Layout formula/method for stairs

Date 04-10-2008 22:37 Edited 04-10-2008 22:39

Hello Harlon Alford, welcome to the forum. I might be able to help you out with that. Along with welding, I teach a fabrication class and we do a fairly extensive review and application for stair layouts. I'll see if I can come up with some information describing the basics when I get back to my office. There are many methods employed by various folks, some are mainly mathematical and others involve the use of stair gage sets and other forms of layout methods. In all cases there are nose to nose distances which must remain within 1/8" of an inch from one to the other within the run of the stair to avoid trip hazards, in many cases there are nosing set-backs from the side stringers to avoid slips to the sides of the risers, and there is generally also a 1" overhang from one riser to the next to keep from stubbing your toe when going from one riser to the next. Consider that many stairs fall under various code requirements, so you need to know whether your application might be one of these. If they are in an industrial setting, there are sometimes exceptions to the code. I'm pretty sure others will chime in here with suggestions and explanations, stay tuned. Best regards, aevald

By Sparkee (*)

Date 04-11-2008 00:01

Harlon, is there a specific area where you need assistance........rise, run, degree of angle? I use a SIN Theory to determine the angles......basically the same as "ratio and proportioning" based off of the total height and total length. I can send you an example if it would help.
Sparkee

By Harlon Alford Date 04-11-2008 00:50

Mainly looking for a "formula" if you will to fabricate stairs for whatever situation I may encounter. Something where I can plug in measurements and get the info i need to fabricate my stairs. Like I said, never had a need to build stairs before. But lately the company has picked up a few jobs and sooner or later my number will be up and I'll end up being the fabricator on a particular job. Just want to be able to do it.

By bullsnbets (**)

Date 04-11-2008 01:37

I use a very simple formula when I build stairs. Assuming your building stairs on a 45 degree angle, measure from the top landing straight down to ground level. Take that measurement and multiply that times 1.414. That will give you your total lenth from top to bottom on a 45 degree stair.

By natecf

Date 04-11-2008 02:25

if your just looking for something to figure out your measurments, try the cheaters way. get yourself a "constrution master IV" calculator from calculated industries. it has a stair function that allows you to plug in all parameters and it spits out all the info you would need : rise, run, angle, stringer length, tread length, riser hieght, # of treads and under/overage for last step. I've used it a couple of times, it makes layout a snap

By Harlon Alford Date 04-11-2008 02:38

i know about the "cheaters" method...was wanting the old school method to go with it.

By Sparkee (*)

Date 04-11-2008 03:26

This is about as old school as it can get, but it works every time. Example: The total height from ground to landing is 131 inches (Side b). With a plumb bob, find point on ground directly below landing. From this point, measure total distance that stairs will cover on the ground. For this example, this measurement will be 178 inches (Side c). To determine the total length of stairs use the hypotenuse theorem "a squared + b squared = c squared". In this example, the total length would be 221 inches. Draw a triangle (90 degree) with the base being 178 inches (Side c), the height being 131 inches (Side b), and the long side (stairs) being 221 inches (Side a). With the triangle labeled as described, now label the angles opposite the sides with capital letters. The 90 degree angle would become Angle A, the upper most angle would become Angle C, and the lower angle would become Angle B. For the remainder of this example, it will be necessary to obtain a Sin Table for Degrees of Angle. Using the measurements above, we can determine the angles using the method below.

Sin A divided by length of Side a = Sin B divided by length of Side b = Sin C divided by length of Side C

Sin 90 divided by 221 = Sin B divided by 131 = Sin C divided by 178 (The Sin of 90 degrees is always 1)

Sin B = Sin 90 x (131 divided by 221) = .59 Now refer to the Sin Table and find the angle of degrees that correlates with .59

Sin B = 36 degrees

If you have a calculator that will convert the Sin Table to degrees, you will be better off. I know this looks like a difficult method, but after you have used it a few times, it will become simple. I hope you can understand this, as it is easier to explain when I can draw the illustrations in front of someone........you know with "talkin chalk".
Hope this helps,
Sparkee

By Jeffrey Grady (***)

Date 04-19-2008 05:07

Sparkee,
Great example of Right triangle trigonomerty. The right angle is never gonna change...it will always be 90deg. The rise and run will detemine the angle in degrees once the hypotnenues has been established. A good calculator Like my TI-83 plus, gives all the needed functions for finding the degree of an angle.
Good post Sparkee!
Respectfully, Jeffrey S. Grady

By DaveBoyer (*****)

Date 04-21-2008 03:20

Does anybody even print those little trig tables anymore? We used to get them from Car Lane, a company that supplied jig & fixture parts.

I think the foreman where I served My apprenticeship had a math teacher named Pathagorus... :-) :-)

By DaveBoyer (*****)

Date 04-11-2008 05:17

Depending on the aplication, You might fall under ADA regs, and that would limit the rise to 7" require a 12" tread, and limit the tread overhanging the riser to 1" with an accepted nose profile. Railings are specified by ADA so the blind can find them with a stick.

