Stair math

mtnrdredux_gwNovember 27, 2012

For those of you that have a single, straight flight of stairs in your two story home, how much space does it take up on your floorplan (assuming an 8' ceiling and thus 9' in total to get to the upper floor).

I just wanted to double check becuase when I google it, i get various answers, but a few work out to about 12.5 feet (eg see link). I think VirgilCarter suggested 16 feet.

I know local codes can vary, but it'd be helpful just to have a few empirical points, as I play around on my own with floorplans before meeting with architects (I've narrowed it down to 3 to meet with)

Here is a link that might be useful: stairs and floorspave

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All I know is that my ARCHITECT and his program got the math wrong and we had to figure out a work around to provide passage by at the foot of the stairs.

    Bookmark   November 27, 2012 at 10:50AM
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Annie Deighnaugh

Best stair run is 7 x11, but they usually are a little less generous for residential use, but that will give you a rough estimate for stair run.

    Bookmark   November 27, 2012 at 11:01AM
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I think you are giving me rise and run or tread numbers. I may have miscommunicated.

Think of my stairs as a user of floorspace on my first floor, almost like a very large sofa. What size rectangle would a straight run of stairs that goes from an 8' first floor to a second floor need?

    Bookmark   November 27, 2012 at 11:31AM
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A tread dimension can be arbitrarily selected using a tread to riser ratio but a riser must be an even multiple of the total rise of the stair so you only get a few choices.

For your condition you will have 3 choices and you should select them based on your preference for how fast you want the stairs to rise and then choose a tread dimension using your preferred rise to run ratio.

Using the Ratio I prefer, T=20-(4R/3), here are the 3 possibilities:

Fast Rate of Rise: 14 R @ 7.7" with 13 T @ 9 3/4" = 10-6 3/4 Total Run
(or 13 T @ 10" = 10-10 if the min. tread size is 10" - which alters the ratio slightly)

Medium Rate of Rise: 15 R @ 7.2" with 14 T @ 10.5" = 12-3 Total Run

Slow Rate of Rise: 16 R @ 6 3/4" with 15 T @ 11 1/2" = 14-4 1/2 Total Run

A different rise to run ratio might change these total run dimensions by a few inches but IMO would not improve the comfort of the stairs.

    Bookmark   November 27, 2012 at 11:59AM
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Reno's calcs and options are on the mark, and exactly the way in which to calculate and evaluate stairs.

The mistake a lot of folks may make is to automatically opt for the smallest footprint for stairs, thus making them as steep as the code will legally allow. This is often a mistake, since stairs are both a comfort and safety issue for occupants, young and old. IMO, it's much better to err in stair design on the side of comfort and safety, using the lowest reasonable riser and the widest reasonable tread. In Reno's calcs above, that would the "slow" rate of rise.

If the additional 4' of total run is really a space and/or a budget issue, redesign the house to accomodate it! You'll be glad you did for as long as you live in the house and use the stairs.

Just a thought...

    Bookmark   November 27, 2012 at 12:10PM
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Thanks, Renovator, that is just what I needed.

    Bookmark   November 27, 2012 at 12:11PM
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Thanks, Virgil, I will keep that in mind. I don't want a "Black Diamond" staircase where you have to strap on your ski goggles first.

In my particular (crude, amateurish and totally hypothetical) floorplan, the extra 4 feet turns into an extra 4x44 feet, times two, and requires me to change the existing foundation. Hence a big expense. I have a few ideas of how to do this without adding 4', but I wanted to make sure I was working with a good number on the staircase.

One last question --- Am i right in perceiving that old homes (not a grand home, but more like a farmhouse) tended to have narrow and steep staircases? I have to admit I like that look. Not so much that I would choose the steepest allowed under code, but enough that I might not opt for the most generous.

Bonus question -- if I am stacking stairs, can the stairs to the basement be less steep then the ones from the 1st floor to the second? I am thinking you could go less steep on those, but not more steep (as youwould not have the headroom). Did I get that right?

    Bookmark   November 27, 2012 at 12:19PM
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The only way to be sure of the headroom of a stair under another stair is to draw a section through them and see. The headroom can be changed by changing the rise to run ratio or by starting one stair at a different place than the other. If they start at the same place and have the same rise to run ratio there should not be a problem since the minimum headroom is 80".

Traditionally a stair to the basement would be steeper but today's codes make it impossible to create a stair that would be uncomfortably steep. However, some states have retained the old riser and tread limits. Where is the project located?

For me the ideal stair is 7 12" x 10" but that only works for a 10 ft floor to floor height.

    Bookmark   November 27, 2012 at 1:43PM
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M, I'm not following your comment about "4 X 44 feet, times two", but if I look at your first and second floor plans, the scale of them suggests adequate room for a reasonable stair that is not at absolute code minimums, i.e., a "Black Diamond" stair (a good term).

Can you explain further?

    Bookmark   November 27, 2012 at 4:41PM
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Time for a reality check.

