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Fan shaped stairs

sarison's picture

I'm looking for the rise/run ratio of an octagonal stair stringer.  I've built two sets many years ago and don't remember the math.  A straight set is based on a 12" run, while a 45 degree is on a 17" run, so is a 22 1/2 based on 14 1/2"?


Thanks in advance

(post #97728, reply #1 of 6)

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(post #97728, reply #2 of 6)

I'm of the opinion that stairs are all about where you put your feet when climbing them. Some folks have issues with winders coming to a point but if the railing is in 5"-6" I don't see why points would make any difference. Most stair charts show the effects of body position related to the rise and run. The shorter the rise the deeper the tread. A good walking tread/riser ratio is 7 1/2" rise to 10 1/2" run. The tread will actually be 11 1/4" but you don't count the overhang of the tread as walking surface in your computations. I shoot for this ratio where people will put their feet. It's not always possible. Someone like Stan Foster, that builds elegant movie star stairs, may be able to use shorter rises and deeper treads. Your rise is determined by the distance from finished floor to finished floor. Many times, the total run is determined by the space that is provided. You can't arbitrarily say that you are going to make the stairs with an 8" rise. The same may go for the tread width. As you know, all risers should be equal in height and treads equal in width.

In the case of a spiral stair, one that may twist over the bottom part, you also have to look at head room. Head room can often be an issue in a straight run too. If there is such a thing as an average person, their inside foot will fall about 9" to the center from the hand rail. This is where I try to fit my rise run ratio. When I'm faced with laying out a unique stair, I draw it out full scale on the floor, determine the rail location and put the feet in the zone. Tight spiral stairs and utility stairs can push the walking zone limits to a degree, often a taller rise and shorter tread can be used. I don't like to get too close to 8" for the rise, this will mean an 8 1/2"- 9" run or a 9 1/4" - 9 3/4" tread with 3/4" overhang. Some areas can have code restrictions on stairs. If these are for someone other than yourself, you should check with the enforcement rules.

Beat it to fit / Paint it to match

Beat it to fit / Paint it to match

(post #97728, reply #3 of 6)

Actually, what I'm designing to build are a set of stairs on an exterior deck that are octagonal and get considerably wider as they descend.  I just can't figure out the stringer that's on the 22.5 degree. 

(post #97728, reply #5 of 6)

The day after I posted my reply, it dawned on me that you might be talking about a gazebo or platform for a hot tub. Some of the same issues apply as to rise and tread depth. Regardless of the application, you have to be able to comfortably walk the stairs.

You are correct that an octagon will have the ends of the treads cut on a 22 1/2° miter where they meet. Joe has given you a number that will figure your length in relation to the tread width. In your case, you will also have to calculate the fact that you may have an overhang on your tread. Also, like a hip rafter, the stringer will have to be beveled in two directions from the center. Another option is to double up your stringers so that you don't have to land on just 3/4" of an 1 1/2" piece of material. I'm always terrible at remembering numbers like .92388 so I would simply cut a piece of tread at 22 1/2°, on my compound slider. It's a simple matter to mark out your overhang along the front edge of the tread and measure from the short point to the mark.

When it comes to stair stringers, I'm a bit of a nut. I won't cut saw teeth out of a 2x12. Instead, I will cut triangular blocks and attach them to a 2x6, 2x8 or whatever I feel is strong enough for the length of the stair. Depending on the 2x12 you cut teeth out of, what is left can be weak and prone to bowing. By cutting individual blocks it is easier to make them precisely the same and in your case, to bevel or double bevel the rise portion.

When you make your bottom and top cuts on the stringer, plumb and level cuts, you just use your framing square and reference 90° to the tread and riser respectively, like any stair. In a different way, both Joe and I are saying that you need to know your tread width in order to know the length of your stringer blocks or cuts. It's a little different than cutting a hip rafter, for example. A hip is always going in an even foot per amount of rise. Your tread will be going in according to either the width of the material you use or job site restrictions as I mentioned in the previous post.

Beat it to fit / Paint it to match

Beat it to fit / Paint it to match

(post #97728, reply #6 of 6)

thank you both for your input.  The 13" number is what I was looking for.


Hammer, The triangular block method sounds interesting, and I am going to play around with it. after applying the triangles, do you gusset the entire stringer with plywood?

(post #97728, reply #4 of 6)

"A straight set is based on a 12" run, while a 45 degree is on a 17" run, so is a 22 1/2 based on 14 1/2"? "

The 17" is correct for 45°.

For your straight run @ 12" your Octagon run would be 13".

Same as an Octagon Rafter Hip.

A Hip Run at 45° you would hold your square let's say the pitch was 8/12, you would hold the square 8/17.

The Octagon Hip Running at 67.5° you would hold your square at 8/13.

That's if your making your tread at 12". If you want to make your tread at 10" your Octagon tread would be 10-13/16".

You can get the Octagon tread measurement/Hypotenuse using any straight run by dividing the run by .92388.

9" Tread - 9/.92388 = 9.74153" or 9-3/4"

10" Tread - 10/.92388 = 10.82392" or 10-13/16"

12" Traed - 12/.92388 = 12.9887" or 13"

This drawing is a Octagon but I just drew in a 12" tread and a 13" Octagon Stringer.

Hope this helps.

Joe Carola
Joe Carola