Stair calculation & design questions & answers:

FAQs about how to use simple arithmetic we explain how to make stair design calculations: number of steps, step riser height, total stair height or rise, total stair length or run.

This article series explains how total elevation change between two levels or floors (rise) and stair length (run) are used to calculate the right measurements when building indoor or exterior stairs to fit the building or the terrain.

Stair Building Calculations: simple arithmetic for safe stair designs to fit any situation

Questions & answers about how to calculate the dimensions of stairs and steps to build stairways, posted originally

at STAIR RISE & RUN CALCULATIONS - be sure to review the easy math given there.

On 2020-09-16 by Guru

Hello sir my aire is 15/8 feet Sir ha can posiba rounding sterces please help mi

On 2020-09-16 - by (mod) -

Gu

For a round stair case, as long as you have sufficient footprint space for the stair on both floors, you can buy a factory-built stair for your total rise between floors;

however if the total height change is 15 ft. you may not get building department approval without an intermediate landing.

On 2018-11-12 by Char - Calculate my rise and run dimensions - don't care if I don't meet code

My run and rise is permanent. 105" by 105". The run cannot be changed. I do not care if it meets code exactly. What would by rise and run dimensions be?

On 2018-11-20 by (mod) - I do not care if it meets code exactly. What would by rise and run dimensions be?

Char


Forgive my confusion but you've told me the run and Rise of your stair and then you've asked me to tell you the run and Rise of your stair. I don't understand the question.

If you mean you want to know the individual step rise and run, you can go through the procedure in this article.

Here's an example of how you can build UNSAFE and HARD TO CLIMB stairs that fit your fixed dimensions of rise and run.

Divide 105" in TOTAL STAIR HEIGHT by a reasonable step riser height of 7" - 105 / 7 = 15 - so you'd need 15 steps to climb UP that height at 7" per step up.

Now divide 105" in TOTAL HORIZONTAL RUN by your 15 steps up: 105 / 15 = 7" - that says your steps would be TEENSY in "tread depth" and someone will fall down eventually or you'll have to put your foot sideways to go up and down those stairs.

Here's an alternative design - just to show how you can play with the numbers:

Divide 105" of HORIZONTAL RUN by 10" as a reasonably usable tread depth (the distance from riser to nose edge of a tread)

105 / 10 = 10.5 - or we'd need 10 1/2 steps to travel that distance if our treads are 10" deep.

Let's change our tread depth to a neat number like 10.5".
Now dividing the 105" of horizontal distance by a 10.5" tread depth:

105 / 10.5 = 10 steps

So if we make our step tread depth 10.5" (walking surface depth) we will travel the 105 horizontal distance in ten stair steps.

Now let's see how high or tall each of those steps must be.

Your total vertical rise for your stairs was also 105" (I call these "square stairs" when total rise = total run).

Since we already know we have exactly 10 steps to travel the horizontal distance we know we have the same ten steps to travel the vertical distance.

105" vertical rise / 10 steps to climb = 10.5" step riser height.

Each step is going to be 10.5" tall in your hard-to-climb unsafe stairs.

Better have some great handrails.

On 2017-04-23 by sajjad - How to calculate & lay out stairs for a 13 foot total rise

Hi I want to build stair insid of house along with e right side of the wall...total height of wall is 13ft and width is 15.6ft ...pls guide me to make a stair ... is it easy to draw a staight stair??? I want straight....pls guide thanks

On 2017-04-23 by (mod)

Sajjad

It's pretty easy to lay out a straight stair: we need to find

- the total stair run - horizontal distance

- the total stair rise - from starting floor to ending floor, that you give as 13 feet

We want stair steps to have a uniform height and somewhere around 7" is good.

We want stair steps to have a uniform depth - 11" is reasonable.

13 ft x 12" = 156" total rise

156" / 7" step height = 22.28 steps, so we will round to 28 step risers or steps

156" / 22 = 7.09" so we can make our individual step height 7.1"

Now we know the stair step height

Now 22 steps x 11" step tread depth = 242" of horizontal run

242" / 12 = 20.16 feet

So we know that the horizontal distance needed for the stairs in a straight run will be 20.16 feet.

If you have room for those stairs - that is if there is at least a 3 foot clear space at the stair bottom and stair top (in the direction of travel) then you're good to go.

