Very small measurement used by toolmakers & engineers, or roughly .0001 or one ten thousandth of an inch. Actual size may vary between shops, but always much less than a pussy hair. About one tenth of a skosh which is equal to approximately one nudge of the dial.
Note: When specified, generally regarded as smaller than the smallest one can measure or produce, since while most people intuitively understand that a gnat's ass is pretty small, few have actually bothered a gnat to measure one.
"Clearance is clearance, Clarance, but that die is only missing by a gnat's ass".
A very small amount
Guy 1: Did you see the newbie at the party? I couldn't get near her all night.
Guy 2: Oh, yeah I saw her. I worked the floor for two hours and I was a gnat's ass away from her when she left with her friend.