A lot of the Gothic boarded stools from the 15th -16th centuries appear to be taller than a modern chair seat, and are also frequently shown in use as side tables. Some surviving stools in European museums are around 22" tall.
One thing I've noticed: when you're wearing joined hose, it's easier to "perch" on a taller stool than to sit in a chair. Is it coincidence that these stools appear around the same time as joined hose?
I started with the seat height as my basis - I measured a standard chair and came up with 18" Eyeballing the pictures Tom Rettie posted, and a number of the period paintings he referenced (and a bunch more I came across as I looked into the idea), I ended up with an equilateral triangle about 15" on a side, which gave me only 13" front to back. In hindsight, I realize that most of the stools shown in the paintings are fairly tall - in many, they seem to be used interchagably as a stool or a side table - check out Pieter Aertsen's "Peasants by the Hearth" http://www.wga.hu/art/a/aertsen/merry_co.jpg I could probably have kept the same proportions, but made it 22" tall and 18.5" on a side and fit pretty well with the images.