Coordinate Conversion

[Mutukwa_BenMusole]

I have a Zambian map in local coordinates in meters and would like to convert them UTM. How do I compute the conversions. I totally have no Idea. Please help?

[RobertBorchert]

Create a new database with a feature dataset in the coordinate system you want with some features from the new coordinate system you wish to be in.

use the data loader to load the Zambian map into the feature dataset.  ArcCatalog will automatically convert the map to the new projection.

I have a Zambian map in local coordinates in meters and would like to convert them UTM. How do I compute the conversions. I totally have no Idea. Please help?

[JimCousins]

Could you be more specific?
Is your "local coordinate" a full system with defined paramters, or is it a "Site coordinate" with a randomly chosen 0,0 point and all coordinates based on the x,y offset in meters from that point?
if it is a defined coordinate system, you could follow Robert's suggestion.
If it is in site coordinates, you will have to use "Spatial Adjustment" tool to reposition your data. This assumes you know where at least 2 features shown in the map are located in UTM coordinate space.
Regards,
Jim