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# Neck Angle Equation

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NECK ANGLE EQUATION

a:action of the strings

f:fingerboard thickness

w:thickness of the wood over the top surface*

h:height of the bridge

y: the levels distance from the bridge’s bottom level to binding’s top level

L:distance from the point where the neck meets the body to the bridge

φ:the angle of the neck

tanφ=[(h+y)-(a+f+w)]/L

*if the top surface is angled (in φ angle) the w is constant.If not then as in the photo the w is not constant

PLEASE TELL ME WHAT YOU THINK

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No disrespect intended whatsoever.

This is the most overcomplicated method I've seen yet to find the answer to what is a relatively easy question. So much so, in fact, that I'm not actually going to take the time to figure out if it is correct or not.

I think that were someone having difficulty trying to figure out their neck angle, reading this post would just make matters worse for them.

IMHO, there is no easier way than a full scale drawing. Your drawing doesn't even have to be of the entire guitar, just lines representing the important pieces of the equation. There are loads of descriptions (Hiscock, Koch, Perry...) easily available, even on this website, that can guide you through making the drawing.

For what it's worth, when I'm trying to figure this out, I'm not looking for an angle, I'm looking for the distance the distance below the plane of the bottom of the fingerboard I need to mount my bridge for a specific scale length. Working in small angles can be difficult (for me, anyway) and a small anlgle error can equal a dramatic error in distance at the bridge.

Just my opinions, mate.

Cheers

Buter

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No disrespect intended whatsoever.

This is the most overcomplicated method I've seen yet to find the answer to what is a relatively easy question. So much so, in fact, that I'm not actually going to take the time to figure out if it is correct or not.

I think that were someone having difficulty trying to figure out their neck angle, reading this post would just make matters worse for them.

IMHO, there is no easier way than a full scale drawing. Your drawing doesn't even have to be of the entire guitar, just lines representing the important pieces of the equation. There are loads of descriptions (Hiscock, Koch, Perry...) easily available, even on this website, that can guide you through making the drawing.

For what it's worth, when I'm trying to figure this out, I'm not looking for an angle, I'm looking for the distance the distance below the plane of the bottom of the fingerboard I need to mount my bridge for a specific scale length. Working in small angles can be difficult (for me, anyway) and a small anlgle error can equal a dramatic error in distance at the bridge.

Just my opinions, mate.

Cheers

Buter

Of course my friend,i accept your opinion,and i will be glad to find if it is wrong....It is just how it is easier for every luthier....

But for Les Paul it gives correct results,and for some prs style...

i dont like drawing ,i prefer calculating...just taste.....the issue is if it is correct.........

Edited by theodoropoulos

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I agree that its complicated but is the formula from a book or have you made it up yourself? I'm just wondering because I do these sorts of things myself. If you have come up with a formula of your own it is not very likely that someone else has done the same thing

I recently made a "Les Paul" body and the fretboard sits flat on the top because the end of the body is routered to the angle. I copied this straight off an LP and I took many measurements. I think the main thing you have to concern yourself with is the thickness of the fretboard and the height of the bridge. The rest would just "fall" into place, like I don't think it matters how much of the neck shows between the fretboard and the top

If you are interested in other pictures of my build. It has a few frets on it but its not finished

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This is the most overcomplicated method I've seen yet to find the answer to what is a relatively easy question.

Yup...one small mathematical error and all of the sudden the guitar is junk.Just for the record,Perry's method lays it out stone cold accurate.

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This is the most overcomplicated method I've seen yet to find the answer to what is a relatively easy question.

Yup...one small mathematical error and all of the sudden the guitar is junk.Just for the record,Perry's method lays it out stone cold accurate.

look guys,this is an effort i made my self.....I just want to understand what i do,and if anybody whants to chat feel free to do it..

It's not an equation of the univercity ,its just an equation for childern and the mistake is zero......If you double check it it's ok.

You can combine it with drawing.....