You do not need to build stairs that are 15.6feet wide - in a residence; instead you'll use a standard stair width
Details you'll want to read are at

STAIR DIMENSIONS, WIDTH, HEIGHT - https://inspectapedia.com/Stairs/Stair_Dimension_Specifications.php

STAIR TREAD DIMENSIONS - https://inspectapedia.com/Stairs/Stair_Tread_Dimensions.php

and if you want to see if your stairs comply with typical building codes see

CODES for STAIRS & RAILINGS https://inspectapedia.com/Stairs/Stair-Code-Details.php

On 2016-10-29 by Lee - How is the rise of an individual step supposed to be measured?

How is the rise of an individual step supposed to be measured?

I have seen measurements taken right at the nose of the step sown along the face of the riser. But the code seems to say that the measurement should be taken step nose to step nose. The difference between these two methods would be the slope of an individual step. Any clarification is much appreciated.

On 2016-10-31 by (mod) - Definition: "rise" is the vertical distance from the walking surface of a given stair tread to the walking surface of the next stair tread up or down the stairs.

Thanks for the question, Lee:

The "rise" is the vertical distance from the walking surface of a given stair tread to the walking surface of the next stair tread up or down the stairs.

We do not measure to the under-side of the tread.

We do not measure to the center or any other radius of the tread nose.

That's because both of those measurement points would give a shorter rise than the actual distance that a stair user has to raise her foot, and as you suggest, measuring to somehere on the radius of a tread nose would also produce inconsistent results.

The walking surface of a stair tread should itself be level and flat and free of trip or snag hazards.

A simple way to obtain accurate stair rise measurements and to get around the problem of reading the measurement point when the tread nose is curved, is to place a level or straight-edge on the upper tread surface, then extend your tape measure, putting the end of the tape measure on the surface of the tread down from the one carrying the straight-edge, measuring up from the lower surface to the under-side of your straight edge.

On 2016-10-27 by Anonymous - best stairs for 18 ft length and 11 ft width with the height of 11ft.

I want to construct a stairs in an area of 18 ft length and 11 ft width with the height of 11ft.

Can you please suggest the design which type of staircase I construct??

On 2016-10-27 by (mod) re: what is the best stair design

Sorry, Anon, I can't suggest a "best" stair design from a brief e-text.

But I can suggest that for a total rise of 11 ft. you will probably be required to include an intermediate landing.

I can't say if your stair run is straight or involves a turn - that depends on the building space and requirements.

I can also note that 11 ft. of rise divided by 18 ft. of run gives an individual step riser height of 0.61 ft.or 7.33". That should get you started.

On 2016-10-02 by Paul - Help with maximum slope on railroad tie steps down a slope

Hi I am going to be replacing some old worn railroad tie steps in a small courtyard that slopes down.

The project area is 16 feet across with a total rise of 65 inches. Steps will not be continuous and there are small walks/platforms in between steps as I'm kind of staying with the existing landscape and putting in granite steps.

I've got most everything figured out except I wasn't sure if there is a maximum slope allowed for my platforms between steps where the platforms will either be brick or gravel and drainage is important in this area next to a building.

Trying to avoid having to do an extra step or two if possible. The existing steps were all done incorrect with no consistency in rise/run. Thanks

On 2016-10-02 by (mod) re: replacing old railroad tie steps

Paul,

You will want to check with your local building inspector to see what he or she will accept.

In my view I would think you want at least three feet of what you are calling platform or what I would call Landing between runsof stairs. That's three feet in the direction of travel.

With respect to slope there will be a judgement call about whether your platforms are so slow as to be a falling hazard. But they do not have to be level to do stair treads.

On 2016-06-15 by brian - figure out the angle of my stair stringers if my total rise is 11 feet and my total run is 13 feet.

How do I figure out the angle of my stair stringers if my total rise is 11 feet and my total run is 13 feet.

Im trying to make these steps as low of an angle as possible.

What do you suggest?

On 2016-06-15 by (mod) re: designing a very steep stair rise: 13 foot run and 11 foot rise is asking for trouble

Your stair is very steep with a 13 foot run and 11 foot rise.

Over at ROOF SLOPE CALCULATIONS we illustrate how to do the calculations to get the slope of stairs (or a roof) in degrees when we know the rise and run.

There you'll see that Rise / Run x 100 = Slope in Percent

or 11 / 13 = an 84.6 percent slope.

