# 3-4-5 squaring method



## DanTheMan6937 (Jan 19, 2012)

what is 3-4-5 squaring method


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## rselectric1 (Sep 20, 2009)

Do a google search for the Pythagorean theorem. It's the same thing. It makes perfect right angles.


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## JustaFramer (Jan 21, 2005)

Pythagorean theorem a2+b2=c2


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## Ninjaframer (May 28, 2011)

Pathagorean therum- a squared plus b squared is equal to the square root of the sum
3x3=9
4x4=16
9+16=25
Square root of 25 is 5


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## skcolo (May 16, 2009)

Imagine a triangle. At the corner, measure 3 ft in one direction, then 4 feet from the corner at the 90 degree direction, then the two furthest points should be exactly 5 ft apart, which would mean the corner is square.


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## TimberlineMD (Jan 15, 2008)

Quoting from 'Swansons Little Blue Book"...

"To lay out a 90 degree corner, measure out 3' on one side and 4' on the other and adjust until the diagonal is exactly 5', or use 6', 8', then 10' will be the diagonal."


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## jb4211 (Jul 13, 2010)




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## Ninjaframer (May 28, 2011)

It doesn't have to be 3,4,5
It can be 12,12,16.97
The formula is usually expressed 3,4,5 becouse there whole numbers.


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## Warren (Feb 19, 2005)

6-8-10 is my personal fav!


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## WNYcarpenter (Mar 2, 2007)

I'll bite...

Crudely....with a right triangle you have have a 90* corner with two legs, and a hypotenuse that connects those legs. Leg A=3', leg B=4' and the hypotenuse(C=5').

If you're framing a form with an inside corner you would measure 3' on one side and 4' one the other. Pull your measurements from the exact same point at the inside corner. If your corner is square, when you measure between the two points you just marked the measurement is 5'. Always use the same edge or your tape when measuring. 

If your form is out of square you adjust the squareness until the hypotenuse=5'......

That's the basic principal.

Edit: what they said...thought I might be the only one to answer this one:laughing:


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## Gus Dering (Oct 14, 2008)

Understanding the mathematical concept is one thing. Being able to apply it in the real world takes time.

Try to make the triangle as big as you can. To do that you just need to multiply the two legs by a common number. If you use 3 as your number then you have a 9 - 12 - 15 triangle.

If you have a construction calculator you can use the same principle with any length sides. Just by entering your two legs as rise and run. Then hit the diagonal button. This way you can check large forms from corner to corner, as an example.


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## Hmbldr (Dec 7, 2011)

Ninjaframer said:


> It doesn't have to be 3,4,5
> It can be 12,12,16.97
> The formula is usually expressed 3,4,5 becouse there whole numbers.


But the point is... the 345 squaring method is easy because it requires no calculation. Also easy because it is expandable, 6-8-10, 9-12-15, etc. If you're going to bother doing calculations, then you would go to the exact dimensions of your box and figure exact diagonals.


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## JustaFramer (Jan 21, 2005)

Lets work with offsets and batter boards. Call in the total station. :laughing:


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## Ninjaframer (May 28, 2011)

Hmbldr said:


> But the point is... the 345 squaring method is easy because it requires no calculation. Also easy because it is expandable, 6-8-10, 9-12-15, etc. If you're going to bother doing calculations, then you would go to the exact dimensions of your box and figure exact diagonals.


12,12,16.97 is significant to framers. You can also look at the brace table on a framing square, It gives diagonals to many rise/runs.


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## Hmbldr (Dec 7, 2011)

Ninja, I agree and understand. :thumbsup: Just relating back to the OP original question.


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## Ninjaframer (May 28, 2011)

Hmbldr said:


> Ninja, I agree and understand. :thumbsup: Just relating back to the OP original question.


For sure


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## skcolo (May 16, 2009)

Actually, the real answer to the 345 method is when a framer has three beers, checks out four girls, then steps back five feet and eyeballs the chalk lines and says, "good enough".


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## WNYcarpenter (Mar 2, 2007)

O.P......This method is only as accurate as the material you're using is straight. A bow in lumber will throw everything off.


