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Theoretical stair design (C) Daniel FriedmanStair Rise & Run Calculation FAQs #2
Q&A on figuring out the stair rise, run, slope, angle & step size

  • POST a QUESTION or COMMENT about measuring and calculating to build stairways & low slope or low angle stairways, treads, risers, stairway run, stairway landings & platforms

Recent questions and answers on how to make the calculations you need to build stairs: figure out the number of steps, step riser height, total stair height or rise, total stair length or run.

This article series explains, using simple math, how to translate the stair rise (total change in height) and run (total horizontal distance travelled) into a specific number of stair treads and risers that will be uniform and of proper (safe) dimension.

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

Theoretical stair design (C) Daniel Friedman

These questions and answers on how to figure out the dimensions of a stair you need to build were posted originally at STAIR RISE & RUN CALCULATIONS, so you will definitely want to read that article too.

On 2019-06-19 by (mod) - stairs built for a ride of 9 ft. And run 6 ft

Darren

At those Dimensions your stairs would not be stairs they would be a ladder.

On 2019-06-19 by Darren

Can I get stairs built for a ride of 9ft. And run 6ft

On 2019-04-05 by (mod) -

Scott

Thanks for the interesting observation & question.

I speculate that the TV or movie-set stair case has to be built with a very low total rise to keep the actors in view.

On 2019-04-05 by Scott

Why are staircases on sets in sitcoms never pitched at a realistic angle? They always look too shallow. Don't set builders have a clue as to what looks right???

On 2019-03-29 by (mod) -

Jose

The total stair height will be 32 x 7 5/8 or

32 x 7.625 = 244"

BUT a stairway of that height is MUCH too tall to build without one or more intermediate landings, so the actual stair will probably not be just 32 simple steps.

On 2019-03-19 by Jose

There are 32 risers in a stare if he tries or 7 and 5/8 in how tall is the stair

On 2019-02-08 by (mod) -

Uj

Divide the total rise - change in height - by 7" to get a starting point of number of risers. Details are in the article above.

On 2019-02-08 by Ujjawal

I have 156"/slope and 114" lanth how many stars and size

On 2019-01-13 by (mod) -

Anon:

A 2x12 is of course about 11 1/2 " in total width. When set on an angle, depending on the slope, one could notch into a 2x12 to build a stair but it seems to me a big mistake to cut deep notches into a stair stringer that has to carry the weight of the stairs.

And you'd never cut a 11 1/2" notch into a 2x12 even when the notch is on an angle - you'd end up with maybe an inch or two of wood carrying the entire weight of the stairs.

Instead I'd use cleats screwed to the stringer and treads screwed to the cleats.

On 2019-01-13 by Anonymous

I am trying to find out if the width of a 2 x 12 11 1/2 inches is wide enough to cut I will rise of 7 inches and a thread of 12 inches

On 2019-01-13 by Anonymous

Can a tread of 12 inches and a rise of 7 inches be cut in a 2 x 12

On 2018-11-12 by (mod) - how to figure the dimensions for "square stairs" in which total rise = total run = 105"

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 2018-11-12 by Char

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 2018-07-04 by (mod) - What is the height " and width " of the steps to be and what is the height from floor to ceiling be?

Rick

Thank you for a great question.

Most of our stair inspection, construction, and repair articles focus on choosing a proper step riser height and stair tread depth since choosing those properly will guarantee a stairway that is also at an acceptable overall angle or slope.

Here I'll translate some of those into degrees:

Stair tread/riser rule of thumb: the dimension in inches of one stair tread and one stair riser should always be equal or greater than 17. 18 in my view is ideal.

Example: using a step rise of 7 inches and a step tread depth of 11 inches gives us a total of 18".

The slope of that step will be 7" of rise over 11" of horizontal travel, or a slope of 7/11. That's an ideal slope of about 37 degrees.

See details at STAIR BUILDING RULES of THUMB

The stair width part of your question is answered in detail at

STAIR TREAD DIMENSIONS

The second part of your question is described as STAIR HEADROOM

On 2018-07-04 by rickburr_ecoquest@hotmail.com

my son wants to buy an old house, I don't know what the angle or slope the stairs are.

The stairs are at an angle that they seem to almost be straight up, ofly hard to climb.What should the stairs angle be set at? What is the height " and width " of the steps to be and what is the height from floor to ceiling be?

On 2018-04-30 by (mod) -

Pete I can't quite see the situation nor the impasse from your note.

If the step is 7.5" rise above the sidewalk that leaves 2.5" as a second step up into the building. Hopefully that 2.5" is across an entry platform - since if it were just another step you'd have two steps of different rise and thus a trip hazard.

