# Dovetail Spacing Calculations



## FlyMaster (May 17, 2007)

I'm wondering if any has come up with a formula for calculating the spacing between cuts when cutting dovetails. By my calculations, it should be sometime like the following: 

spacing = cutter_diameter x sin(90 - cutter_angle) x 2.
so if you had a 3/4" 7 degree cutter, your spacing should be ~1.35"

This is for those of us that DON'T have all the Incra templates.

Can anyone confirm? (I'm trying to be accurate while working on a project with a few remaining boards of 200+ year old oak)


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## bobj3 (Jan 17, 2006)

Hi FlyMaster

This may help with your question...▼

http://www.canadianhomeworkshop.com/toolbox/toolbox_dovetail.shtml

http://www.ukworkshop.co.uk/forums/viewtopic.php?p=181999&sid=63856dc67434a7ede9a85b89bf5d2278

Bj


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## Mike (Nov 22, 2004)

In one issue of The Woodworkers Journal Ian Kirby details his method for hand cutting dovetails. If you want to use a router to cut your dovetails you can buy a jig from Harbor Freight for about $30 that is virtually identical to Rockler's 1/2 blind dovetail jig but at less than half the cost. You will find that routers are too difficult to control for accurate dovetails without a jig.


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## Dr.Zook (Sep 10, 2004)

Hello FlyMaster and welcome to the RouterForums. I like the fact that you jumped right in and asked a question.


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## FlyMaster (May 17, 2007)

Dr.Zook said:


> Hello FlyMaster and welcome to the RouterForums. I like the fact that you jumped right in and asked a question.


Dr. Zook - Love the quote - no scrap, only fire wood. Matter of fact, we've been using left over sawdust (in cups w/wax) as campfire starters. 

Update on the calculation, I think there should be a factor on the depth of cut multiplied by the sin of the angle. Still playing around with in to confirm.


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## harrysin (Jan 15, 2007)

FlyMaster, why on earth would you need to do any calculations, especially using higher maths. when making dovetails either hand or jig made? I'm surprised that others, especially Bobj3 and Joe haven't raised the question or has it just been beginners luck that my dovetails have turned out OK?


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## bobj3 (Jan 17, 2006)

Hi Harry

I was going to BUT some woodworker look down on any one that needs to plug in a tool to cut dovetails ,,, I call them the Roy Underhill type and will only use hand tools that are made in the 1700 to 1800s ,it's true the dovetail joint has been used in wood const. for a long ,long time and most the pros.don't need to use math they just mark it and cut it out, my grandfather was like that but I'm sure it took him years to get it down right....but now days you and I can do the same thing with a router and a jig in about 1/10 of the time and they come out right every time unlike the hand cut type. 

But then woodworking is about having fun in your own way...

Bj


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## FlyMaster (May 17, 2007)

Gents,
Thanks for the link to WWE (woodworkersedge). The needle pin jig on next on the list after I get a handle on this other stuff. 
Harry, The reason for the calculations is for my first crack at double/inlaid dovetails using different cutter sizes & angles. I need to be dead on for the tail/pin alignment on those (or at least close as the eye can tell). Base on that, I’ve invoked the “higher math”. Not sure that I’d really call sin, cos, tangent “higher math”, more of a jr. high level math don’t ya think? I remember calc 1, 2, 3, differential equations, and linear algebra as needing a bit more gray matter than the old “opposite over hypotenuse” stuff. But hey, I’m still learning this router & wood stuff so it’s back to school for me too. Once I get the hang of getting it right on the router table, I’ll try the hard stuff – by hand.
Thanks again!
FlyMaster (aka –O.F.I.S.)


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## harrysin (Jan 15, 2007)

Flymaster, you must forgive me for not remembering much about calculus but I finished school at the end of 1949 and although I spent fifty years in the consumer electronics industry, reaching the top of my profession, manipulating simple formulae was the only maths necessary. Going back to dovetails, wouldn't an Incra jig solve all of you're problems, whilst I haven't used one, I have seen several live demonstrations and was very impressed.
Finally I really would be interested in finding out how many members of the forum could still pass a calculus exam. and how many could not.


