# How to use dividers



## wombataholic

I was reading through the Anarchist's Tool Chest this morning and I don't understand the use of dividers. In the book, the example given is dividing a 43.238475758" long board into 7 sections with 1/2" in between each section. I understand starting half an inch in from the end, then marking out the 7 sections, then going to the other end and doing the same, but how do you determine how wide each section is when using dividers? The steps right now read to me:

1. Start with a mark 1/2" in from the edge.
2.


> ?


??
3. Mark off 7 equal sections.
4. Repeat from other edge.

What am I missing in step 2? Thanks!


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## Roadster280

Er..divide…

43.238475758 - (8×0.5) = 41.238475758

41.238475758 / 7 = 5.89121082257143 (or 5 57/64" for government work). Plus the half inch spacing.

Set your dividers to 6 25/64". How you do that of course is another matter, especially when the dividers will not be perpendicular with the plane of the rule. Equally difficult is sticking the point of the divider in the far edges of the piece.

Personally, I'd go with 6" and cut the rest off, waste pieces at each end.


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## JJohnston

If the distance to be divided is smal, eyeball 1/7 of the distance and set your dividers there; otherwise, do the rough division (only subtract the half inch once): a little less than 43" divided by 7 is a little more than 6", so set the dividers to 6" or so. Then, step off 7 segments. Unless you're really lucky, you won't hit right at the end of the board; you'll have some error. Adjust the dividers an amount equal to 1/number of segments x the error, or in this case, 1/7 of the error (eyeball this). If you're short, open them up. If you're long, close them. Then try again. Do this a couple of times until you can't get any closer, and that's it.


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## Sylvain

I don't have Schwarz 's book.
Are you sure the goal is to have exactly 1/2" between each section?

Normally the goal is to have the spaces between the sections of equal width and regularly distributed in order to layout the pin's width for a dovetail assembly.

The exact space width (being anything, let's say, between 3/4" and 1/8") is not important as long as it suits you (and you use the same on the four corners of the chest).


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## Tedstor

I bought a pair of dividers and attempted to use them. I quickly found myself thinking "whats easier/better about this over a tape measure"? 
Pretty much on par with chopsticks. Isn't a spoon or fork an easier way to get it done? 
And I can't use chopsticks either.


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## MrRon

Why are you starting at 1/2" from the end? The board is 42.238475758 long. There are (6) 1/2" spaces. Subtract (6 x .5) from the total length =39.23847575 and divide by 7. Answer: 5.605796536. Round to the nearest 32nd = 5-19/32. Mark the first point from the edge. Add 1/2" = 6.105796536. = 6-3/32. Step off that dimension from the starting point. Return to start and mark off starting from the point previously marked (1/2" from the edge).


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## CplSteel

I don't clearly understand what the book is asking you to do, but there is no step two. The point of dividers is that you guess at the right width, walk them out, and adjust the width, in your case 1/7th of the error. Then do it again. You may have to adjust one or two more times but in the end your dividers will be set to exactly 1/7th the board. The measurment in a number is irrelevant.

It is very fast and easy.


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## Gshepherd

Well the principal was right. Ditchin Math class would come back to haunt me…..


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## renners

A case for going metric if ever I saw one.


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## Sylvain

Usually the goal is to layout evenly spaced pins of equal width without even knowing the length of the board and without any calculation. 
You eyeball 1/6 of the length between the end marks (whatever they are)

In the example you end up with 7 equal "spaces" :
between the left 1/2" mark and mark "l" 
between mark "a" and mark "k" 
between mark "b" and mark "j" 
....
between mark "e" and mark "g" 
between mark "f" and the right 1/2" mark










Being metric or not is irrelevant. (I am metric)


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## xylophage

I thought I was going to have to set everyone strait on this until I saw Sylvain response. He is absolutely correct on how to use the dividers correctly. They are a great thing to have around in the shop. I use mine all the time. Once you get the hang of them. Its by far faster than figuring out the math. Good luck


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## CplSteel

Sylvain is probably right, and I just do not understand the aim of the measurment. For a more general example of how to use dividers, see this Underhill video where, around the 7:20 mark, Roy lays out some even spaces on a random width board. In fact, I think he lays out the entire project without measuring (by number) anything. Everything is laid out in reference to the material.


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## Tedstor

OK. This thread has been an eye opener for me. Dividers suddenly make perfect sense. 
Definitely easier than a tape measure, but still light years more useful than chopsticks.


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## Dal300

7 equidistant marks on a wide rubber band or piece of elastic work easier.

Stretch from point A to point B and mark where the marks on the band fall.


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## CplSteel

@Dallas, that would work well if the rubber band stretched consistently across its length, which it might, at least while new. Of course, getting the marks equidistant is important, and doing so on the smaller scale is harder and the error rate will be magnified when you stretch it out, but yeah, it will save you 45 seconds or so.