Handrails and guardrails are in my opinion a smart idea on ALL steps regardless of the total rise, but in must jurisdictions (we don't know where you live, not country ,city, province or state), a total rise under 30" or less than 3 step risers is not required to have handrailings nor guardrails.

Still a disabled person would prefer to have those features. I'd add them.

On 2018-04-30 by Pete D.

I have a concrete front stoop with one step. The step is 7.5 inches off the sidewalk but is 10 inches below the stoop. Also the step is narrower then the stoop so there is no way to add a rail. Help!!!

On 2018-04-18 by Anonymous

I have a house that needs 4ft wide stairs,rise is 4ft,and I need one rail,show pic!!

On 2018-03-19 17:29:33.839372 by (mod) -

Thanks for commenting, Lost.

On 2018-03-17 by Lost Adams

@Osama,
You may want to use a landing apx halfway down on an even rise run ratio and then return or do a 90 deg for the rest of the run to the floor.

On 2018-03-03 by Kunal

I want to build stairs in a area of 8*10 sqft. How many stairs can I build in 8*10 sqft area. In how many ways

On 2018-02-06 by (mod) -

Seems to me you're still would be non-compliant in a trip Hazard is used for regular access between two building areas.

On 2018-02-04 by Osama

If my staircase angle exceeds 50 deg due to some limitations then may I keep the tread depth of 7" and riser height upto the 8" ?

On 2017-12-01 by (mod) -

Verma,

If we used for example a 7.5" step rise, to ascend 15 feet that's (15 x 12") / 7.5 = 24 steps.

If we then assume that each step has a minimum of 10" of tread depth that'd be 10 x 24 = 240" or a 20 foot run.

You cannot fit 20 feet of horizontal run in a straight line into eight feet of horizontal distance.

You also can't fit it reasonably into even 8 feet when making a single intermediate landing to turn the stairway.

So you need to either re-design the stair run to give longer horizontal space or you need to go to a circular stair.

On 2017-12-01 by Verma

Hello, sir i have 8 feet area from wall to make stair and Height is 15 feet. How can I mange stair in 8 feet area. Can u help me?

On 2017-11-08 by (mod) -

Phillip,

First lay out your stairs to obtain the required dimensions.

Once that's done you can use concrete and forms that you cover with stone, or you can build stairs with large stones, properly sized and stacked.

Don't forget the handrail and stair guard.

On 2017-11-08 2 by phillip ku

Hello I am considering tackling an Eagle Scout Project using Natural Stone and or CinderBlocks for a steep slope stairway in a park in my home state of CA.
The project coordinator does not want me to use wood, as we have the potential for warping and rotting wood.

I will be planning on physically visiting the site that the project coordinator would like me to consider for my project to take pictures and ask questions about the site.

My dad and I have worked on several projects in our backyard, retaining walls, gazebo, planting, and I have also taken 2 yrs of woodshop in highschool so I am good with power tools in case I will need to include a hand railing as well. I have also taken 3 yrs of Art Classes and I like to draw and have a good spacial sense and my dad does as well.

I would need to involve other potentially older Boy Scouts for this project as If it requires Natural Stone, It will be quite difficult to lift and move, especially if the area is sloped and steep.

Please send me any ideas and pictures of what I could potentially use when I have the meeting with the site's project manager.

Once things become more clear when I see the area physically, I will be able to be more precise about needing help with calculations ect.

I will find out the measurements, but before hand If you can e-mail me tips and what to watch out for and how to go about things, It would be greatly appreciated.
Thank You, Phillip Ku.

On 2017-10-24 by Anonymous

Thank you for helping me up, but can you help with the distance calculations?

On 2017-06-30 by (mod) -

Anna

Working in inches just because I am better at that dimension,
Your ceiling is about 106" to which you need to add the thickness of the floor above to get to the level of the floor surface over that; Let's guess that's another 10" so we have a total rise of 116" for your stair.

If you used 6.5" risers you'd need 17.8 which I'd round to 18
If you went to 7" risers you'd need (116 / 7 = 16.47) 17 risers. (since we have to make all our risers the same height)

So we build a 17 riser stair. Since the top riser gets us up to the level of the floor above, there are 16 intermediate stair treads between floors.

If we used a minimum 10" tread depth that'd be 10 x 16 = 160" of horizontal run.