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## Ninjaframer (May 28, 2011)

The op hasn't had any questions so we must have answered pretty well.


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## cleveman (Dec 28, 2007)

I was at church the other day, and there was a new pastor they were introducing. He was also a mathematics teacher and had traveled a lot.

I have heard and read a bit about the Pythagoreans. I think there may be some reference to them in the bible as well. Anyway, some think the theorum is based on the teachings of one man. I figured the Pythagoreans were a group of people from a region, like Pythagorea. See Sparta-Spartans, Athens-Athenians, etc.

So I asked the guy what he knew about it, if it was one man, a region, etc. and he said it was a region and specifically probably one person, but they had built a whole religion around the use of the numbers.

I'm not sure there wouldn't be some connection to the free masons. Once you master this knowledge, it would be very powerful. Just think of the respect given to someone today who can master all the information on a framing square.


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## Willie T (Jan 29, 2009)

How come 3,6,9 keeps sticking in my head?






................. Oh yeah... "3,6,9, the goose drank wine, the monkey chewed tobacco on the street car line."

.......... "da line broke, the monkey got choked, an' dey all went to Heaven in a lil' row boat."

Guess it doesn't work out for this stuff.....


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## Paulie (Feb 11, 2009)

Willie T said:


> *How come 3,6,9 keeps sticking in my head?*
> 
> 
> 
> ...


You've gone kookoo?


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## Ninjaframer (May 28, 2011)

cleveman said:


> I was at church the other day, and there was a new pastor they were introducing. He was also a mathematics teacher and had traveled a lot.
> 
> I have heard and read a bit about the Pythagoreans. I think there may be some reference to them in the bible as well. Anyway, some think the theorum is based on the teachings of one man. I figured the Pythagoreans were a group of people from a region, like Pythagorea. See Sparta-Spartans, Athens-Athenians, etc.
> 
> ...


The framing square is a piece of cake, now the Chappell square- that's got some info on it!


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## knucklehead (Mar 2, 2009)

Which one would be the hypotenuse ?


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## Hmbldr (Dec 7, 2011)

knucklehead said:


> Which one would be the hypotenuse ?


The long side of a right triangle is the hypotenuse. The shorter sides commonly referred to as the legs.


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## JustaFramer (Jan 21, 2005)




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## Ninjaframer (May 28, 2011)

Lol!


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## JustaFramer (Jan 21, 2005)

You mean it isn't plural for hippopotamus?


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## loneframer (Feb 13, 2009)

Willie T said:


> How come 3,6,9 keeps sticking in my head?
> 
> 
> 
> ...


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## CO762 (Feb 22, 2010)

cleveman said:


> Once you master this knowledge, it would be very powerful. Just think of the respect given to someone today who can master all the information on a framing square.


I'm still working on perfectly square cuts on larger stock using a japan saw. It really is a zen thing. However, zen don't pay!


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## Willie T (Jan 29, 2009)

3, 6, 9! See, Paulie? You're just too young.
I think it's growing up doing songs that kept you thinking that makes us wonder what has happened to that ability in so much of the younger generation.

Here's another one of hers.




 
And can you imagine many kids today even being able to follow The Hand Jive?


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## SC sawdaddy (Oct 15, 2008)

Willie T said:


> How come 3,6,9 keeps sticking in my head?
> 
> 
> 
> ...


You crack me up Willy.:laughing:


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## kyia (Jul 4, 2011)

skcolo said:


> actually, the real answer to the 345 method is when a framer has three beers, checks out four girls, then steps back five feet and eyeballs the chalk lines and says, "good enough".


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## Seven-Delta-FortyOne (Mar 5, 2011)

cleveman said:


> So I asked the guy what he knew about it, if it was one man, a region, etc. and he said it was a region and specifically probably one person, but they had built a whole religion around the use of the numbers.
> 
> I'm not sure there wouldn't be some connection to the free masons. Once you master this knowledge, it would be very powerful. Just think of the respect given to someone today who can master all the information on a framing square.


Yeah, his name was Pythagoras. He was a mathmatician and philosopher. And no, not related to the free masons. They wouldn't come along for about another 2,100 years.