Degrees = Tan-1 (Slope Percent/100)

That means that your 84.6% slope = Tan-1 x 84.6 = 40.23 degrees - that's incredibly steep.

Furthermore, you don't have room for reasonably comfortable stair rise and tread depth.

Let's see how tall each step has to be in order to climb 11 feet in just 13 feet of run.

Suppose each stair tread will be 12" deep (we could go a little less deep but 12" makes the math easy).

13 horizontal 1-foot treads / 11 feet in height = 1.18 height per one foot of horizontal run or one foot of tread depth.

1.18 x 12" in a foot means each step will have to rise 14.16" - Waaaay over what people want to climb (though the Pyramids in Mexico City and other locations demonstrate that when you have to build your stairs by carrying heavy stones, tall steps may indeed be the order of the day).

A comfortable step rise for those of us who aren't Mayan or Incan is about 7".

I suggest either using a much longer run or if you can't fit that into your space you need to go to a circular stair or a winding stairwell.

Details

Over at our roof/stair slope calculations page - the link I gave above we explain that if rise = run (or your steps had to climb 13 feet up in 13 feet of horizontal run), then that's a 45 degree slope.
We can say also that Tan 45 deg = 1
We can say also that Tan-1 (1) = 45 degrees - that's how I snuck up on the answer to your question.

That article explains the various ways to calculate slope, rise, run, and angle of stairs or of a roof slope.

Since 11 is rather close to 13 I knew before doing the math that your stairs were pretty close to 45 degrees - that's very steep.

Question: seal stairs against dust movement from carpeting?

(Mar 25, 2013) Toni Fleischmann said:
I have a question about sealing (not surface sealing) but end sealing of stairs so that dust does not come up and stair ends of carpet. A Carpet guy told me the stairs should have been sealed on the ends to prevent this? Any thoughts as to what to use to do that? Thanks.

Reply:

Toni,

The way I read your query leaves me a bit confused. Stair tread ends, typically oak, do not emit dust particles againt which sealing would be needed.

However,if there are AIR LEAKS through the stairs the dust deposited by moving air could show up as dark stains. IN that case the air leaks might be at any of the four sides of a stair tread and would probably vary from one step to another.

Question: building code on stair construction materials using natural stone?

(Oct 22, 2014) Anonymous said:
Is there a code for building outdoor steps made of natural material such as used granite curbing?

Reply:

No, Anon. Building codes typically are performance-based in thinking and do not usually address specific materials. You can use granite curbing or any other material for steps provided the steps are properly constructed.

Question: sometimes the stair design just does not fit in the available space?

(Jan 24, 2015) andy said:
HI. I am building a new staircase to my basement via a big utility closet which I do not use (36x36). It is a walkout basement with patio doors from a rec room.

Existing stairway will be demo'ed and floored over for larger dining room (pre 1950 house). Closet floor to be removed and extended to accommodate stairs and headroom.

My problem is that the stairwell will need to be very, very short as I do not have that much space for it as it will end close to a foundation wall.

There will be approx. 6 ft of open space after opening up and extending the closet flooring space for some length of the run.

Town code needs one means of egress which is already present via the walkout basement doors. How can I build a short stairwell with short treads and risers? And what calculator can I use for this? Thnx !

Reply:

Andy

If you can't meet safe stair tread dimensions of rise and run with your existing design you most likely need to change the design to make a longer total stairway run and then include a turn or intermediate platform.

STAIR RISE & RUN CALCULATIONS shows how to calculate stair rise and run.

See STAIR DIMENSIONS, WIDTH, HEIGHT to read a complete series of articles on stair dimensions.

Question: spliced boards to make stair treads

(Apr 16, 2015) Marion - a rare female do it yourselfer said:
I took down some red oak trees at my house and had them milled into 1" and 7/8" boards. I planed them, jointed them and dried them.

I am now looking to turn them into my new stairs, as mine were made with 2x10s before I bought the house, not exactly attractive.

My problem is, I do not have a lot of boards that are at least 10 inches wide and was wondering if I can splice together two smaller boards to make some of the treads, especially if I put the narrower board towards the back.

For example, maybe a 4" board biscuited to a 6" board that will overhang the rise. Is there any reason I cannot do that? Especially if I use them on less used stairs?

Thank you for any guidance you can provide.

