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I am trying to convert Web Mercator (3857) to NAD 1983 StatePlane Texas Central FIPS 4203 (2277) in ArcMap but whenever I use the Project tool (Data management) it says there are no transformations available.

What is the correct way to do this transformation using ArcMap 10.5?

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    EPSG:3857 is Web Mercator, not WGS84 (Geographic Decimal Degrees). Please Edit the question to specify the exact release of ArcMap.
    – Vince
    Commented Jun 7, 2019 at 15:44

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If you don't get any geographic/datum transformations, that usually means we couldn't recognize either the input or output geographic coordinate reference system. The geographic/datum transformations contain the input/output geographic coordinate reference systems.

While a person can tell it's WGS 1984 being used by Web Mercator or that the state plane zone is using NAD 1983, the software is stricter. When you look at the layer properties in ArcMap, does either one say the coordinate reference system's well-known ID (WKID) is zero? If so, try redefining the coordinate reference system of that dataset. There's something in the definition that doesn't match what ArcGIS expects.

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