I think the info Tommy found ends up being pretty good.
You know me... I had to go put my mad food scientist hat on for this one!
I weighed both ground cinnamon and cinnamon sticks, and here's what I came up with:
A teaspoon of cinnamon weighs about 2.6g
The 3" cinnamon sticks I have weighed roughly 3g - 4g each.
That means a 3" cinnamon stick, ground up, would yield between 1 - 1.5 tsp ground cinnamon.
HOWEVER... ground cinnamon is a lot stronger than stick, because it has a lot more surface area, and it STAYS in a dish, whereas a stick imparts some of its flavor and is usually removed. So, it will take much LESS ground cinnamon to get the same flavor as cinnamon stick.
So... 1/2 tsp ground cinnamon should work as a substitute for a 3" stick