ROOF FRAMING CALCULATIONS

Review of basic geometry, Pythagoras' Theorem and Similar Triangles, needed for roof calculations

[@MichaelDavidHiltner]

I'll be building a 12x18 shed to join to my existing 12x12 shed (will remove the sheathing from the joining side), remove my existing roof and tie it in to my new shed, later this spring. This has been extremely helpful for my understandings. Thanks Professor! This is what I use the internet for!

[@glennunderwood4690]

Very nice explanations and drawings. ..thank you for your help. Clearly shows the need for math skills and some knowledge of building.

[@montaguechristian1]

Great break down. Thanks for the informative tutorial.

[@tammyghashghaie3406]

Dear professor amazing and informative lecture truly Tammy

[@michaelnauth]

Thank you Tammy

[@tammyghashghaie3406]

i will look forward to watch more of you video by the way your tone of voice makes audience to understand and follow you more

[@allamericanhandyman7633]

Detailed explanation. Worth watching!

[@KennethDFranks1]

Great math lesson with practical uses of Pythagoras' Theorem.

[@michaelnauth]

+Kenneth Franks Thanks Kenneth

[@jrquidi2572]

I love it .... learning is the BEST way to get to be the best in subjects

[@flankerroad7414]

Great video offering detailed insight on the math of cutting rafters...the better grip you have on this the more confidently you'll approach your work.

[@michaelnauth]

Thanks Jacob

[@bobalicon1000]

Finally after looking over 20 videos I found this one that I understood how to measure and cut the rafters properly.

[@michaelnauth]

Excellent!

[@MariaSearsmercy13]

Explained well. Even if ones math skills are rusty. Thank You.

[@robindevellen7038]

Maria Sears if I had math skills to begin with🥴

[@unclemony5939]

Hello professor, ur lecture is impeccable, BUT!! Simplicity is what I live for. I have paid dearly, but mastery is never too far around the corner.

[@BushcraftPaolo]

Clear, polite... Perfect! Tanks a lot.

[@michaelnauth]

Thank you.

[@machia0705]

Good lecture professor , but I can do all of this with a pencil and my tool belt. A circular saw and a T-square on the bench too. As for design work, I have a book of tables . However your in depth look at this and explanation are impressive. Great presentation.

[@timbarry5080]

That's why its easier to measure your span and run from the inside of the top plate rather than the outside. This way your measuring line is on the bottom edge of the rafter than being inside the width of the board. And your measuring line ends right at the edged of the ridge board instead of its center. Don't forget to subtract the thickness of the ridge from the span before calculating the run..

[@markpenn4831]

Very clear and concise ! Many thanks...

[@michaelnauth]

Thanks Mark.

[@gabrielgonzales8163]

buenos videos construccion #1

[@AFFarms444]

Superb explanation! Thank you.

[@mariosioannou4346]

Hi Michael, I found your lecture very interesting and informative. I think its good to explain fully how it all works. I, personally, will remember this lecture and put it to good use in the future. I just have one question at 18:13 onwards where the small triangle at the top shows a ratio of 1:1.5 re the slope. Is this a mistake or maybe I'm not fully understanding this. Can you please clarify?

[@michaelnauth]

+Marios Ioannou Hi Marios In the Canadian Building Code the roof slope is given as a ratio relative to a rise of 1(Metric or S.I.). So a 1:1.5 roof slope is the same as 8:12 in Imperial terms and also the same as 150:250 when using the Metric (SI) framing square. Good catch - I forgot to note that. First guy in 351 000 to ask that.

[@naturalmystics-kd9vt]

Mr Michael nauth thank you for this video I learn a lot from you video you are a good gentleman and a good teacher I thank you

[@michaelnauth]

You're welcome.

[@calbinoIa]

I used to cut roof rafters for framing conventional roofs with a calculator also and then built them. I understand how to do this, but after listening to you explain this I see why I hated math in school. Sorry, but while this is an excellent explanation, it is dry enough to put me back to sleep.

[@wallacelux]

Ungrateful.

[@arturovarela8395]

I felt like a was back in high school too!!! I rather skip class and go take 3 lunches!!!

[@someonespadre]

I'm building a small shade structure. In order to figure out how to frame the roof I watched carpenters on KZbin with their speed squares and their framing squares and their construction master calculators and figured out all the pieces and parts then, like this guy, I sat down with paper and pencil and broke down all the little triangles. It's all just Pythagorean theorem or simple proportions, don't really need trigonometric functions except to calculate angles for a miter saw. Then I did it again in my cogo (coordinate geometry) software to confirm my numbers.

