Staircase Math – Calculating theFootprint, Rise and Treads
Stairway Geometry Simplified
This is my second article on stairways and their design. In this brief article, I would like to talk about the math of stair design and a few of the more important standards required throughout the US.
A colleague recently told me that his architect had not permitted enough distance for his staircase while constructing his new house. He asked me come over and see if I could help. I started by determining the dimensions of his foyer and the height between the finished 1st and 2nd floors. We determined that he did not have ample room and had to ask his builders to push the staircase 2 feet into his living room. This was one surprise he was not very excited about.
Allow me to start by describing a basic approach to determine the “footprint” of your stairs.
Floor-to-floor height
First determine the height from the finished 1st floor to the 2nd finished floor. Next, divide this height by 7 ½ inches. This will inform you the number of risers will be needed. Risers are the vertical distance between two steps. You will need to {round} this number to the nearest whole number. For example, if your finished floor to finished floor height is 123 inches you will then need 16 risers (123 / 7 ½” = 16). 16 risers will require 15 treads (you always need one less tread than the number of risers). If you’re treads are 11 inches deep then your stairway is 165 inches long (15 X 11″=165″). This would make your stairway’s “footprint” 165 inches in length and whatever width is necessary. It is very simple. Of course, it is probable that a landing be needed to either make a turn or to breakup a long straight run. In either case, the required number of risers and treads do not change. If you require a landing, remember that it needs to be as deep as your stairs are wide. This means that if your stairway is42 inches wide, a landing 42 inches deep needs to be istalled.
My friend and I commenced the project by dividing the vertical dimension by 7 ½ inches since this height is regarded to be the most accommodating. I believe there used to be a rule of thumb that two rises and one tread should equal 25 inches. 7 ½ x 2=15 + 10(tread) = 25 inches. If you require 8 inches for a riser, this would shorten the legnth of your tread since 8 x 2 = 16 + 9(tread) = 25. And so, the theory says that the greater the rise, the smaller the tread; and -vice versa- the lower the rise, the deeper the tread. However, this brings us to the International Residential Code stating that the riser height should not exceed 7 ¾ inches and the depth of the tread should not be under 10 inches. In the old days, if one was short on space for a staircase it was not unorthodox to eliminate a tread and a riser which resulted in a greater riser height. This is known to be hazardous today (exceeding 7 ¾ inches).
Do not include the tread nosing when measuring the “run”.
The rake height is the vertical measurement between the apex of the hand rail and a tread. It has to be gauged from the top of the tread (just above the riser) to the top of the hand rail. Typically, I will line up a 4 foot level with the face of the riser and then “plumb” the level noting where it converges the top of the hand rail. Determine this dimension to achieve the rake height.
The International Building Code states the rake height should be between 34 and 38 inches. Also, a balcony height should be at least 36 inches.
Hopefully, this brief explanation will be practical to those in the beginning stage of staircase design. And if you find yourself, as my buddy did, in the later stage of home construction with not enough area for the staircase, this piece may help to solve the problem of where to place the thing.
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Tags: architecture, home improvement, home remodeling, interior design