If the applicable code for any project is the IRC, it is not possible to create a stair that is uncomfortable or unsafe so there is no reason to talk about Black Diamond stairs unless the applicable code is less strict or nonexistent.

IMO the code minimum of a 10" tread is ideal. Then if you use a good ratio the riser will be 7 1/2" which is also ideal IMO.The problem is that this is not how a stair is designed; a stair riser must first be selected to evenly fit in the floor to floor height and that is 7 1/2" only for very limited conditions. Stair designers are entirely at the mercy of the dimensions of drywall panels and floor joists.

If it will fit the floor to floor height, the steepest stair that the IRC will allow is 7 3/4 x 10.I would lower the riser but the tread is ideal and it would be a lot better than the 8 1/4 x 9 stair that was allowed before 1993.


To be clear, I would not recommend the slow rate of rise stair in the 3 examples above unless the stair was in a public building. My ideal residential stair would be between the medium rate of rise and the fast rate of rise but unfortunately the floor to floor height will not allow a compromise. I would let the Owners make the decision.

This post was edited by Renovator8 on Tue, Nov 27, 12 at 17:16

    Bookmark   November 27, 2012 at 5:01PM
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Yep, stair design should definitely be about reality--the owner's family reality.

Just measure the length of one's shoe and compare it to the tread width when walking down stairs. Remember that one almost never puts one's heel against the riser when stepping down onto each tread. Said differently, one's heel is often an inch or more away from the tread, and most people put their weight on the ball of their foot as it descends and lands on each tread.

What all this means is that adults, children and older folks like me may often find the ball of their foot at the very edge, or beyond, of code-minimum treads. A 10" tread may be ideal for some folks, but it may be very dangerous for others, particularly those not always focused on there they may be stepping.

Why risk falling and injury with stair design, when it's not necessary? Just design the stairs to be safe and comfortable, and not designed simply to meet code standards, minimum or otherwise.

It's good to remember that what may be ideal for one, may not be ideal at all for others. Always good for the owner to make the decision that's in their best interest--safety!

Only a thought, not trying to get into an argument!

    Bookmark   November 27, 2012 at 6:34PM
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I will add, a stair too deep is also a problem though. I watched my grandfather recently nearly fall backwards while going up a set of stairs in a restaurant because their rise was so shallow with too long a run (imo). He is losing his balance in his old age, and after about the 3rd step, his feet weren't making it far enough onto each stair (therefore, nearly falling backwards. I caught him and he adjusted for the next 3-4 stairs, and we did it again). The body is used to climbing stairs in a certain parameter and anything outside that (too steep or not steep enough).

    Bookmark   November 27, 2012 at 7:17PM
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Thanks guys, I really appreciate all this input. I hope it is helpful to others and/or an interesting intellectual discussion for you, because I am half afraid that, once we sit down with professionals, we will go a totally different way and you'll be left wondering why you spent so much time helping me size stairs that will never be built!

You have me curious now so I went and measured our steps. The tread is 11.5". The rise is 8 (7.25 if you don't include the thickness of the tread?). These steps always struck me as easier than most. I will have to try the basement ones next, which like most basement steps are at least a Blue trail. : )

PS Virgil, not to waste too much more of anyone's time on my hypothetical amateur plan, but in the latest version I posted, the stairs took up 10'10" IIRC.
When you suggested I might need 16', I scrambled. My first though was to leave everything the same, just try to make up the 5' by making the house deeper than 24', which we can probably get approved. Of course then I thought, there goes my plan to use the foundation. Then I thought, what about cantilevering? We cantilevered a room we built on here in order to save tree roots. I googled it and it looks like I can't hope to gain more than 4' by cantilevering (if code even allows it). So I figured I can just make the rectangle 28x44 instead of 24x44, and maybe not need a new foundation. All well and good, but then I have added 4x44x2stories, or 352 square feet. That's another 100k or more.

Then, I had another idea that I think is even better. One side of my hall will be stairs and nothing else, the other side will be the PR, plus the closet and the pantry, and it should fit. I would move the stairs to the N side though, so that I have a pantry near the kitchen. I will post what I'm thinking later.

But again, i feel guilty about people spending so much time on something totally preliminary!

    Bookmark   November 27, 2012 at 8:47PM
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Annie Deighnaugh

I always remember the 7x11 as the safest stair run...not only because it is the numbers in craps, but I learned it in a pleasant conversation with an airplane seat mate who happened to be some big honcho in the government on safety regulations and injuries. I insisted in our house that we get as close to that ratio as possible, and as a result, our stairs are very comfortable.

As far as steepness, I remember the stairs at the old house...they were not only steep but extremely narrow, with low was an absolute struggle to get a double mattress up those stairs...with the ceiling and floor scraping the edges. Awful.

    Bookmark   November 27, 2012 at 9:15PM
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LOL, Annie, that's one way to supplement my budget. Maybe I can try my hand at the craps table. Foxwood?

Here is a version where I expanded the size of the staircase to 12'3" from my last version which was 10'10". I moved the stairs from the S side of the hall to the N side. I think it'd be an OKAY plan, except the basement needs more thought.