@Tedstor, chopsticks have their uses too.

@wombataholic and Jonathan - as it appears that all the project is trying to accomplish is 5 or 6 evenly spaced gaps, with 1/2" offsets on the top and bottom, then as long as the size of the gaps is irrelevant, sylvain is right on point. Just don't change the spacing on the dividers between the right direction run and the left direction run.


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## JJohnston

Sylvain, why would you set the dividers to 1/6 of the length if you wanted 7 segments? Everything else is right, and it's what I said up higher. I did this in AutoCAD today, if anybody wants to see essentially what Sylvain drew, but with computer neatness.


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## Sylvain

Oops,
I didn't read the specifications attentively. ;-))
Replace ~ 1/6 by ~1/7 and proceed the same way.

Anyway it was just to illustrate the principle. and to show that no calculus was necessary.

C.S.choosed a length of 43.238475758" just to make calculus difficult in order to show the advantage of the divider method.


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## Sylvain

To finally answer Wombataholic question,
If you want a given gap between the sections, here is the extra step to set the divider without calculation:










It uses a "sector" or a "folding rule".
The distance between the two "1" marks is 1/7 of the distance "L" between the two "7" marks.

The graduations may be in any unit that suits you (imperial, metric or your own arbitrary unit).

see here :
http://www.popularwoodworking.com/article/make-a-sector-from-a-crappy-folding-rule

If you don't have a sector, you can draw on the board and use the (Thales) Intercept Theorem to find 1/7 of the segment AC on my sketch.
See : http://en.wikipedia.org/wiki/Intercept_theorem
look for "3.2 Dividing a line segment in a given ratio".
Note that AB in wiki is AC on my sketch.
No calculation needed either.


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## waho6o9

Thanks for the post Sylvain.


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## fury

Megan Fitzpatrick of Popular Woodworking just posted a video using dividers to lay out dovetails for the Anarchist's Tool Chest that she is building.

 
Use Dividers for Quick & Easy Dovetail Layout - No Measuring


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## Sylvain

Megan ends up with the point C (in my sketch herebove) between the point B and the right edge.
This means that she doen't know in advance how beefy or thin her half tail will be.
If too thin it could be fragile when assembling the two boards.
I would think the good practice should be to define in advance the minimum width of the half tail (at the bottom where it is narrower ) and then find the points A and B with the dovetail template (whatever its slope). Then setup the divider such that point C is on the left of point B.


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## Geoff93

I know this thread is super old, but in case someone else finds it and wants a good video explanation. This is the author of that book showing the layout method:


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## Foghorn

Old thread for sure. For what it's worth, I use an old Deitzen proportional divider. Way easier, at least for me to lay out a set number of identical spaces.


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## TraditionallySpeakin

If you want to dive into the deep end of using dividers then check out Jim Toplins book By Hand and Eye. You can get the pdf on LAP website for fairly cheap. It is a complete eye opener when it comes to using dividers.

Think of it in its simplest use and extrapolate from here. You want to divide a board in half. You place one point of the divider at the boards edge. You then slowly open the dividers to a point that looks to your eye to be halfway across. You easily set the other point of the divider there (don't dig in in case you guess wrong, you don't want to mark the wood at the wrong spot) and then swing the original point (the one that started on the boards edge) over toward the opposite edge. Your eye will probably have been a little off and the point will land a little ways from the edge (if you over guessed start over, the goal is to guess exact or under guess the distance). Anyway this little gap between the divider point and the edge of the board - just divide that in half by opening the dividers to half its distance (without lifting the point of the divider that is sitting in your guessed middle). Now lift the dividers off and start at the edge again and recheck. Most likely it will be dead on or you may have been a tiny bit off on your second guess and may have an even smaller gap to divide in half again but usually you get it on the first try.


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## jglen490

Other than knowing that you want to end up with equal 1/2" spacing on each end, you don't measure anything and you don't "do the math". If all you have is a pair of dividers, and don't have a sector, the rest is guesstimate the width of 7 or 5 or 9 or 3 dovetails. Mark the 1/2" spaces on each end, march off 7 in one direction, then 7 in the other. If you're close, the actual mark will be about halfway between the divider marks from one starting point. This is what the excellent demo/drawing above is showing. If you "do the math", you're no better off as most of the time you end up with unwieldy fractions.

Proportions, ratios, and basic overall dimensions are easier to start with than some sort of precise number. Tolpin's book(s) on the subject are excellent. By Hand and Eye, and the accompanying By Hound and I are great demonstrations of the old ways of creating perfectly proportioned and properly sized pieces - whether you are building a shelf or a castle.


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