[@michaelnauth]

You're correct David. It's simple geometry.

[@emilyeilene]

Thank You for making this!

[@kenjimrankin7485]

hi useful refresher worked out roof in 15min thks, however i could have did it on the computer in 2min, and got my purlins sized into the bargin.

[@Chevy-ud1ec]

how did you come with the number 15Thanks Harvey

[@davido3026]

Excellent including Metric equivalences!!!

[@michaelnauth]

Glad you like them!

[@samanthayau3141]

thanks for showing. It is a very tutorial, educational video. I built a roof and did the calculation. The rafters always came off a bit and could not fit right in. The problem is the rafter with a birth mouth that accutally sit two inches or whatever inches inside from the outside walls. You have mentioned about this problem by dropping the ridgeboard height. Can you explain to me how you get a 3/4? And why use 16 as a base when calculating ridge drop (x)? And what did you mean by cut/left on the flat? I am not sure i got it. Appreciate any help.

[@michaelnauth]

For a roof that has a 7 in 12 slope, 7 is the rise (vertical) and 12 is the run (horizontal) . You would compare it to a similar triangle that has a run (base) of 3/4 of an inch or one-half the thickness of the ridgeboard. So the vertical (rise, r) of the small triangle would be found using ratios: r ÷ (3/4) = 7 ÷ 12; r = 7 x (3/4) ÷ 12 ; r = 7/16 . If the ridgeboard is 1½" thick then, the drop for the ridge is the unit rise (in this case 7) over 16. This works for any roof slope as long as the ridge is 1½" thick. An 8/12 slope would have an 8/16 drop or ½".

[@samanthayau3141]

Thanks so much of your information. Appreciate so much. I am not in this trade. But i love to build and design houses.

[@SuperCyril2]

Remember to add on your overhang to your rafter length.

[@jonienglish3231]

Michael @17.37 - X Calculation getting to Technical just say the 5ft + HAP 4 1/2 - Ridgeboard Width = the Actual Height for the Ridgebeam Pending the Width of the Ridgeboard .

[@charlesgreen239]

Very well explanation of the geometry. I still did not see how you calculate the rafter stand or HAP? You had 4 1/2 on the drawing.

[@michaelnauth]

Hi Charles Sorry it took so long to reply. I started to and then thought that a diagram would make it easier. I still haven't figured out how to post a diagram in the comments section. Well, here goes - in words. I had just stated that the Stand was 4½", I did not calculate it, but I measured it after the birds mouth was laid out. To calculate it, you would use Similar triangles and Pythagoras's theorem. First, to get the length of the plumb cut on a 6 in 12 sloped roof (1:2), draw a Ridge Plumb Cut line on the end of the 2 x 6 rafter and you will form a right triangle that is 5½" on on side, 2 3/4" on the other and the hypotenuse can be calculated using Pythagoras to get 6 1/8" [or you could just measure the plumb cut line]. Second, setting the horizontal Seat Cut line at 3¼", the Heel Plumb Cut line would be a half of that or 1 5/8" (again because it is a 6/12 roof slope). Subtracting 1 5/8" from 6 1/8" gives you 4½".

[@Koumondji]

wow, this is a lot of Math. Good knowledge tho, I just cannot keep up, lollll

[@LouieHarmston]

+Angelo Koumondji, lol don't even try to, this is useless information..

[@majorkonfuzion1007]

+Angelo Koumondji me too my head is spinning.

[@ArtisanTony]

It is really not this complicated. It is basic math and can be done in seconds mostly i your head. You just need a basic calculator that does square root which every calculator does.

[@omarcortez5962]

Easy way kzbin.info/www/bejne/mWW1pYGhmK2SlbM

[@juginstr1019]

Great video!.Thanks a lot.

[@gregwarner3753]

All of these calculations can be done on an old fashioned framing square . All you need is a set of instructions .

[@defy2598]

Yes but this is only the beginning this math builds on its self alowing you to do octagon Pentagon and any other gon roof

[@unclemony5939]

@@defy2598 🤣🤣🤣

[@zero00044]

Seems much easier to eyeball everything. Didnt understand half of this because things like trigonometry and calculus arent taught in all high schools and never in the basic math classes. Just the optional classes. Heck, I dont even know what trigonometry and calculus are. Most we got was algebra and I dont remember 99% of it lol.

