I'll give you the short version. While actual armor thickness doubles at 60 degrees and is about 1.5 times vertical at 45 degrees the effective thickness is more like double at 45 and triple at 60 degrees.
Now, there are a considerable number of of other factors involved in this including the type of metal, its manufacturing process (cast steelis less effective than rolled plate armor for instance by a slight amount), the type of shot being used, etc.
For a basic introduction to this see: "Design and Development of Fighting Vehicles" by R. M. Ogorkiewicz.