If you're asking how to know the overall size, there are many variables that have to be turned into values. Consider at first the offset of the nozzle center to the extreme edge of the carriage on both sides of the carriage. If you have 20 mm distance to each edge of the carriage, then you know the bed will be 40 mm larger than your x-travel. The carriage travels on a gantry and you will probably have asymmetrical measurements from the nozzle to the front of the carriage and from the nozzle to the back of the carriage.

Progressing outward, the mechanism containing the belts and pulleys add to the dimensions.

It's not going to be as simple as your suggested formula, I believe.