real dimensions of 2 by 4 in inches/centimeters
A dimensional 2x4 is 1.5 inches x 3.5 inches.  The reason being, 2x4 describes the rough dimensions before the boards are milled down to their "dimensional" (flat/even) size.  So you start with a rough 2"x4" board that might be somewhat warped, crooked, rough, etc..  then it is passed through the mill, where it is planed/cut down to the final smooth/flat/hopefully not warped 1.5"x3.5"

Note that this applies to soft woods like pine.  For hard woods, you typically talk in terms of the number of sides that have been Surfaced, and there is less material taken off.  A 2x4 oak board that has been surfaced on all 4 sides, for example, ends up being 1 3/4" x 3 3/4"