# Is there a formula to derive a square from round stock?



## Twmaster (Nov 10, 2009)

This is where my falling asleep in geometry shows..... :

I'm wondering if there is a formula to determine what the largest size square can be made inside of a circle?


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## black85vette (Nov 10, 2009)

Hmmm.  If you connect the 4 corners of a box in a circle you get 4 right triangles with each equal leg the same as the radius of the circle. So the square root of the sum of the squares of both sides will be the side of the box inside the circle. Can't remember how to notate it.  Try: Square root (R squared + R squared)= side of the box inside the circle.


Edit; changed the word square to box when it refers to the shape inside the circle. With two uses of the same word it became confusing.


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## hammers-n-nails (Nov 10, 2009)

diameter / square root of 2(1.414)= side of square


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## Engine maker (Nov 10, 2009)

Yep, sure is. Remember the song, the square of the hypotenuse of a right triangle is equal to the sum of the square of the adjacent two sides? So just do it backwards. The hypotenuse is the diameter.

Say you have a 3" round -
3" X 3" = 9
9 divided by 2 (sides) = 4.5"
The square root of 4.5" = 2.1213203"
2.1213203" is each side

This is how I lay out bolt hole patterns, Easier than a rotary table and just as accurate for me. Just X and Y on my milling table feed.

Jim


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## Twmaster (Nov 11, 2009)

That is great! Now to work the math backwards...

Thanks!


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## Maryak (Nov 12, 2009)

Hi Guys,

an easier solution is to multiply the diameter of the circle by 0.707 and this will give you the maximum sized square which will fit inside said circle.

Hope this helps

Best Regards
Bob


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## ChooChooMike (Nov 12, 2009)

HEY MARV !! 

I would have thought by now that you'd have a program ready for this calculation 

Mike


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## mklotz (Nov 12, 2009)

Way, way too trivial to merit a program.


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## Artie (Nov 12, 2009)

awww.. forget HiTech... Maryak has the answer... I just love simplicity.... and complexity..... some would say Im a walking talking oxymoron... others would just drop the 'oxy'..... :-[


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## hammers-n-nails (Nov 12, 2009)

what maryak said is the same thing exept inversing it so you multiply instead of divide


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## shred (Nov 12, 2009)

A slightly more interesting question is what sizes of flat-stock can you get out of a given diameter round-bar.
I suspect Marv's TENON program does something pretty close to that, but I've not investigated it further than reading the description.


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## mklotz (Nov 13, 2009)

TENON won't be of any help. It calculates the DOC needed to cut *regular* polygonal tenons.

Rectangular stock would still require that the diagonal of the stock correspond to the diameter of the round.

a,b = stock dimensions
D = diameter of round

a^2 + b^2 = D^2

So, once you've chosen one of the stock dimensions, a, the maximum size of the other dimension is given by:

b = sqrt(D^2 - a^2)


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