Stair Slope in Degrees and Rise and Run Relationships

According to people that know the rise of a step with the run:

• The sum of one rise and run should equal 17" - 18"
• The sum of two risers and one run should equal 24" - 25"
• One rise times run should equal 70" - 75"
• The acceptable slope is between 20 and 50 degrees, with the preferred slope being between 30 and 35 degrees.

If your choice of the rise and run ratio matches or comes close to the above measurements, you are doing OK with your stairs, and if it is within the restrictions of your building code, you are good to go!

A study conducted by the National Library of Medicine (NLM) found that the optimum riser was 7.2 in (183 mm), and the optimum tread (run) was 11 or 12 in (279 or 300 mm). These dimensions were acceptable to both males and females, young and old.

With these measurements, the slope of the preferred stairs equals 32.9 degrees, the sum of the rise and run; 18 3/16", the sum of 2 x rise and run; 25 3/8" and rise * run 79 1/16".

There are multiple ways to develop the ideal slope for your stairs, but the ideal slope depends on your personal preference. It has to work with the stairs' overall height and the room you have for a total run, plus it has to be in the range of max and min measurements as set out by your local building code. The problem you can run into is not having the required headroom, and the landing size could become too small. Problems can be resolved by either making the staircase opening into the next floor longer(new construction) to gain more room or increasing/decreasing riser height and tread depth. And this, of course, will change the slope of the stairs.