# Stair Slope in Degrees and Rise and Run Relationships

According to people that know, the rise of a step in relation to 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"
• Acceptable slope is between 20 and 50 degrees, with the preferred slope being between 30 and 35 degrees

If your choice of 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!

Rise in n
d
Run in n
d

#### Results:

 Slope ° Rise plus Run # Two x Rise plus Run # Rise x Run #

#### The Calculator

1. enter the rise in inches plus fraction of an inch
2. enter the run in inches plus fraction of an inch

#### The Results

1. the slope of the stairs in degrees
2. result of rise plus run
3. result of two times rise plus one run
4. result of one riser * run

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 equal 32.9 degrees, the sum of 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 come up with the ideal slope for your stairs but the ideal slope depends on your personal preference and it has to work with the overall height of the stairs and the room your have for total run plus it has to be in the range of max and min measurements as set out by your local building code. Problems you can run into is not heaving the required headroom, the landing size could become to small. Problems that can be re-solved by either making the stair case 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.

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