# wooden box formula

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• posted on January 1, 2005, 1:55 am
I remember seeing an article where some clever fellow had created a formula for calculating the size of the cuts required to make a box from a single piece of wood. The point of this was that it told you the most efficient way to make the largest box possible from a board of given dimensions with no waste. Does anyone remember where I might find this?
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• posted on January 1, 2005, 2:24 am
Fri, Dec 31, 2004, 5:55pm (EST-3) snipped-for-privacy@cox.net (r) wants to know: I remember seeing an article where some clever fellow had created a formula for calculating the size of the cuts required to make a box from a single piece of wood. The point of this was that it told you the most efficient way to make the largest box possible from a board of given dimensions with no waste. Does anyone remember where I might find this?
I remember seeing that too. Here. So, I'd suggest checking the archives.
JOAT People without "things" are just intelligent animals.
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• posted on January 1, 2005, 1:52 pm
Yeah, I searched the archives before I posted. No joy. I could figure it out myself (the formula, that is), but I was just hoping not to have to reinvent the wheel. I guess I'll get out my spokeshave....
r
J T wrote:

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• posted on January 1, 2005, 3:49 pm

I have the diagram someone posted on ABPW stored on my drive, but, sadly, my ISP just doesn't allow its members to post there. Used it for the kids at the shop.
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• posted on January 1, 2005, 4:21 pm
I tried an upload. Who knows, it might make it.

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• posted on January 1, 2005, 4:10 pm

OK, I 'm happy to be corrected, since I'm not in the best of shape, but here's my first effort, not allowing fo kerf cuts:
Box length L, width D.
The box has to have two sides as squares If not, the only length for one of those sides must be less than D. That is, with one side D, there are only two others to consider. So, divide the rest of the length as follows:
D D x x y y
Now you can get messy with this, or since D is alread max and constant, look to maximising the area x*y. That's simple, and occurs when the side are equal.
So, give or take [some wood allowance always], measure twice the board width along the length for two of the ends. Then divide the remainder ito four equal parts. If you want all the math I'll put it here, but it might get to be more boring than the personal junk nobody wants to hear about "Gee, I hurt my thumb. Has anyone else done anything this dumb?". So I'll leave it.
There it is:
D D x x x x
That's the theory. The practice is to allow for type of assembly: butt, box, mitre ... . So add a bit to each accordingly.
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• posted on January 1, 2005, 9:51 pm
Sat, Jan 1, 2005, 5:52am (EST-3) snipped-for-privacy@cox.net (r) says: Yeah, I searched the archives before I posted. No joy. I could figure it out myself (the formula, that is), but I was just hoping not to have to reinvent the wheel. I guess I'll get out my spokeshave....
I recall, I had saved that post. But, then decided I'd never be using it, and discarded it. I don't make boxes that often, and when I do, usually wind up not cutting all the pieces from one piece of wood anyway.
JOAT People without "things" are just intelligent animals.
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• posted on January 3, 2005, 3:48 am
(r) wants to know:

A little different spin on things...
While I can appreciate wanting to not waste any wood I'd be concerned that the aesthetics of the box would suffer by simply maximizing the dimensions and volume of the box via a maximization formula. Personally I'd rather "waste" some wood and end up with something that looks "right" than end up with no waste.
What is needed is a maximization formula that incorporates the golden mean in the dimensions of all faces of the box... ;-)
John
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• posted on January 1, 2005, 3:05 am
On Fri, 31 Dec 2004 17:55:31 -0800, r wrote:

Well, it was a standard problem in my high school analysis class... You have to make the second derivative of dx/dy equal zero, or something like that. Not a big help, I know.
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• posted on January 1, 2005, 4:26 am
On Fri, 31 Dec 2004 21:05:29 -0600, Australopithecus scobis

No need since it will turn out to be quadratic and you can do that with high school algebra. Calculus is simpler though, the HS method being a bit longish.
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• posted on January 1, 2005, 9:26 pm

I remember those problems. I believe it was the first derivative though since dx/dy is the slope of the tangent line to the curve. Therefore the only time when the slope of the tangent to the curve would be zero is during a local maximum/minimum. It is a simple quadratic using the ratio of surface area to volume, probably just as easy to use algebra.
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Joe

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• posted on January 1, 2005, 11:39 pm
I'm not sure I see the problem or possibly, I'm not assuming correctly. Why wouldn't you you simply cut two pieces of the width you want the box and divide the remainder by four?
Don

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• posted on January 2, 2005, 2:00 am
conversely, decide what size box you want and then buy enough wood to build it...
John Emmons

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• posted on January 2, 2005, 2:12 am

Oh my god. I'm having a nightmare. I'm in my calc 3 class, I have a test I didn't study for, and I'm naked....
I have a calculator that works in fractions, and a tape measure with the 16ths printed on it. I am such an idiot.
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• posted on January 2, 2005, 4:07 am

Don't feel too bad. I just finished a Calc 3 course so it is a little fresh in my mind. I could've brought up partial derivatives or triple integration for volumes. I think I will have nightmares about those problems for a long time.
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Joe

Who is about to start modern differential equations in two weeks.
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• posted on January 2, 2005, 3:10 am

Anyone can do that. Recently I wanted to make a box but the dimensions were not critical. I guessed at a size and had some scrap that was, well, scrap. Using this formula, I could have better utilized what I had.
I could have come up with a particular size, Figured the wood I'd need. Drive 90 miles round trip to the wood store, Instead I used what I had and in less time than the trip to the store, I was done.
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• posted on January 2, 2005, 10:49 am
I guess the idea of making a box just cause you've got some scraps just doesn't appeal to me. I tend to make things I can use or to give away, not just for the sake of using algebraic equations to maximise the use of scrap wood.
To each their own.
John Emmons
wrote in message

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• posted on January 2, 2005, 2:58 pm

I would not call a 7" wide by 60" long piece of cherry scrap. The system is to eliminate scrap. But at times, the dimension of the box are not all that critical. If you want a "catch all" for your bureau, what is the big deal if it is 10 x 6 or if it is 9 1/2 x 5 3/4 as long as it looks reasonably proportional?
If you feel it is worth a 90 mile drive to get the exact dimension, feel free to do so. When I buy wood for a project I always get a little extra. This is a good way to utilize that top grade wood so it does not become scrap.
To each their own.
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• posted on January 2, 2005, 5:53 pm
John Emmons wrote:

I think that should be "To eaches their owns" or "To each his/her own" : )
But I digress.
What if the board you have is a special board - one with a very nice, unusual grain pattern and you want to make a coherent, wrap around grained box? I had a wild grained oak board I'd cut from a fallen branch on a friend's ranch. The grain pattern was unusual enough to warrant a name - The Van Gogh Board because of the frenetic, contrasting wavy grain pattern.
Alas, the top didn't look right so I went with a sycamore top.
charlie b
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• posted on January 2, 2005, 9:51 pm
On Sun, 02 Jan 2005 10:49:31 +0000, John Emmons wrote:

Quite. I do get my jollies from squeezing every last chip from lumber. So far, 4.8 bf of 5/4 ash has yielded: 28" frame resaw, 28" frame saw, stair saw, panel gauge, huge mallet, drill press fence (check on the end, useless for anything else), a couple pair of bar gauge heads, and just today, a skew rabbet plane. I'm down to 1 piece ~9.5" x ~1" x 5/4". I'll think of something...
Oh, and I used a Rockler coupon for the ash, 20% off..
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