[@mrreason9697]

I'm really struggling with the rafter stand part ad the actual length, done some practice cuts and keep screwing up

[@michaelnauth]

Hi David I am not sure how to help. Maybe you can give me the dimensions of the building and the slope of the roof and the lumber dimensions so that I can respond in context.

[@jonienglish3231]

@17.00 Michael is making it Confusing Ridgeboard STAND = Total Rise + 4 1/2 ( HAP) then Subtract Width of Ridgeboard ( 2x8 or 2x6)= Ridgeboard Stand

[@hillcountrygarage]

Very, very informative and helpful. Two questions: how important is it to subtract the ridge drop from the actual rise calculations? Wouldn't the total rise plus the rafter stand calculations be sufficient for most structures?

[@michaelnauth]

The subtraction is mainly a test for carpentry competitions where the ridge is flat on top (a standard 2x6) as opposed to one that has been bevelled to a peak.

[@michaelfahandez5042]

Thx u sir godbless clever made it easyer for me

[@michaelnauth]

Thank you Michael.

[@roxydog-db1pu]

If This Old House talked about this it would have lasted about two episodes

[@ebroevets9542]

I think I'm just going to steam bend some long boards into shape...hehehehe then all I have to do is cut the birds mouth on them.

[@blueXRPdynamite.]

OOOOh. If only i was intelligent. Life would be so much easier..

[@foobar3139]

You’d think so...

[@Valentina_-lw9ui]

Winner of a video, been searching for "what is the maximum span of a roof truss?" for a while now, and I think this has helped. Have you heard people talk about - Beybigail Nonpareil Breakthrough - (search on google ) ? It is a good one off product for discovering how to create better sheds and improve your woodworking without the hard work. Ive heard some amazing things about it and my cousin got cool results with it.

[@neilarreola7841]

Just draw the truss diagram in autocad, right click on any line to show its properties and the length will be given. No need for calculations.

[@ricardomontalvo963]

+neil arreola Haha, yes super easy, but not everyone has that soo the old school way is the way to go

[@JohnzeeMr]

Leonardo De Mao: Very nice finding the length of the rafter is exactly what children who do child's play need to get into mathematics, if I was a kid and got hooked into the practical application of triangles and somehow become aware that it is my social responsibility or necessary for a bright future then transitioning into more complex mathematics would have been a breeze if I learned the basics. Individual buildings may be child play but imposing structures have complex mathematics build into them like take into account the ever important but not visible sway of tall buildings as a result of wind, new materials have to be developed and chemistry comes into play to test the elasticity of various new substance made. Most people are good at climbing and hammering and it takes a lot of their brainpower to have no time to dream but a very few who just have enough experience as a carpenter or an excellent craftsman will have imagination to create innovation and an entire civilization will depend upon this people for its survival and prestige, Edison, Newton, Einstein etc, including the ultimate personification of cuteness the Supreme Leader Uncle Kim Jung Un.

[@jimmy21480_midnight_special]

what the??

[@brentstarkes9682]

Well done!

[@michaelnauth]

Thanks Brent!

[@germaniumoxide6382]

Are you Mr. Smith from the Matrix movie..!!!!!????

[@sbk162]

can you do your calculation without using calculator

[@michaelnauth]

To find the hypotenuse of a right-angled triangle you can use the framing square and similar triangles. For instance, locate 5" on the tongue of the square and 12" on the body and measure from 5 to 12 and you will get 13" which is the square root of 5 squared + 12 squared. Also this number is etched on the framing square on the body under 5". You would then take the RUN of the roof in feet and multiply it by the 13" and that will give you line length of the common rafter from the centre of the ridge to the outside of the wall which is where you will cut the birdsmouth of the rafter.

[@sbk162]

thanks for the info

[@nilsbruhner1983]

Sketchup

[@addaimartin6237]

I like the way you are teaching

[@michaelnauth]

Thank You Addai.

[@HsingSun]

What do they call "side by side triangles" under both sides of roof rafters?

[@michaelnauth]

Not sure - together they form the Gable End.. Each one is a mirror image of the other.

[@TR-rn3pd]

Can you or someone tell me what the hip/valley line length ratio “secant “ is of a 5/12-8/12 bastard roof is . I don’t know if I’m doing the math correctly or not.

