How is a transformer capacity rated?

The current rating for a transformer depends on the gauge of the wires used in the windings. The usual rating is 1000 amps per square inch so a wire of 1/100 square-inch cross section would be rated at 10 amps.

The voltage rating is set by the amount of magnetic flux in the core, which is chosen to give a reasonable amount of power loss due to eddy-currents in the core. This depend on the peak flux-density rating for the core material, and a rule of thumb would be to use 1 Weber per square metre.