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## curiousgeorge (Nov 6, 2006)

Duh. What's calculus?
I subscribe to the Bob & Rick no math methods.


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## Dr.Zook (Sep 10, 2004)

Calculus, ain't that what you get on your hands from doing manual labour???????


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## Drugstore Cowboy (May 17, 2007)

As long as you can calculate the time it takes you to get out the back door - before her husband comes in the front -- you should be ok math-wise.

Well - ok -- so you also need to know the proper ratio of rum to Coke and enough applied geometry to find your way around a pool table.


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## AlanWS (May 2, 2007)

You have a lot of flexibility in spacing if you use a sophisticated jig or cut them by hand, or some combination. However, if you are cutting half blind dovetails using the type of jig where you cut both parts in one operation, the spacing must be even. This means the tail at half height must be the same width as the socket at half depth. The point of an equation to describe these is that it can help you to see how to modify the joint with varied bit angle and cut depth. The deeper the cut, the narrower it is at half depth.

The idea is to find the depth where the width of the tail and the recess are equal at half depth. That will depend on the angle of the bit (a), the width of the cutter (c), the bushing size (b), the finger width (f), and the dovetail size (s = the average of the width of a finger and the width of a space between fingers.)

Cut depth d = (s + c - f - b)/tan(a)

Treat this as an approximate setting, try it, and adjust the bit depth shallower if too loose, and deeper if too tight. If your bushing is off by 0.001", your cut depth would change by .007" for an 8 degree bit.

To use the same bit to cut deeper dovetails, use a smaller bushing. Likely it will be easier to use a bit with a smaller angle, or a wider bit of the same angle. 

But the equation also shows how sensitive the depth setting is to these measurements: all you need is about 1/64" wider cut to change the depth from 1/4" to 3/8". If the cutter is actually wider by that amount, or if there is that much play between the fingers of the template, it would do it. To measure s most accurately, measure the width of the entire template, including an even number of fingers and spaces, and then divide by the number.

But whatever the measurements, you will need to make test cuts and fine tune the depth for fit. For those who like equations, this can let you use a cheap jig to cut a wider variety of dovetails.


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## TWheels (May 26, 2006)

harrysin said:


> Flymaster, you must forgive me for not remembering much about calculus but I finished school at the end of 1949 and although I spent fifty years in the consumer electronics industry, reaching the top of my profession, manipulating simple formulae was the only maths necessary. Going back to dovetails, wouldn't an Incra jig solve all of you're problems, whilst I haven't used one, I have seen several live demonstrations and was very impressed.
> Finally I really would be interested in finding out how many members of the forum could still pass a calculus exam. and how many could not.



Harrysin, I teach college students and teach a course in which I use a great deal of math, including calculus. I retain the calculus from roughly 4 decades ago that I need in order to teach my subject. There is absolutey no way I could pass a calculus exam today. If I were serious about it I could probably start today and be able to pass rigorous calculus exam at the end of the summer.

The problem that started this thread does not require calculus; it does require trigonemetry. Again, if I had the summer, I could probably pass a rigorous exam by the end of the summer.

As for the answer to the original question, give me some more time. My year just ended and I am still brain-dead exhausted. (I do not even trust myself to get out my router yet!)


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## harrysin (Jan 15, 2007)

Thanks for you're answer mftha, I don't feel quite so inadequate now.


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## FlyMaster (May 17, 2007)

To all:
Thanks for all the feedback! This is definitely the place to go when answers are needed in short order. 

AlanWS has the right approach. It’s tangent of the angle not sine. Shows how much trig (let alone calc) I remember…

So if you used the calculation for depth of cut d = (s + c - f - b)/tan(a), tweak it a bit, you get 

cut spacing = 2 * bit diameter - 2 * (depth of cut * tan(angle))

Happy routing!

FlyMaster (aka – O.F.I.S.)


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