Please, stop.
http://en.wikipedia.org/wiki/ISO_216#A_series
A4 is an international standard of paper size- ISO 216 to be exact, which was determined by geometrical and mathematical regularity.
It's 210mm by 297mm, or 8.27in by 11.69in
http://en.wikipedia.org/wiki/Letter_paper#...can_paper_sizes
Letter is a somewhat archaic standard- it's theoretically based on 1/4 of the average stretch of a vatman's arms- from the days of traditional papermaking.
It's 8.5in by 11in, or 215.9mm by 279.4mm.
These are
height and width size standards,
not thickness standards. Each can be cardstock, or regular paper, or tracing paper, etc.