Look,i just made a proposal.If you disagree it's ok,just forget it....

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Well it is very beautiful...

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Guys, neck angles are very, very simple trig. I usually draw mine out schematically (ie, not terribly accurately, and not necessary 100% to scale) when double-checking things. I don't do wedges like what's pictured above, bit it is just a simple tangential equation once you figure out where the legs of the triangle live. Perry's method is easiest/best if you don't want to do any math at all, and should be the one used first if you've never fiddled with a neck angle before, if only to let you understand what measurements are important, but after that, if you've got even a little bit of a math-y background, trig works fine and dandy.

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Guys, neck angles are very, very simple trig. I usually draw mine out schematically (ie, not terribly accurately, and not necessary 100% to scale) when double-checking things. I don't do wedges like what's pictured above, bit it is just a simple tangential equation once you figure out where the legs of the triangle live. Perry's method is easiest/best if you don't want to do any math at all, and should be the one used first if you've never fiddled with a neck angle before, if only to let you understand what measurements are important, but after that, if you've got even a little bit of a math-y background, trig works fine and dandy.

my personal opinion is that drawing the angle will take about 15 minutes and id the pencil line is thick the angle will not be very accurate.It all depends on the

ability of drawing EXACTLY....On the other hand a luthier knows exactly what he has done,knows the constants and if you look it carefully its only a division ...it takes about 1-2 minutes.....

but its matter of taste and habbit.....We are all here to say our opinion in democracy and make a dialog to gain experience..isnt that we are looking for???

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my personal opinion is that drawing the angle will take about 15 minutes and id the pencil line is thick the angle will not be very accurate.

Scratch that first post.It sounds aggressive...Let me just say that trying to downgrade a simple straight line diagram as something "inaccurate",and implying that it is for simpler minds or some such is only making you look like you are awfully defensive...it is not actually making anyone else look silly...

You always stick with the simplest method for YOU...personally,I think you just like math...in this case there is no need for it as the first step to building a guitar should be to draw up plans of what you are building to check all of your work from.And when you have all of those plans that you already made drawn full sized in front of you,then all of that fancy math and those equations become redundant.My "plans" are only two diagrams..one of the neck angle,and one of the fretboard taper...everything else is "art"

Some people mistake math as logic...keeping it simple is ALWAYS the most logical way.When you figure out your angle via your equation you still have to set up your tools for it,draw templates,or draw it directly onto the wood...every single part of which is going to put you more than a pencil width out of accuracy..

So if you take the guitar you build and measure it for accuracy,it is going to be no better than those done with the simple straight line method...and the straight line method is much simpler,therefor more logical in this application.

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my personal opinion is that drawing the angle will take about 15 minutes and id the pencil line is thick the angle will not be very accurate.

Scratch that first post.It sounds aggressive...Let me just say that trying to downgrade a simple straight line diagram as something "inaccurate",and implying that it is for simpler minds or some such is only making you look like you are awfully defensive...it is not actually making anyone else look silly...

You always stick with the simplest method for YOU...personally,I think you just like math...in this case there is no need for it as the first step to building a guitar should be to draw up plans of what you are building to check all of your work from.And when you have all of those plans that you already made drawn full sized in front of you,then all of that fancy math and those equations become redundant.My "plans" are only two diagrams..one of the neck angle,and one of the fretboard taper...everything else is "art"

Some people mistake math as logic...keeping it simple is ALWAYS the most logical way.When you figure out your angle via your equation you still have to set up your tools for it,draw templates,or draw it directly onto the wood...every single part of which is going to put you more than a pencil width out of accuracy..

So if you take the guitar you build and measure it for accuracy,it is going to be no better than those done with the simple straight line method...and the straight line method is much simpler,therefor more logical in this application.

I THINK I WASTE MY TIME HERE.IT WAS MY MISTAKE TO SHARE MY THOUGHTS WITH SUCH PEOPLE WHO THINK I OFFEND THEM....

