HOW TO CALCULATE STAIRS, PERIOD.

Your basic straight run stair. The flat
parts are "treads", and the vertical parts
are "risers".

Years ago, when I worked as a framer, I always got stuck building staircases because I was the only sucker willing to do the math involved. After a while, I earned the title of Exalted Stairmeister around the job site. Secretly, I had to chuckle at this, because in reality stair design involves nothing more than basic arithmetic. Try it yourself:

First, decide on the basic stair configuration—straight, L-shaped, or U-shaped. Unless you’re a masochist, don’t even think about building a curved stair. The correct choice depends on how much room you have in your floor plan, the sort of look you’re after, and a few other factors that, lucky for you. we don’t have room to address here.

Once you’ve decided on a straight, L-shaped, or U-shaped configuration, determine the total rise of the staircase—the vertical distance from one floor to the next. For this example, let’s assume a typical height of 106”.

Traditional U-shaped stair with a half-landing
is space efficient and less strenuous to climb.

Next we have to choose an appropriate height for the riser (the vertical distance from one tread to the next). There a re several guidelines here. For starters, most building codes don't allow any stair riser to exceed 8” in height. Moreover, few good contractors will use a riser greater than about 7 1/2”, since anything higher will yield uncomfortably steep stairs.

Okay.  Let’s say we want our stairs to have a fairly gentle slope, so we’re looking for a riser height somewhere around 7”.  To determine the exact height, we divide the total rise from one floor to the next—in our hypothetical case, it’s 106”—by whole numbers (representing the total number of risers) until we arrive at a figure as close to 7” as possible.

Through trial and error, we find that dividing the total rise of 106” by 15 gives us about 7.07”.  That’s as close as we’ll get to 7” using a whole number, so we’ll settle on that. This means our staircase will have 15 risers of 7.07” each, yielding a total rise of 106”.  Go ahead—check it out on your calculator. It works.

Rise, run, and total rise and total run. Not rocket science.

Now we have to choose the "run" or tread depth measured front-to-back. There’s a handy rule of thumb to help us do this:  Rise+Run=17.  Ergo, since we’ve already settled on a riser height of 7.07”, our tread run should be about 10”. Simple, no?

Now we know both the rise of our stair—7.07”—and the tread—10”. On a straight-run stair, all that’s left is to find the total run or length of the staircase. To do it, we multiply the tread width times the total number of treads to find the total length required by our staircase. Here's the catch: There's always one less tread than the number of risers, since the top tread is formed by the upper floor itself. So, in our example, the total run of the staircase would be:  10” tread x (15-1) risers = 140”, or 11’-8”.

Exterior stair risers should not exceed six inches, and treads
should be at least twelve inches deep. The gentler the slope,.
the better

Now you can check whether your stair actually fits in the space allocated to it (it probably won't; underestimating the space required for stairs is a common problem for both architects and amatuers). If there’s an intermediate landing, as in an L- or U-shaped stair, it’s just counted as an extra-large tread, and it's added to the total run of the stair.

Remember that the total rise is always divided by a whole number representing the number of risers. You can’t start by arbitrarily choosing a riser height, because when you get to the top of the stair you’ll end up with an orphan step that’s lower than the rest. Note also that this works for any number of risers, including deck steps that have only a few risers between landings. However, for any outdoor steps, the riser should be no higher than 6", and treads should be at least 11" deep.