On 2017-06-30 by Anna Grace Sun

what will be the total run (sorry) pressed it

On 2017-06-30 by Anonymous

hi is it possible to get a 6.5 step rise for a 270cm ceiling height? what will be the total

On 2017-05-21 by (mod) -

Thanks for clarifying. I agree that at the high side of the top tread just below the landing, at the right side the step-up is 1" higher than at the left side of that tread. And I agree that "fixing" that is ugly.

I definitely do not want to start building pitched stair treads on the lower steps - that's building a mess and possibly more trip hazards.

If you were rebuilding the platform I'd choose to bring it into compliance by reducing its pitch.

*IF* there is adequate clearance at the building threshold to add a layer of concrete leveling compound to bring the surface a bit closer to level that might be an option, though I'm nervous about thin slab coatings as without meticulous surface prep and use of a bonding agent they may spall and chip off; similarly one could add a layer of slip-resistant stone, adjusting the stair rise accordingly.

If you don't want lift or bring closer to level the top landing (which can be costly if the whole landing is a masonry structure) to reduce its pitch to be in compliance, the stair users will have but to rely on sound stair guards and handrails. If your local building inspector doesn't accept the stair with that pitch I'd ask what she would find acceptable as a solution.

You'll see that while typical codes want the outdoor and indoor floors to be at the same level, saner heads know about issues with snow and water and even the problem of a snow-and-ice-blocked frozen-in-place exterior, swinging-out storm door: all conditions arguing for an outdoor entry platform a bit below the door threshold - which would or can allow for a less sloped top landing, reducing the fall hazard there while still allowing for drainage.

For other readers here are some model code example citations from the 2006 IRC

R311.4.3 Landings at doors.

There shall be a floor or landing on each side of each exterior door. The floor or landing at the exterior door shall not be more than 1.5 inches (38 mm) lower than the top of the threshold. The landing shall be permitted to have a slope not to exceed 0.25 unit vertical in 12 units horizontal (2-percent).

Exceptions:

1. Where a stairway of two or fewer risers is located on the exterior side of a door, other than the required exit door, a landing is not required for the exterior side of the door provided the door, other than an exterior storm or screen door does not swing over the stairway.

2. The exterior landing at an exterior doorway shall not be more than 7 3/4 inches (196 mm) below the top of the threshold, provided the door, other than an exterior storm or screen door does not swing over the landing.

3. The height of floors at exterior doors other than the exit door required by Section R311.4.1 shall not be more than 7 3/4 inches (186 mm) lower than the top of the threshold.

On 2017-05-21 by Anonymous

The top landing or platform is 8 ft x 5 ft . 8ft against house ,the 5ft side pitches 1/4 in per ft.the stairs will be 4 ft wide on that side .

when you reach the top tread there will be 1 in difference from right to left from tread to platform.ithought to be in compliance there can only be 3/8 difference .so if yourwalking up the left side of stairs you encounter a 1 in difference in riser Height on the left side .

On 2017-05-21 by (mod) -

Fred,

I need a more complete understanding of the dimensions involved: the dimensions of the platform, which side is against the house, and to which side the stairs ascend, and the width of the stairs.

Stair tread slope (out of level on walking surface) - (slope or "rise" must be <= 1 in 48) -- source: irc

so if the stairs are ascending on the side of an entry landing so that, for example, the top landing sloped 1" in 48" down from right to left where it also forms the top step, you are very close to conforming (e.g. > 48" of width at that point would comply).

So first, what's the width of the steps? If they are >= 48" wide and all rises and steps are level, the top tread, across the full width of the steps will be just 1" in 48 and close to compliance.

If I've mis-guessed and your steps approach the front edge of the landing, you should be measuring total rise from ground (at the first step) to top of the landing, and making all of your step risers the same height.

On 2017-05-21 by Fred

Back door platform which I. Pitched 1/4 per ft away from house. The stairs would be attached perpendicular to platform pitch.the rise is approx 29 in.so.so you would need 4 treads ,if you level each one the top tread would be 1 in out of level.how would you adjust each tread to maintain level.

On 2017-05-20 by (mod) -

Sounds as if the stairs need rebuilding or leveling if its a prefab construction. Details depend on the existing stair construction materials and details.

On 2017-05-20 by Fred

You have 4 risers on a 4 ft wide stairs of 71/4 in. which attach to a platform with a pitch of 1/4 in per ft. How do you adjust that

On 2017-05-02 by Derrick

Ok I have a 45 1/2 rise from a landing how many steps do I need

On 2017-04-23 by (mod) - example of calculating stair dimensions

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

STAIR TREAD DIMENSIONS

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 2017-04-23 by sajjad

Hi i want to build stair insid of house along with the 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


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