SUCH A PITY...

PLEASE CASE CLOSED....DONT CONTINUE THE CHAT...

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I think that this is a great tool to use. Thanks, Dimitris.

Its simple trigonometry and I agree with you that the math is the most precise method of calculating the neck angle and probably the fastest. Coming from an engineering background, I'm totally into explaining things mathematically. This, in combination with a full scale drawing should be fool proof.

A lot of people are set in their ways and are resistant to change. Don't let this affect you.

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The last line of your post says

PLEASE TELL ME WHAT YOU THINK

Near as I can tell, that is what has happened.

Perhaps you should have written 'PLEASE DON'T OFFER AN OPINION IF IT IS NOT COMPLIMENTARY, I REALLY JUST WANT YOU ALL TO TELL ME HOW CLEVER I AM'.

All that really matters is the end product. Nobody really cares how you acheive it. Quite contrary to what the above poster says, I think most of us on here are completly open to change. I personally look at this site as often as possible specifically looking for better ways to do things. The flip side to that statement is that most of us have tried several methods of acheiving a specific task and have settled on the way that works best for us (until someone shows us a better way).

If you post on this site (or any other, for that matter) you are most likely going to get responses - good, bad and somewhere in between. If you specifically ask for responses, you will definitely get them; don't throw your toys out of the cot when it happens.

B

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theodoopoulos,

Your formula is theoretically fine. I'm curious about it's application. Are you using the formula to determine the neck angle of an existing guitar? Or are you using it to calculate the desired neck angle of a new guitar design?

Sincerely,

Ken

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Using Perry's diagram for the neck angle, trigonometry can be used to calculate it. When dealing with a right triangle, the tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side. In this case, the right triangle is formed from the bridge, the bottom of the fretboard where the body joins, and the guitar top under the bridge. The right angle is at the bridge, and the angle you want to find is at the fretboard. The legs of the triangle are the bridge height and the length from bridge to FB, and the hypotenuse is the length from the FB to the top of the body under the bridge. Tangent = Opposite divided by Adjacent. Therefore...

Tangent of the angle = bridge height divided by length from bridge to fretboard. Let's say your bridge is .5 inches high, and the distance from your FB to your bridge is 6 inches.

Tan (x) = .5 / 6

Tan (x) = .0833

x = arcTan .0833

x = 4.762

The angle in this example is 4.762 degrees.

Pick whichever method works best for you. Both work fine.

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Whenever i go to post a question the answer is already there for me, but his clears alot up for me thanks guys, i just can't believe i didn't think of something so simple lol. Time to make a slopped jig for the router

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I did not had intention to continue this dialog but as far as i can see some people are open minded so its my pleasure to discuss in DEMOCRACY..

@Ken Bennett

OK,the equation works to make an angle and to check it..you see its just what we see...

@ooten2

i think i transformed the triagle to trapezoid just because i think we must put there the action ,the fingerboard thickness and the wood that gets over the surface....

this diagramm i had in mind

could we confirm this type for another guitar?its seem ok to me..

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The poor guy is just trying to represent neck angle mathematically. Of course, guitarists are notorious for their inability to learn new tricks.

For myself, I might prefer to use an equation. I just don't trust my pencils. When I'm drawing a neck-length line, the pencil can start out with a perfect point, but how do I know the point isn't changing as I make the line? Also, how can I be sure I'm keeping the pencil perfectly steady against the straightedge? There are so many variables there, and it's all about muscle control!

I think adjustability in bridge height covers a lot of slop. Still, why not take the formulaic approach? It looks like fun.

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wow, if you are that worried about holding a pencil, I dread to think how much you worry about holding a router!

I dont get it, surely you guys are drawing onto the wood before you are cutting it? or at least drawing onto templates? So why all the fuss about inaccuracy when drawing a scale plan?

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it's a pitty that instead of helping us each other ,many clever people here try to put the dialog into very low level....