By Jeffrey Grady (***)

Date 04-19-2008 04:33

Harlon,
The "old school" method requires an understanding of the Pyhagorean Theorum, (Geometry) and Right triangle trigonometry, and maybe some of the more elementary graphing methodes ...Slope of a line - rise over run. You can also use a framing square and use the the 3-4-5 method. That's about as old school as it gets. You may want yo invest in a good calculator. Many have the programs and formula's already in them. Simply input your raw data and it produces a real easy layout for you. Just my $0.02
Respectfully, Jeffrey S. Grady

By thomasyyz (**)

Date 04-25-2008 18:39

that would be the square root of two, but usually you need to look at 32.5º.

By RGL

Date 04-15-2008 15:48 Edited 04-16-2008 18:07

There is a calculator that will layout any Staircase at any angle or height and it will give you the exact ANGLE of the stairs, total number of lands, the width of lands, the riser heigth, total length of the DIAGONAL run and the DIAGONAL distance from toe to toe, by picking any of three options, *Run & Rise, *Rise & Degree, *Run & Degree, (Click on the X23STAIRS attachment below), and you don,t need to know the math. It also does handrail layouts, straight and spiral. This is a TRUE Hand Held LAYOUT CALCULATOR. I consider this unit a tool rather than a computer because you always have it nearby and it is an excellent Companion for the Bench, Shop, Field and Office. It will layout just about anything including *Intersecting TEE's including the HOLE layout, *Cone's, *Square to Rounds, *Round Elbows, *Pipe, Tube & Sheet Metal Round Offsets, *Custom Kitchen & Fireplace Hoods, *Handrails, *Crickets & Saddles and much more. Its very user friendly. It asks you for specific Inputs by NAME and gives you specific outputs by NAME, you don,t have to guess at what it's trying to ask or tell you. It always reads dimensions in DECIMAL form 1st, then in FRACTIONAL Form 2nd, to the closest 1/32",+/- 1/64", (this can be changed to your preference I.E. to the closest 1/16", 1/8", 1/4" etc., what ever you can read easily). This is for the person that doesn't know his/her Decimal readouts. It also has Utility programs for *Drill & Tap sizes, *Metric Conversion, *Arc's & Radius's, *Solves Oblique & 90 deg. Triangles, *Pulley sizes including RPM and Belt lengths and more. A good tool for company shop employee's to have. This TOOL will easily save time on Bench & Field Layout. Click on the WebSite below to see more about this tool, you can view all the pages from the manual which was written to be used like a computer Monitor if needed for Visual Instruction, direction and hole Layouts. REMEMBER, you don't need to know the math. Be sure to read the "NOTES" in the Layout Manual Page section, they help things make sense. These programs were actually used to layout these fittings & handrail below. The Square to Round program was used on the 1st item. The Radius Stretch, Round Elbow & the Square to Round programs were used on the Jet Engine Test Cell Exaust, (ready to be insulated). The Modual2 & the 90 deg. Triangle programs were used on the handrails fabricated by a local Custom Sheet Metal Shop in San Diego, CA. (Excellent crafstmanship). The burns were taken off the welds with low heat and straight phosphoric acid (mild stuff). No welds were ground!! I was blown away when I saw these handrails. This was one of four rails, who ever did the welding was an artist! This tool is NOT a toy!!

http://www.sheetmetallayoutcalculator.com

Attachment: x23STAIRS.pdf (335k)

By mountainman (***)

Date 04-16-2008 01:30

a rise and run is really all you need in addition to the connection method on both ends. (that comes into play with your overall height and run). stringers and treads will more than likely be required to have engineering calcs. everything from bottom to top will be dictated by the code your abiding by, like noseline, rise to rise tolerances, run or tread surface depth, overhang, or if risers are required. are your staircases already detailed into a shop drawing? if they are, the detailers can make or break ya. the first staircase is always intimidating no matter who you are, but after that it gets easier and easier. good luck to you.

regards,
JJ

By motgar

Date 04-11-2008 15:29

Harlon,

Some visuals that can help you understand the above posts. Different material but, relatively the same principle. Hope it will give you a better understanding.

http://pages.areaguides.com/ubuild/MakingStairs.htm

By Bob Garner (***)

Date 04-16-2008 18:57

Here's a pdf file of stair geometry of the tread and stringer.

Bob Garner

Attachment: StairDetails.pdf (55k)

By crawler30 Date 04-20-2008 06:57

I used to be a carpenter and have done many stairs. the easiest and most used (in carpentry ) method is to measure your total hight from landing to landing ( for multiple landings ) or landing to floor. devide that number by 7" ( this being your basic riser code ), this gives you the number of stairs which has to be rounded to the nearest whole # or stair. Multiply this number by 11" ( this is the basic tread code ). this number will give you the measurement of your run. Of course the 7" and 11" measurement can be fudged a little, I think no more than a 1/4" on residential. This is why stair section of prints always notes "to be field varified".

By swnorris (****)

Date 04-21-2008 20:46

Harlon,

Try this link:

http://www.hammerzone.com/archives/framecarp/technique/stairs/outdoor.htm

By Jeffrey Grady (***)

Date 04-22-2008 03:28

swnorris,
Great link. Information was well presented and best of all...easy to understand, without all the Trig. I use Trig to figure theses things out, but I probably will be investing in a layout calculator pretty soon. I would rather use the technology available instead of spending valuable fab time doing Mathematics. However, it is always a good idea to have an understanding of trigonometry incase the calculator is left elsewhere.
Respectfully, Jeffrey S. Grady