how long does a caterpillar stay a cocoon for?

Answer 1

There are many factors involved like:
the temperature, the species of caterpillar, the humidity, the barometric pressure, the food sources available to and general health of the caterpillar prior to formation of its cocoon, and general climate.
For a Monarch caterpillar I caught in Wisc. in late June and fed milkweed to years ago, it took approximately 3 weeks to come out of the cocoon.

Answer 2

It depends on many, many variables, such as species, temperature outside, light, whether it is an overwintering cocoon, etc. You would need to find out what kind it is to determine that. Also, do NOT take cocoon's inside to hatch. This will alter the emergence time of the butterfly/moth and it will lose the opportunity to feed (if it is the type that can) and mate. Not nice!