# How to calculate the length of roof rafters (captioned)

I’m Duane Lardon and I teach Construction Technology classes at Crockett High School and here at Austin Community College. This is a continuation of our speed square discussion (another video). We’ll be using this speed square to cut rafters, and to design rafters to fit our needs. (off camera voice) What are rafters for? Good question. Rafters are the structural members that support the roof of a house. The first thing we need to do is understand pitch or slope. The slope of a roof is the correct term; pitch is typically used by the architect. If we have a house … This is the rafter and there’s an angle across here. We need to find a way to describe that angle with a universal term so everyone can understand what the roof pitch of the structure is. This is a graph that you may recognize. When you’re talking about a roof slope or roof pitch, it’s always described in terms of… you’re running over a certain distance and then you’re rising over a certain distance and that will define the roof pitch or roof slope. The trade standard is you’re running over 12 units. It could be 12 inches or 12 feet. But it’s 12 units. Whatever the units are here, you have to use the same units here – feet and feet or inches and inches. 12 is always the unit you be running over. In this case I have 12 marks across here. To describe a roof slope, if I’m going over 12 and I come up 2 then this is what the roof pitch or slope looks like. If I come up 5 then that’s what the angle is. Let’s go 8. This is the way you describe a roof pitch or slope. Architects use a graphic. They say typically the pitch is equal to in this case 8/12… which means that is your rise over your run. When you’re talking about this, the run is always going to be units of 12 over. Then the number of units up is the rise and that’s the visual description of the slope of the roof. Now comes the question: how long is the rafter? To figure that out, we have to do math. This is one of your favorite formulas, I know. We’re going to be using this to figure out the length of our rafter. If we look carefully, we can see that that is the hypotenuse of a right triangle. We need to change these letters A, B and C into carpenter’s words so that we can work our problem. I change the C squared into Rafter squared. . This says A squared plus B squared equals our rafter squared. To understand this, we need a bit of vocabulary. The distance between the support walls, outside to outside, is called the Span. You can find the span on your set of blueprints. They’ll say this building is exactly this wide. That’s what your span is. By definition, one half of the span is equal to the run. And this is our rise. One half of our span is our run and this is our rise. If we’re substituting our carpenter words for the Pythagorean theorem, we have our run squared plus our rise squared is equal to our rafter squared. And that will tell us exactly how long this rafter is. Anytime I have a numerical value for one of my words I substitute that value into this formula. So now my run is 14 squared plus – I don’t know what my rise is… …but the architect tells us on the plans exactly what our pitch is. We don’t know what our pitch is at 14 feet. Here is 12 feet. At 12 feet we’re going up 5 feet. But we’re going over here 14 feet and our rise will change a bit. The way that we figure it out is we work a formula. Here’s our formula. We know it to be true because the architect told us. Anytime you see a word that has a numerical value… …you substitute that in the formula. Our run is 14 so we substitute that in the formula. We now have an algebraic equation with one unknown. I will solve it by cross multiplying. If the run is 14 feet for this situation I’m going up 5.8333 feet. Any time I have a numerical value for one of my words, I plug it in, keeping in mind that… …in the earlier (video) conversation I want to leave this as engineer scale (decimals) and not convert to architect scale (fractions)… …because I can do this math easier than if I convert this 5.833 feet into feet and inches. I’m going to do the math. My rafter is 15.1667 feet. So that’s what this is if my span is 14 feet and my rise is 5.833 feet. I don’t have this 15.1667 feet on my tape measure so I have to convert this into architect scale (fractions) See the Converting Between Architectural and Engineering Scales video for details There’s the math. Now we’ll go (into the workshop) and I’ll show you how to mark a rafter. (next video)

## 5 thoughts to “How to calculate the length of roof rafters (captioned)”

1. Eva luna Lopez says:

good video

2. Dwight E morgan says:

this was the clearest explanation of rafter calculation. well done

3. Jerry Gemetro says:

this is the best explanation yet!! Thanks !!

4. Fil Solano says:

I was under the impression that he was gonna figure out the rafter length w/o using the calculator, by using the square alone. Great video tho. Thanks for posting.

5. Alistair Milner says:

Just a bit of feed back but the when it came to the crucial part of the maths and fully understanding it you speeded up the video, I think anyone trying to learn how to do this wouldn't pick up on where you've gone with the maths. In the past I've struggled with it and part of that is you obviously can't decimalise feet and inches, not easily. Say if it was an extension on an old house and the rise just happened to be 8ft 6 and 3/4 inches, the calculations are all getting a bit tricky, better to slow down the video at the difficult part not speed over it.