The general conversion process is outlined in the diagram below. Projection coordinates are first transformed to their geographic equivalents and then to the new projection if it is in terms of the same datum. If the target projection is in terms of a different datum then the geographic coordinate must be converted to this using a datum transformation then to the new projection.
Coordinates can be converted between projections using the formulae described in the section below if the parameters defining them are known. These formulas are also implemented in the online coordinate conversion utility that is available on this site.