My first stair building experience sort of took the mystery out of it all. I didn't have to do much figuring because it was a deck replacement job. All I did was save the old stringers from the demo of the old deck. In doing so it all started to make sense to me. How the stairs were attached, the width of the treads, and how high each step was became less of a secret to me.
Anyone with the courage to take on this job needs only patience, basic math, a framing square and the ability to stand back and look at the big picture.
The first thing I look at is how high it is to the top of the landing or deck the stairs will be rising to. A comfortable step is in the 7 to 8 inch range. With this in mind I divide the height to the landing by seven. If the height to the landing is 70" then it will take 10 rises to get to the top of the landing. I used 70" to simplify this example. Ninety-nine times out of a hundred it will be 7" and some odd fraction. For instance if the height was 73 1/2", the rise would be 7 1/2".
When building stairs there is always one less tread than there is risers. In this case with 10 risers, that means there are 9 treads. When cutting my stringers, I like to make the cuts for my treads 10" long. At this dimension I can use a 2x12 for treads without ripping them to a narrower width. This gives me a nosing or overhang of 1 1/4". It also makes it easier to figure out how much room the stairs will require. In this case 9 treads X 10" = 90". The total run of the stairs is 90".
An example of how easy this works are stairs that go from the 1st floor to the 2nd floor of a house with an eight foot ceiling. This takes 14 risers at 7 and 5/8 inches (I've cut so many of these it is forever imbedded in my mind). This means there are 13 treads. Thirteen times ten is 130". I always made my stairwell opening 120". This lets 10" of the stringer (a full tread) sit on the deck or concrete floor. It also leaves plenty of headroom for the stairs below if there is a basement. The same well opening above (120") also gives you enough headroom.
This can seem like an overwhelming project. Like any other project, if you take the time and patience and a little thought you can acquire the ability.
