# Basic Equations For Roof Framing

today we're learning how to lay out and cut common rafters using a framing square in two simple equations gable roofs like our mock-up here are made up of common rafters which are rafters that come 90 degrees off the ridge board and in order to know the total height of a roof and the length of the rafters you need two equations the first equation is used to find the diagonal measurement or the rafter's theoretical length the second equation is used to find the rise of the rafter in order to use these two equations you need to know four things total run unit run unit rise and length of common rafter per foot of run first is the total run total run is half the distance of the total span or width of the building minus half the thickness of the ridge board material for our mockup the total run is 23 and a quarter inches next is the unit run this number is easy because the unit run for all common rafters is 12 inches third is the unit rise so for every unit of run which is 12 inches a rafter will rise a certain amount which is normally predetermined by a set of plans or codes however unit rise can also be determined by you the higher the number the steeper the roof the lower the number the shallower the roof so for our mock-up we're going to be using a four inch unit rise last is the length of common rafter per foot of run and this one's easy as well because once you've determined your unit rise which again is four inches for our little roof simply look on a framing square under 4 to find the length of common rafter per foot of run which is 12.65 inches now that we know all the numbers let's simply plug them in to the equations starting with the diagonal measurement equation 23.25 divided by 12 times 12.65 for a total diagonal measurement of 24.5 inches next is the rise 23.25 times 4 divided by 12 equals 7.75 inches of rise therefore our total run is 23.25 our rafter length is 24.5 and our rise is 7.75 now if you're paying attention you'll notice that these numbers along with their lines do not line up with the top side of the rafter but rather are below the actual rafter height almost all the equations and or methods that are used to calculate the length of common rafters all brings us to this same line and that line has a name and it's called the measuring line let's lay out the common rafters first and then i'll come back and we'll talk in more detail about the measuring line but before we do that i'd like to thank skillshare for sponsoring today's video for those that don't know skillshare is an online learning community with thousands of inspiring and creative classes for anyone who loves learning skillshare is a great place to invest in yourself and your personal growth and if you have specific skills you're trying to learn skillshare is a perfect place to start so i started a diet about five weeks ago but honestly i started it without knowing a lot about it and i tend to do things like that anyway i found a class called the ketogenic diet made simple and brady the instructor did a fantastic job at teaching me things that i didn't know and should know about the diet like supplementing with minerals for me it was learning more about a diet for you and maybe something completely different but if you'd like to make 2022 a year of new learning growth and connection through creativity sign up today and the first 1000 of my viewers to sign up using my code or the link in the description will get a one month free trial of skillshare so that you can start exploring your creativity today jumping back in using the numbers we just figured out lay out a framing square with the 4 on the tongue side which is our unit rise and the 12 on the blade which is our unit run draw a ridge plumb cut line and cut it out using a circular saw the next number to use is our diagonal measurement which is 24.5 inches so measure down from the ridge cut line and draw another lime this line represents the outside building line in the heel cut of the bird's mouth generally the seat cut of the bird's mouth is the same length as the top plate and the exterior sheathing combined or something really close to that next flip the square around so you can measure over for the c cut draw a line and this is the bird's mouth which gets cut out next lay out your desired overhang and soffit amount in our case that's eight inches over from the outside building line and then down six and a half inches for the soffit cut and everything with an x gets cut out the overhang amount and soffit cuts really can vary from roof to roof it really comes down to personal preference or drawings or specific codes and design and ultimately what size trim you're going to be using on the roof all right let's talk more about the measuring line and the rise of 7.75 inches which for those that are keeping track we haven't even used that number yet as far as the measuring line it's helpful to think of it as a fixed number meaning that this number is a constant and the only two numbers that change from roof the roof are the overhang amounts and the deduction for the ridge thickness the other thing the measuring line does is helps to solve for the total height of the roof which is not the same as the rise we originally solved for therefore in order to get the total height of the roof we need two things first the measuring line and second something called the height above plate if we look back at our original rafter layout we can still see our outside building line or what's left over after we've cut out the bird's mouth the measurement of that line from the corner of the bird's mouth to the top of the rafter is called the height above plate which for this two by eight rafter is six and an eighth inch therefore if we add the rise of seven point seven five inches with the height above plate of six and an eighth we get a total roof height of 13 and 7 8. and now you can see by using a framing square and those two simple equations you too can build your very own common rafter roof if you'd like to stay up to date on what's happening at training hands academy with courses and anything else i have going on to the shop please follow me on instagram and more importantly if there is any way that i can pray for you and your family just let me know i would love the opportunity to do so thank you so much for watching this video god bless [Music]