In the basement, moving the stairs means that I am left with only a 3' hallway to the guest room. Maybe that feels ok if the stairs are open, maybe it's not code, IDK. The interior wall of the playroom and guestroom as shown is the original stone wall from 1925, before an addition. Don't want to mess with that too much. I didn't even try to adjust the basement bathroom because maybe I can make a landing and turn the stairs, but to size that I'd need a PhD in Stairology.

BTW --- no comment necessary everyone --- just completing my stair math saga. Let's save our energies for analyzing a professional's plan!

thanks all, again

    Bookmark   November 27, 2012 at 11:26PM
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Off the top of my head, the number 126" popped up. Then Renovator8's first (steepest) stair proportion proved it. I keep that number in my head as the "bare minimum" figure for layouts/floorplanning. I forgot the 3/4"!

    Bookmark   November 28, 2012 at 12:09AM
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"The tread is 11.5". The rise is 8 (7.25 if you don't include the thickness of the tread?)"

That doesn't seem right by any standard. I assume you have measured the nosing and the actual tread size is about 10.5" . However, an 8" riser should have a 9" tread and a 10.5 tread should have a 7.25" riser so something is very wrong.

For design purposes a "tread" is the distance from the face of one riser to the face of the next riser measured horizontally and any nosing is ignored. A "riser" is the distance from the top of one tread to the top of the next tread measured vertically.

7 x 11 is the minimum code requirement for stairs in public buildings in order to accommodate as many kinds of physical limitations as possible. It would be on the slow rate of rise side of the spectrum in a residence and doesn't work for a 9 ft floor to floor height.

    Bookmark   November 28, 2012 at 12:12AM
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Ahh yes, Renovator, when I went to measure it, I realized yet again how complicated a stair is! I did stop and wonder about tread thickness, but then I forgot about the nose. I am just curious so I am going to try again!

Sombreuil, I was kind of hoping for a simple number like that, and was surprised when I couldn't get it googling.

    Bookmark   November 28, 2012 at 12:26AM
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Here is a chart I put together years ago. It shows the possible stair designs for 8, 9 and 10 ft floor to floor heights using the rise to run ratio recommended by the AIA.

All you need to do is select the floor to floor height and then choose the preferred rate of rise to get the tread size and total run. After that riser heights would not be used. For the builder a stair design is adequately described by the number and size of the treads and the total run [14T @ 10.5" = 12'-3"] The stair builder would then divide the actual floor to floor height by 15 (14+1) to get the true riser height. The total run tells him any nosing would be added to the tread dimension.

This chart shows the math in graphic form.

    Bookmark   November 28, 2012 at 8:57AM
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Reno's chart is an excellent aid for designing stairs and gives options for everyone's evaluation. It should be a part of every prospective homeowner's notebook of ideas. It's a lot easier to start with a properly designed stair than to try to fit one in after the plan is largely complete.

    Bookmark   November 28, 2012 at 10:14AM
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FWIW, I was able to find the applicable code on line, and it does allow for a Max riser of 8.25 and minimum tread of 9. Whoa! I think common sense will dictate something a bit gentler.

    Bookmark   December 1, 2012 at 11:11AM
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Usually when local codes allow these minimal stairs the goal is to allow as much flexibility as possible to homeowners and builders. That said, this type of stair is really very steep and seldom advisable, except, perhaps in ships and ocean-going vessels! Little joke, there!

    Bookmark   December 1, 2012 at 11:54AM
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Rennovator 8, why do you not suggest the slow rate of rise design? I had seen your stair chart on Garden Web in the past and thought that the 'monumental' design best suits the home we are planning for our retirement.

    Bookmark   December 4, 2012 at 9:56PM
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Stairs must be designed for a specific house design and in this case the OP has a serious space problem. Also, for a slow rate of rise stair the OP's floor to floor height would dictate a 6 3/4" riser with a 11 1/2" tread run which I believe is too slow for an active family but would be fine for a public use building or for the elderly.

    Bookmark   December 5, 2012 at 6:55AM
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Something that also needs to be taken into consideration is the height of the joists between the floors. In our case, that is 14" for one floor and 16" for the other floor which translates to an additional 2 to 4 inches of rise than the chart above.

    Bookmark   December 8, 2012 at 8:44PM
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Angela, yes, of course the floor joists for each higher floor have to be considered. Reno's chart made the common assumption that the joists are 2 X 12s--frequently used, so a common assumption. Your engineered joists suggest a clear span of greater than normal distance--very important to know when calculating stairs, and another reason to figure this out early in the design process in order to have the needed room.

I'd point out the obvious for everyone, ie, the risers will be the result of the calculation of the floot-to-floor height, and the height most comfortable and safest for occupants and visitors.

Horizontal tread dimension is, however, a variable, within accepted standards for stair design, and can vary an inch or more, one way or another. So pick the combination of riser height and tread width that works best, and isn't simple the minimums allowed by the building code.

    Bookmark   December 9, 2012 at 9:27AM
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