Calculating Wood Dimensions for Outside Corners
George VondriskaDescription
George Vondriska shows you how to use basic algebra to calculate the wood dimensions for cutting an outside edge on your woodworking projects. The key is finding the right size so the dimensions are the same for the thickness on one side and the width on the other, which will in turn help you to use only one piece of wood.
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It's not uncommon that on projects like this garden planter I make the leg up by making an outside corner. So we've got a skinny piece here a wider piece going the other way. But the key to this is that when you look at the leg from the outside it's exactly the same dimension this way as it is this way. And that's what this is all about is how do we do the math to make sure that we're going to get exactly the same dimension in both directions and get both pieces cut from one board. The legs for this project were cut from what's called five quarter decking. So what I've got here is a piece of material. that's one inch thick, five and a half inches wide. It came from a home center. Now, the way that this leg looks and what's called section view, if we were looking right down at the top of it, is that we've got one piece this way another piece that butts into it. And like I said, the key out of this was I wanted this dimension and this dimension to be exactly the same when you look at it from the outside. Added to that, I wanted to make sure that when I rip my board I can get both of these pieces from one cut from this board. So what I have to do is take you back to junior high or high school algebra. We can figure this all out and it's really easier than what you think. So here's what we've got. I'm going to have some width of X. And I'm going to see if I can do this upside down so it's right for you but upside down for me. X is the width of the narrow board in my leg structure. Then when I add to that another piece, that piece is represented by X plus one. One is the thickness of my material. So although this stuff is called five quarter it's been planed so it's actually down to a one-inch-thickness right now. So what I have here is that this piece is X. This piece is X plus one. It's an inch wider than the first one. Now we've got a little addition problem going here. Equals, let's see if I can do this, five and one, oh I got to do an upside down two, half. Cause that's the width of my starter material. So board A plus board B has to add up to five and a half cause I want to rip 'em both out of one piece when I'm done. So now we combine all of this and we'd end up with two X plus one equals five and one half. Take a one away from both sides. So then we have two, whoops X equals, subtract one from both sides, four and one half. So then X, to get that by itself, we divide the two away from both sides. So X divided by two or two X divided by two is going to leave just the X alone, four and a half divided by two, two and one quarter equals X. So what does that tell me, coming back up here, this board, the narrow one, is going to be two and a quarter inches wide. The big one is going to be three and a quarter inches wide. If we want to test our work, do the math two and a quarter plus three and a quarter equals five and a half the width of our original board. So a little bit of algebra walks you through what you need to do in order to get these boards to come out just right. Make sure that the corner looks good and your yield is good 'cause we can rip both pieces from one board.
Good tip except for one major thing. You Didn't account for the kerf of your saw blade in your equation. so when you cut that 51/2 inch board at 21/4 you will come up short in width on the other board. Just saying.
Great math on the outside corner except, (not that it would make a noticeable difference)you forgot to subtract the width of the blade.
George lost me after he said "Algebra"
You don't need to figure or the saw kerf. All you have to do is measure to the center of the blade when you set your rip fence and the kerf problem goes away.
George, you haven't taken the width of the saw cut into account.
When you say algebra you scare people - it need not be that scary, and if someone is many years out of school they don't have to be dragged back kicking and screaming. Let's do it using practical math: You know one side will be some width and one side will be some width minus the thickness of the stock. On your piece, first measure over the thickness of the stock from the edge (1" in your example). Now measure from that mark to the other edge (4-1/2" in your example). Now split that and make a mark (2-1/4" in your example) and that's where you rip your stock (allowing for the kerf of course). It's exactly what you just said, but the process takes place on the wood rather than on paper - which is easier for some folks to remember and/or understand. I know a lot of very smart carpenters that don't know algebra.