[@michaelnauth]

When calculating rafter lengths for an Unequal Slope Hip Roof, all measurements need to be made to the fascia line in order to maintain an equal projection on all sides. For the roof in question, let's call the 5/12 side the 'Side Roof' and the 8/12 side the 'End Roof'. For a Side roof run (to the fascia line) of 2' or 24", the rise would be 2 x 5" or 10". Therefore the End roof rises a total of 10" with an 8/12 slope and thus the End Run is 10" x 12 ÷ 8 = 15". The Hip or valley rafter then has a run equal to the hypotenuse of the 15/24 triangle or SQ Root of (15 squared + 24 squared) or 28.30". But it still has the same rise of 10". The length of the Hip/Valley rafter would then be SQ Root of (10 squared + 28.30 squared) or 30.01". [you can skip a step and take the SQ Root of (15 sq'd + 24 sq'd + 10 sq'd). The Hip angle is found by taking the INV TAN (ARCTAN) of 10 ÷ 28.30 or 19.5°. You can also take the ARCSIN of 10 ÷ 30.01 .

[@TR-rn3pd]

@@michaelnauth when calculating the run for the unequal slope hip. Do we use the run of the shallow side or the steep side.

[@michaelnauth]

@@TR-rn3pd When calculating the rise for the Unequal Slope roof, you would use the run of the shallow side, measured horizontally from the fascia line to the centre of the building.

[@TR-rn3pd]

@@michaelnauth made sense to me after reading your last comment a few times . Thank you for your help.

[@00skeletor00]

You can enter into the calculator 4sq + 3sq =25 2ndF sq = 5

[@framingvagrant]

Simple. Thanks pal.!

[@michaelnauth]

Glad it helped

[@moods5114]

You have to come with some practical examples its difficult for new learners , like you have to out values and calculate

[@michaelnauth]

Check around 21.00 mins on the video.

[@jackf498]

how does the .839 get converted to 10in 1/16?

[@00skeletor00]

Jack F .839 x 16 = 13.424 or 13/16 not sure where the 10 1/16 comes from...

[@michaelnauth]

. 839 ft. x 12 = 10.068", .068 x 16 = 1.09 which rounds to 1, hence we have 10 1/16"

[@thakery5720]

So now I know why I was taught trigonometry....... still haven't found a use for algebra though........

[@michaelnauth]

Solving similar triangles is algebra in action. Anytime you use 'x'.

[@felixgonyo1809]

Thanks for your teaching

[@michaelnauth]

You're very welcome.

[@glennunderwood4690]

The outside of a birds mouth does not sit flush over the sheathing, it sits flush over the top plate...😊

[@russelleldridge3726]

And then your notching he plywood around every rafter?

[@glennunderwood4690]

Some framers I've seen run the sheathing up to the the rafters, some up to the soffit nailer, I've never seen birds mouths' up against sheathing, Although after thinking about it, it's a good idea To not have to cut the sheathing to length. Unless you live in an area with high wind loads And have to install hurricane ties, which would have to be inspected before sheathing goes on. That being said....thanks for the input, and your Drawings, they're very nice.😊

[@russelleldridge3726]

glenn underwood I always have sheathed walls and stood them up and then install rafters.....or I'll add an extra 1/2nor 5/8" to the seat cut so I can slide plywood up if the rafters are already installed

[@mohamedissakamara6142]

Thank you Sir 🥰

[@JoseSanchez-xd1oz]

Thanks Michael

[@okusitinotahitua1020]

sounds academically steps by steps , the other carpenter don't know how to add 2 + 2

[@elfantasmadeatx8807]

I don't get how you get to 3/4 (19) from 12 ?

[@michaelnauth]

3'4" (19 mm) is one-half the thickness of the ridge board, which is 1½" thick.

[@simonrosoery9467]

how do you work out A ? total run is 4940m which is B . Trying to work out A on a 12 12 pitch roof?

[@michaelnauth]

Not sure what you mean by 'A'. For a 12 in 12 roof, the Total Rise is equal to the Total Run.

[@cb-vp5gp]

from where the 3/4 (19)?

[@michaelnauth]

3/4" (of an inch) is 0.75 inches or 19 millimetres.

[@jrquidi2572]

👍😎

[@MH-qg1ky]

So basically if you take trapezoid and a triangle and smack them against the wall it will turn into a circle. Is that what you're saying????

[@michaelnauth]

The trapezoid plus the triangle together make a Rectangle.

[@MH-qg1ky]

I was just trying to be funny dude

[@leoayoroa7217]

Good stuff

[@michaelnauth]

Thanks Leo

[@mafirearmsafety]

Gads! I don't feel like any of this is 'simple'......

