So I was experimenting with half-blocks and stairs, and made this structure:
and since I was inside it when I placed the last stair, I found that I was trapped.
This surprised me since the space inside the structure is 2 blocks tall and 2 blocks wide, and the gap between the stairs in the corner looks quite large. Doing some basic geometry, it's clear that the gap is 1/sqrt(2) or a little more than 0.7 units wide (where 1 unit is the width of one side of a block). It is already obvious that Steve can fit through a 1 unit wide space, but noticing also that doors have width(thickness) and Steve can still fit through the space in an open door seems to imply that Steve's width is somewhat less than 1 unit but more than 0.7 units. I've checked out the Minecraft Wiki and did not find anything detailing this aspect.
How fat is Steve (and the other Steve-sized mobs)?
Edit: I did a bit more research and found that doors take up 3/16 pixels of 1 unit, leaving 13/16 or 0.8125 units of space that Steve can fit through, with some wiggle room left. This can be seen in the following screenshot:
So the range now is 0.7071 < Steve < 0.8125.