I have a polygon which is in Arc 1960 UTM Zone 37S coordinate system and I need to transform it to to WGS 1984 UTM Zone 37S. I have not been successful in doing this using ArcMap.
Is there a solution for this?
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Esri has geographic/datum transformations between Arc 1960 and WGS 1984 for:
You can look these up in the PDF file, geographic_transformations in the Documentation folder of your ArcGIS install. Or by following the link near the bottom of this doc page: What are map projections?
None of them have particularly good listed accuracies. If your data is outside these areas, and you have a version post 10.4, you may be hitting a restriction based on the data's area of use versus the transformation areas of use. The data area of use must touch or intersect a transformation area of use for the transformation to be considered appropriate.
You can get around this in ArcMap itself by adding more data that does fall in the transformation's area of use to the point that you can pick it in the Transformations dialog (data frame properties, coordinate system tab). It will be applied to all Arc 1960 data. You can then right-click the layer in the table of contents, select Data, Export Data to open a dialog. In the dialog, choose to export in the data frame's coordinate system.
Disclosure: I work for Esri.