: enter image description here

I understand it can be differences in angles or areas between both projections but why the same scale doesn't give similar zoom level?

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    How does it look if you compare projections in Reykjavik ? – Kirk Kuykendall Dec 9 '16 at 15:29
  • This site shows area where projections are useful. spatialreference.org/ref/epsg/isn93-lambert-1993 – Kirk Kuykendall Dec 9 '16 at 15:30
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    Web Mercator is used for the whole world, while Lambert 1993 is designed for France. – mkennedy Dec 9 '16 at 18:25
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    That's a good point. If both maps were really in 1:10000 scale, they shouldn't look such different! ..However, ArgGIS does not seem to compensate the distortion caused by Web Mercator ESRI FAQ. No wonder we feel as if the map was enlarged going apart from equator. This nice blog post by Oren Gal suggests a workaround (i have not tested). So I do agree with @KirkKuykendall and @mkennedy; stick to Lambert93 (RGF93?)...when it comes to scaling issue. – Kazuhito Dec 9 '16 at 20:33
  • Now that's confusing - there's a difference between Lambert 1993 and Lambert-93. The former is used for Iceland, and the latter for France. spatialreference.org/ref/epsg/rgf93-lambert-93 So @mkennedy, I guess you really mean Lambert-93. – Kirk Kuykendall Dec 10 '16 at 2:31
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Map scales are never constant: they vary with location and even can change with orientation. The nominal WebMercator scale applies only at the Equator.

Inherent distortion in the Mercator projection must increase the scale uniformly in all directions as a function of the latitude. In France, it will expand all distances by about 50% or so, varying a little from south to north.

The distortion factor (for a spherical model of the earth) is the secant of the latitude. When 153 meters on the earth appear to be 226 meters, for instance, this indicates the secant of the latitude is 226/153. That corresponds to a latitude of 47.4 degrees (north or south). In the North, that would place you right in the middle of France (near Tours).

Any projection designed for a small country (spanning perhaps ten degrees in any direction) will have relatively little distortion. We may take the map in the Lambert projection to be accurate. Thus, we should expect the Mercator map to show features about 50% larger than they will appear on the Lambert map.

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    Good explanation, thanks a lot. You guess almost right, it was Angers at the same latitude than Tours! So if I understand right, when I produce a WebMercator map (I do that for a webapp compatibility), I have to recalculate the scale depending on the latitude if I want to add a scale bar in the print map. – superrache Dec 12 '16 at 8:56

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