if it is a fabric cut like a fq...the measurements actually vary by shop...a (normal) fq is 18"x 22" (at a shop they start with cutting a 1/2 yard, then cut this in half at the fold. so 18" = 1/2 yard, 22" is the cut at the fold so, if your fabric is only 36" wide your fq is only going to measure 18"x18"...
now moving on...a fat 1/8 is that fq cut in half...here is where you get different measurements. one shop will cut it in half the long way...giving you a cut that measures 18" x 11" sometimes you get 22"x9"...i always check where i'm getting them. so for a fat 1/16 it would be 1/2 of that fat 8th...normal would be 9"x11" it all still depends on the actual width of the fabric that does vary bolt to bolt...but pieces 9"x11" are considered fat sixteenths.