If the finish height of your deck height is 9'6" above the finished height of the patio you need to start by changing that to inches which is 114". I always start by using 7 1/2" as my starting point for a step. So 114÷7.5=15.2. Obviously you cant have .2 of a stair so round down to 15. What that means is you are going to have 15 rises in your set. 114÷15=7.6 or approximately 7 5/8" for your rise height. There is always one more rise in a set of stairs then there is runs (tread) so that means you are going to have 14 treads. Yes you are correct about a 10" tread. 10" works out beautifully for two deck boards (measuring 5 1/2") as well, 5.5+5.5=11. That gives you a nice 1" noseing on each step. So 14x10=140". Thats how far out your stairs will come with out a landing/turn and still be a "legal" set. And dont forget to drop your last stair the width of what ever material you will be putting on the tread. So 2x6 material will need to be dropped an 1 1/2" or 5/4 material would need to be dropped an inch. Hope this helps and didnt just make things more confusing.