Reply:

Sure, Marion. Use splines or a biscuit joiner to glue up the needed width. with a little attention to wood grain and alignment, after sanding the treads will be beautiful. Use the email at our page bottom CONTACT link to send photos if you like.

I've often built-up wider boards using a biscuit joiner and Gorilla glue or other polyurethane glues.

The mating edges of boards must be dead flat to get an attractive joint. A combination of clamps to secure the boards during gluing is key.

I clamp both edge to edge and I use additional lumber and clamps to hold the boards dead flat against cupping during drying of the glue. When the glue has dried I remove the clamps and sand the extruded extra glue off leaving a nice surface.

In my experience these glued-up wideboard joints are very very strong.

When I've tested the joints by trying to split such a board the split breaks elsewhere in the wood, not at the joint.

Question: how to build stairs up a very steep slope

(June 13, 2015) Anonymous said:
Building stairs up a steep slope using 7 inch riser... half way up but slope is now at a higher angle. Stairs going into slope so the stair rise was increased by an inch. Still digging into slope but dirt is so solid I must use a chisel and hammer. Slope in front of me is now 12 inches above next step. Any solutions?

Reply:

Anon I would not change the stair riser height - that's a trip hazard. Rather you'd want to make an intermediate landing. That seems to me the only choice if you've already built a portion of the stairway. Better would have been an original calculation of the total number of steps and risers for the whole stair run, making all steps identical in rise and run.

Question: I can't walk down standard steps, how can I make the step rise shorter?

(July 3, 2015) bonita said:
I am no longer able to walk down stairs with the standard drop. How can I make my drop from step to step shorter?

Reply: you need room for a longer (in horizontal run) stairway or else to install a chair lift.

Bonita:

When I'm no longer able to make it safely up and down stairs to my office I will probably install a chair lift - see STAIRWAY CHAIR LIFTS

The problem is this: you can indeed re-build a stairway to reduce the riser height but to do so the depth of each tread has to increase significantly too. That means that the entire run (horizontal length) of the stairway will get much longer than it is now, perhaps double.

In the inteiror of most homes, doubling the run of a stairway between floors would be horribly expensive - if it would fit at all, or making a long stairway that winds or turns - taking more room in other dimensions.

I suspect that the cost of a stair rebuild indoors would be much higher than the cost of adding a stair lift.

What do you think?

Question: can I fit 15 shallow steps into 100 " of run?

(Oct 11, 2015) Maryann said:
I have a stairwell that measures 100" horizontally fm edge of top stop to edge if bottom step.

There are 15 steps which are very shallow -we have to go down sideways bec feet won't fit on steps. Will a regular set of steps fit in there?

Reply: not very usably

100 / 15 = 6.67 that suggests that in 100 inches of horizontal run, if you insist on building 15 steps, each step tread depth can be only 6.7" deep - that's too small for comfortable walking - as you say, feet don't fit on such steps.

You'd need a longer horizontal run or taller steps to get the tread depth closer to 10" or more.

Question: how many treads can be instaled before you need a landing?

(Oct 22, 2015) dan said:
how many treads can be instaled before you need a landing

Reply: 12 feet of rise is the controlling factor, not number of treads

Dan the final answer rests with your local building code department; See our code citations on stair landing requirements over at

inspectapedia.com/Stairs/Stair_Landings.php (mostly focused on landing dimensions)

Often building departments and codes look not at the number of treads but the total rise in the stairway before an intermediate landing is recommended.

The International Residential Code - model code or IRC - specifies 12 feet as maximum rise for a stairway without an intermediate landing. This is true for both straight and circular or winder stairs.

R311.5.4 Landings for stairways. There shall be a floor or landing at the top and bottom of each stairway. Exception:Afloor or landing is not required at the top of an interior flight of stairs, provided a door does not swing over the stairs.

A flight of stairs shall not have a vertical rise greater than 12 feet (3658 mm) between floor levels or landings. The width of each landing shall not be less than the stairway served. Every landing shall have a minimum dimension of 36 inches (914 mm) measured in the direction of travel.

Question: how many steps needed to climb 35" from bottom to top (total rise)

(Dec 17, 2015) Anonymous said:
Have 35 inches bottom to top how many steps would that be

Reply:

If you used a comfortable 7" rise, you'll need 35 / 7 = 5 risers.

