Stairway Rise Angles

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History is a tool used by politicians to justify their intentions.

— Ted Koppel

Figure 1: I Consider A Well-Done Stairway to be Mathematics in Wood.

Figure 1: A Well-Designed Stairway is
Mathematics Carved Wood (Source).

I was reading this month's Journal of Light Construction (JLC) when I saw an article on building safe stairways per the International Residential Code (IRC). I have written about stairway rise angles before, but from the standpoint of three commonly used stairway design rules of thumb. The IRC provides a hard upper limit that is lower than the maximum permitted by the most liberal of these rules of thumb.

The JLC article (which I cannot find online) provides an interesting graphic (Figure 2) that shows a maximum stair angle of 37.78° (red line).

These angles are important because people are quite sensitive to even minor changes in stair rise angles.

Figure 2: JLC Graphic Showing IRC Maximum Angle.

Figure 2: JLC Graphic Showing IRC Maximum Angle.

The IRC sets the maximum allowed stairway rise angle by setting the maximum rise and minimum run. Figure 3 shows how to use these values to calculate the maximum stairway rise angle (green highlight) allowed by the IRC. I have also included the stairway rise angles for some other common rise/run combinations. The vast majority of stairways have rise angles between 30° and 35°.

Figure 3: Angles for Common Stairway Risers and Tread Lengths.

Figure 3: Angles for Common Stairway Risers and Tread Lengths.

I have to admit that I love designing stairs and roofs. There is something magical about using a few formulas to create something that is both beautiful and functional.

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2 Responses to Stairway Rise Angles

  1. Peter says:

    "Tread" appears to represent the total depth of the flat piece of wood you step on - typically called the tread!
    But slope ratios are properly based on the run - which is the horizontal increment from one riser to the next, or from one nosing to the next.
    Run = tread - nosing overhang

    • mathscinotes says:

      Good catch! I have updated the post and included a reference with the rise and run mandates.


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