# Calculating bolt circle diameter



## mklotz (Nov 13, 2007)

Recently I was involved in a discussion on another forum concerning how to determine the diameter of a bolt circle given the (chordal) distances between any three points that lie on said bolt circle.

Long ago I wrote a program to do just this calculation.  (It can be downloaded from my site - look for CIRC3).  However, this revisit to the problem led to a much simpler method that can be easily carried out on any scientific calculator.  I thought it might be worthwhile passing it along to others who might encounter this problem.

Call the three chords you've measured a,b,c.  They form a triangle and we'll label the angles opposite these sides as A, B, C respectively.  Now, the law of cosines says:

a^2 = b^2 + c^2 - 2bc*cosA

from which:

A = acos[(b^2 + c^2 - a^2)/(2bc)]

Since a, b and c are known (measured) quantities, we can plug in their values and find the angle A.

Those who didn't sleep through trig class will also remember the law of sines which says:

a/sinA = b/sinB = c/sinC

If you really, really paid attention in trig class you'll remember this common ratio is also the diameter of the circle which circumscribes the triangle.  Thus, since the circumscribed circle corresponds to our bolt circle, the diameter of the bolt circle, D, is given very simply by:

D = a/sinA


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## compound driver (Nov 14, 2007)

Ha!

Been using that for years and hadn't given it a thought. I slept most of the way in school only waking up for the metal work class.
If you have a look in the back of the Zeus book its all in there for the taking.
Mind you its nice to see it written down on here much appreciated.

Cheers Kevin


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## Bogstandard (Nov 14, 2007)

Kevin,
I have already mentioned the Zeus book to them, but it seems that they don't have this little pocket bible available over there, or it has fallen on deaf ears. Mine is over 20 years old by now and now needs replacing.
It is worn out through being used dozens of times a day.
Maybe we should buy a few and try to break into the US market.


John


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## mklotz (Nov 14, 2007)

I apologize for trying to teach you guys how to suck eggs.  Though I've often heard of the Zeus books, I've never seen one over here in the erstwhile colony.  We have various 'pocket reference' books but I've never seen one that addressed the problem of finding the circle diameter from three chords.


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## greenie (Nov 18, 2007)

Hhhmmm, this site certainly seems to ring a bell.

http://cr4.globalspec.com/thread/7377/The-little-zeus-reference-book

Now did you, or did you not, acquire one of these little wonders?
They are worth their weight in gold!!!!!

regards  greenie  :mrgreen:


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## crankshafter (Dec 21, 2007)

Try Machinist's Calculator, easy and simple 
http://www.machinist-calculator.com/


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## mklotz (Dec 21, 2007)

crankshafter  said:
			
		

> Try Machinist's Calculator, easy and simple
> http://www.machinist-calculator.com/



I see nothing there that will calculate the diameter of a circle from the length of three chords on the circle - which is the subject of this thread. Did I miss something?


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