Question: What can be done to make a high rise with a short run more user friendly?

(Jan 22, 2016) Scott said:
Hi this article has been helpful however I have a situation not really addressed. What if anything can be done to make a high rise with a short run more user friendly? The problem is getting out of a cabin loft with a rise of 89" and a run of 69". Space dictates that cannot make a landing and turn.

The result is a steep angle but more problematic is a vey short tread width. Using a housed tread design and not closing off the riser helps going up but not down. I understand there's no way to make this code but looking for anything that might improve what I have.

Reply:

Address all other fall hazards you can. Lighting, graspable handrails, good color cues, uniform rise.

Or install a circulator or winder stair in the space.

Question: am I figuring the stair angle correctly?

(Apr 6, 2016) Ross said:
To build interior stairs from basement to first floor I have a total rise of 9' and a total run of 10'5". I believe this produces an angle of 41.99 degrees. An I correct in these dimensions and if so, is this degree of angle comfortable?

Reply: your stairs are not safe - too steep

Ross:

108" rise / 7" step riser height = 15-16 risers or steps between levels.

15 steps with a minimum of 10" deep treads = 150 inches.

10'5" = 125" of "available run"

125" is only 83% of 150"

Your stairs will not be safe if built as a straight run in that space. You'd need a winder stair, a landing, or a circular stair, or you'd need to increase horizontal the run distance.

Question: another terribly steep stair

2016/06/15 brian said:
how do I figure out the angle of my stair stringers if my total rise is 11 feet and my total run is 13 feet... Im trying to make these steps as low of an angle as possible.. what do you suggest?

Reply:

Your stair is very steep with a 13 foot run and 11 foot rise.
Over at ROOF SLOPE CALCULATIONS we illustrate how to do the calculations to get the slope of stairs (or a roof) in degrees when we know the rise and run.

There you'll see that Rise / Run x 100 = Slope in Percent
or 11 / 13 = an 84.6 percent slope.

Degrees = Tan-1 (Slope Percent/100)

That means that your 84.6% slope = Tan-1 x 84.6 = 40.23 degrees - that's incredibly steep.

Furthermore, you don't have room for reasonably comfortable stair rise and tread depth.

Let's see how tall each step has to be in order to climb 11 feet in just 13 feet of run.

Suppose each stair tread will be 12" deep (we could go a little less deep but 12" makes the math easy).

13 horizontal 1-foot treads / 11 feet in height = 1.18 height per one foot of horizontal run or one foot of tread depth.

1.18 x 12" in a foot means each step will have to rise 14.16" - Waaaay over what people want to climb (though the Pyramids in Mexico City and other locations demonstrate that when you have to build your stairs by carrying heavy stones, tall steps may indeed be the order of the day).

A comfortable step rise for those of us who aren't Mayan or Incan is about 7".

I suggest either using a much longer run or if you can't fit that into your space you need to go to a circular stair or a winding stairwell.

Details

Over at our roof/stair slope calculations page - the link I gave above we explain that if rise = run (or your steps had to climb 13 feet up in 13 feet of horizontal run), then that's a 45 degree slope.
We can say also that Tan 45 deg = 1
We can say also that Tan-1 (1) = 45 degrees - that's how I snuck up on the answer to your question.

That article explains the various ways to calculate slope, rise, run, and angle of stairs or of a roof slope.

Since 11 is rather close to 13 I knew before doing the math that your stairs were pretty close to 45 degrees - that's very steep.

...

Continue reading at STAIR RISE & RUN CALCULATIONS - topic home -how to calculate the rise and run of stairs, or select a topic from the closely-related articles below, or see the complete ARTICLE INDEX.

Or see STAIR RISE & RUN CALCULATION FAQs-2 - more recent questions and answers about calculating the rise and run of stairways and steps.

Or see these

Recommended Articles

• CALCULATE stair tread depth or riser height from stairway slope in degrees
• FRAMING TRIANGLES & CALCULATIONS
• ROOF SLOPE CALCULATIONS - mathematics of calculating stair or roof slope, angle, pitch, rise, run, etc.
• STAIR RISE & RUN CALCULATIONS
• STAIR RISER SPECIFICATIONS

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STAIR RISE & RUN CALCULATION FAQs at InspectApedia.com - online encyclopedia of building & environmental inspection, testing, diagnosis, repair, & problem prevention advice.

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