IF YOU HAVE NOT TO SAY SOMETHING USEFUL PLEASE DONT WRITE NONSENSE...

SPEAK WITH NUMBERS,INFOS,PICTURES AND NOT WITH IRONY.....

IS THAT ALL THAT YOU HAVE?????????????????????

Edited by theodoropoulos

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I am not being ironic. My point was that, although this formula may be correct and very helpful, at some point the dimensions that are calculated need to be transferred to the materials being cut. So the idea that maths is more accurate than a pencil line becomes irrelevant.

Personally, I like to draw things out in CAD. I know other people do things different ways and people find ways of working that suit them individually.

I do not know if your formula works, I would never use it even if it did, but that is just my opinion and my preference for the way I work. I would rather 'see' how parts fit together than figure out numbers that, theoretically, make it all work

I am not being critical of you posting ideas and calculations, it would be a sad day if people stop doing that

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i think everyone should be asked 'why?' more often. I guess that makes me like a 3 year old - or it could be because i have just been writing an assignment about the importance of using multiple perspectives in higher order thinking.

anyway - lets imagine for a second that this thread had stayed as you wanted.

1. You post the equation

2. Every one agrees, says bravo and moves on.

3. The thread becomes part of the forum and will come up on any searches about neck angle or calculating neck angle

4. The thread is used as reference and helps some understand neck angle OR the thread is used as reference and convinces some that guitar building isnt for them.

What we actually have is multiple perspectives commenting on your ideas. This means step 4 becomes

4. The thread is usefull reference and allows people to decide the best way for them to work out neck angle using the skills they have. Some will appreciate your equation, others will be glad they dont have to!

Thats what the forum is really about!

i am a paper and pencil designer, (why?) its just the way i find easiest and i have found it to be very accurate for me, and doing it this way from the start gave me a clear understanding of neck angle geometry and how to change my manufacturing techniques to get the results i want.

I always sharpen my pencils regularly, but since the difference between a sharp and blunt pencil over a line as long as the guitar would be less than my manufacturing tolerances(for everything exept fret position and neck pocket) i dont think i need to stress

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thanx for the response.I would like to double check the equation with the drawings....i would appreciate to see some plans to have a better idea

and check it better...My all concerns begunn with my project which demands to find the correct angle to have the best action.....

neck scale 24.562"

height of the bridge 16mm

fingerboard thickness 6mm

the neck meets fretboard at 17 fret(or L=25cm)

i would like to have 1-2 mm wood over fretboard(w=1) not as Les Paul with no wood

i was just looking for the angle.............

this is the target guitar

sincerely,

Dimitris

Edited by theodoropoulos

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it's a pitty that instead of helping us each other ,many clever people here try to put the dialog into very low level....

IF YOU HAVE NOT TO SAY SOMETHING USEFUL PLEASE DONT WRITE NONSENSE...

SPEAK WITH NUMBERS,INFOS,PICTURES AND NOT WITH IRONY.....

IS THAT ALL THAT YOU HAVE?????????????????????

You're the only one taking the dialog to a lower level, friend - what with these raging admonitions of yours every time someone seems to disagree....

I agree with SamC and Wez, worrying that pencil lines are not accurate enough would suggest that my manufacturing techniques were more accuarate than pencil lines. I wish.

For what it's worth, I would never use a piece of hardware that demanded my calculations and construction be more accurate than what I can draw with pencil lines - and I'm not sure such hardware even exists. For example, the TOM bridge in your reference image above will allow your neck angle to vary widely and still work just fine. We're not talking pencil line thicknesses here, were talking a couple of degrees.

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ive sketched it out quickly in CAD, but Im not 100% sure Ive got your required measurements in the right place. Plus, Ive assumed fret wire height to be 1.4mm and used a metric scale length of 623.875mm. so this is based on a 16mm high bridge (in its lowest adjusted setting, with strings touching the top of the frets)

edit: Im coming up with an angle of approx 1.865 degs.

Edited by sam_c

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