[@guillo2388]

You can bypass all the time-consuming math by using any drawing program and or using a Speed Square

[@hillcountrygarage]

Or you can take the time to understand the geometry behind the calculation and have a better understanding of the construction. Lazy and stupid is no way to go through life.

[@brianfield792]

Does measuring and cutting roof rafters have to be this difficult,I think not, get a good roofing square, read the numbers imprinted on the square,or learn how to read it, it will give you everything you need to know, including rafter length of any pitch down to the birdsmouth,

[@michaelnauth]

True - just follow the correct steps.

[@gerrigerbils1413]

I still don't understand

[@JoseSanchez-xd1oz]

Good class

[@MedelGeorge]

Very helpful thanks

[@michaelnauth]

You're welcome , George.

[@addaimartin6237]

And the professional carpenter know that they knows everything but not yet every day new are coming

[@benl1612]

can you please do one with millimeters instead?

[@michaelnauth]

Hi Ben I will work on an SI version (mm) and post it ASAP.

[@michaelnauth]

Hi Ben (sorry for the late reply). In the SI system, roof slope is stated as Rise : Run, but with the Rise being '1'. So a 6/12 Imperial roof slope would be a 1:2. Using that ratio, and Similar Triangles, a roof with a span of 8m (run of 4m or 4000mm) and a slope of 1:2, would have a Total Rise of 2000mm (or 1/2 times 4000) and a rafter length of 4472.1mm (√(2000² + 4000²)). For the same roof with a slope of 1:1.5, the Total Rise would be 2666.7mm (1/1.5 times 4000), and a rafter length of 4807.4mm (√2666.7² + 4000²)).

[@davidgentile4576]

how about just laying it out on the slab itself. little math and actually gets done quicker

[@michaelnauth]

Works well also.

[@carpentryzucconiltd7875]

Why making things complicated. In ancient carpenters brotherhood calculations, we calculate hypotenuse using your given run measurements Multiplied to the secant at your given pitch and that's it. Example your run measurement is say 345.8 cm and the pitch is 45 degrees, just do 345.8 X 1,4142 ( secant number from periodic tables at 45 degrees ) equal 489.03. that is exactly your hypo. However good lessons for beginners it yours.

[@mickmac3360]

There is no need to calculate the length of rafters and framers will not be interested in getting into the math. All you have to do is mark run and rise at right angles on the flat, put the rafter in correct position with respect to wallplate and ridge and mark as required.

[@valhallanews5675]

What if you have a tall building with long rafters? Are you gonna climb and place 6 meter wooden studs at 10 meters above the ground while your assistant applies a tape measure? Don't be a fool.

[@jaferalmoosawi6116]

Thanks

[@michaelnauth]

Welcome

[@russelleldridge3726]

I thought your video was awesome. I see a lot of people complaining and it's obviously because they only know how to do one thing. Take away their rafter book, and square and they are lost. I wanna see calculations for rafters with a ridge already set. How would you do that?

[@Redandranger]

Just subtract half the width of your ridge beam from the horizontal measurement of "B" before you use it in A2 + B2 = C2

[@edwardcharles9764]

This is a math lesson nothing more.

[@chamroeunsdoeung4422]

I'm not good at math, this video is not for me.

[@nguyenhiep580]

This was great, thanks, I been tryin to find out about "how to build rafters for a shed" for a while now, and I think this has helped. You ever tried - Beybigail Nonpareil Breakthrough - (just google it ) ? It is a smashing exclusive product for discovering how to create better sheds and improve your woodworking minus the normal expense. Ive heard some great things about it and my brother in law got great results with it.

[@atv55803]

4+3 =5 no it doesnt its 7

[@microtrance1234]

Many thanks, I have been researching "how far apart should rafters be on a shed?" for a while now, and I think this has helped. You ever tried - Beybigail Nonpareil Breakthrough - (should be on google have a look ) ? It is an awesome one of a kind guide for discovering how to create better sheds and improve your woodworking without the normal expense. Ive heard some awesome things about it and my co-worker got excellent success with it.

[@marauderconvoymcoc4259]

If you Really want to learn about how to build a Roof - please look up the best " Larry Haun" Seriously - I fell asleep watching this video - then woke up and still the video was on when I woke up. Learn to teach - no disrespect to the author 😬

[@jeremyfoster6942]

There are plenty of apps and ready reckoner books that do all this maths for you, even a basic knowledge of how to use a framing square will do the trick, this is archane and pointless

[@addaimartin6237]

I like the way you are teaching

[@michaelnauth]

Thanks