>I've decided to build some TTBH that will take medium frames so I can do nucs. I know a medium frame is 6 1/4
From top to bottom.
> and that the bottom should be 6 5/8.
I don't understand what you mean. The box is 6 5/8" deep. The bottom is a whole other piece of equipment and the depth of the box is irrelevant to the dimensions of the bottom.
> Is the measurement of the frame (6 1/4) from the top of the frame to the bottom
> or from where the frame hangs?
> How far from where the frame hangs to the bottom of the floor should my hive be?
The box should be 6 5/8" deep. The frame should be 6 1/4" deep. The bottom should be 3/4" deep. So from the top of the box to the bottom of the bottom board that's 7 3/8". If you're making a long hive, then make it out of a one by eight and leave it full depth. If you're making a long hive where the space between boxes isn't an issue, I'd make the frame rest rabbet 3/4" deep and 3/8" wide.
>How long (stretching across the hive) is a medium frame?
The frame is 19". The box is 19 7/8" outside. the rabbet is 3/8" on each end.