Can someone give me a formula for figuring required roof slope for bonus room above an attached garage. The bonus room is to have 8 foot ceilings. Garage is 22' wide and has 9' ceiling.

What is "required" slope. Since the roof is already there you have a slope. Unclear what you are asking. Do you want to determine existing slope? If you want 8 ft. ceilings, find the point where the roof rafter angle is 8'1" above the floor, drop a line, do the same on the other side and connect with a string level. How high is the roof above the garage? Was the garage ceiling built to support live load?

Thanks for trying to assist me. Sorry for the confusion. I am drawing a new house plan that has a bonus room above the garage. So the roof can really be any slope at this point. I am trying to find out the slope needed to have approx 8' ceiling.

That depends on how wide you want the ceiling. For a straight gable you will need at least a 12/12 to even get a small ceiling. Have you considered a Mansard roof, you have a lot more flexibility with the 60/30 degree angles?

I have little expertise in detailed housing construction. But I have a room over my garage and I had to check the roof slope a few weeks ago for other reasons, and it is 9/12 (too steep for me to walk on).

But there are many possible variations. Our room is 8 feet high for a width of about 6 feet (+/- didn't measure it)in the center and slopes off on each side to about 5 feet height, but works well. The room has a half bath but did not have a closet. We just built a closet which was expensive to do properly. Try to include a closet in your design if you want to count it as a bedroom later on.

The slope of roof should be governed by slope of main house for artistic reasons. This would be for traditional designed house.

Chuck

Draw it on graph paper.
If your garage is 24' x 24', a common size, then a 9/12 roof is easy: it's 9' to the ridge.
An 8' ceiling (under a gable roof) gives you a flat ceiling width of 32", but if you make kneewalls that are 5' high, you have a room width of about 10' 9'' by 24' long, with sloping ceiling. And windows at each gable.

A 5' high kneewall is good for built-ins. Or short people like children.

The exact inches of all this will depend on how the rafters are connected, of course. Once you have designed the construction, you can find calculators online to tell you exact measurements.

(PS: put a gable end over the garage opening, so you don't have water pouring over the gutters onto you as you go in and out. And even though windows in gables provide ventilation, you still need channels and a ridge vent when you insulate rafters.)

http://i819.photobucket.com/albums/zz111/lacogada/askroof_zps4a4b2da3.jpg (http://s819.photobucket.com/user/lacogada/media/askroof_zps4a4b2da3.jpg.html)

Very nice, dannac!

Whether 9, 10, or 12/12 pitch, there isn't a lot of sense I guess in having a tiny flat part of a ceiling. Just continue the sloping wall up to the ridge.
Unless you want ceiling lighting. But it adds more work regardless. And with the heat generated under roofs, I am not a fan of any wiring running through or above rafters. I think it's a fire hazard.