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## detroit687 (Sep 4, 2008)

WNYcarpenter said:


> O.P......This method is only as accurate as the material you're using is straight. A bow in lumber will throw everything off.


It's a good thing somebody invented a chalk box.
When laying out walls 6 8 10 is usually used but I have found that when I'm working by myself I would rather snap a line and pull equal meaurements from my point of origin in opposite directions and then draw intersecting archs and snap through. It just seems easier when working by your self. And on sites where there's allot of crap in the way such as gang boxes the pls5 works great


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## AustinDB (Sep 11, 2006)

also known as Pythagorean triple's, the 3/4/5 is joined by the 5/12/13 and a few other combinations whose numbers are whole. The 3/4/5 is great when laying out a pole barn to create perpendicular walls (as in 12/16/20).


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## SC sawdaddy (Oct 15, 2008)

72chevy4x4 said:


> also known as Pythagorean triple's, the 3/4/5 is joined by the 5/12/13 and a few other combinations whose numbers are whole. The 3/4/5 is great when laying out a pole barn to create perpendicular walls (as in 12/16/20).


I know its the Pythagrorean therom but I learned it as the 6 8 10 way to square up two perpendicular lines. Also that there are different combinations of numbers that will work but always dirived from 6 8 10.

The combination I would use would depend on the size of the floor or wall I was trying to square.

6 8 10 
(x2)= 12 16 20
(x1/2) =3 4 5
(x 6) =36 48 60

I havent done the math to check but 5 12 13 doesnt sound right.


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## Ninjaframer (May 28, 2011)

SC sawdaddy said:


> I know its the Pythagrorean therom but I learned it as the 6 8 10 way to square up two perpendicular lines. Also that there are different combinations of numbers that will work but always dirived from 6 8 10.
> 
> The combination I would use would depend on the size of the floor or wall I was trying to square.
> 
> ...


It's absolutely right
5 x 5 =25
12x12=144
25+144=169
Square root of 169=13


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## NYCB (Sep 20, 2010)

Just remember after you 3-4-5 to double check your diagonals. If your two diagonals aren't the same measurement, you aren't square.


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## Willie T (Jan 29, 2009)

sitdwnandhngon said:


> Just remember after you 3-4-5 to double check your diagonals. If your two diagonals aren't the same measurement, you aren't square.


VERY IMPORTANT because the 3-4-5 method lends itself too easily to being somewhat inaccurate at longer distances.


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## Gus Dering (Oct 14, 2008)

I figured you two whiz bangers could find a way.

Lets see if some of the youngsters can come up with a decent way. 

The math is one thing. We are working in a ditch.


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## Ninjaframer (May 28, 2011)

I will respectfully bow out then  if you want to delete the pics I posted go ahead


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## loneframer (Feb 13, 2009)

Ninjaframer said:


> I will respectfully bow out then  if you want to delete the pics I posted go ahead


I used the exact same method. I'm out too.:thumbsup:


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## Willie T (Jan 29, 2009)

Go ahead and erase mine too if you want to.


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## loneframer (Feb 13, 2009)

Gus Dering said:


> I figured you two whiz bangers could find a way.
> 
> Lets see if some of the youngsters can come up with a decent way.
> 
> The math is one thing. We are working in a ditch.


Pretty sure todays youth would just use the global positioning app on their I-phone to locate the points.:thumbup:


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## Ninjaframer (May 28, 2011)

I used the cm pro with trig app on my iphone


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## loneframer (Feb 13, 2009)

Ninjaframer said:


> I used the cm pro with trig app on my iphone


I used the old school method....

TI30XA scientific calculator:laughing:


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## Ninjaframer (May 28, 2011)

One last thing- Gus your problem is solve able with geometry, I have been on commercial jobs where hours were lost becouse there was not enough information on the plan to lay out a footing (hospital) without using trig formula. Eventually one of the superintendents came down out of the office looked at the problem went back and 20 minutes later had the hypotenuse for a triangulation we could use to find this critical location. If I knew then what I know now I could have done the same thing on the spot in under 3 minutes.

I'm not tooting my own horn, I'm saying it's worth the time to learn the math skills behind our trade.


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## AustinDB (Sep 11, 2006)

I would use Willie T's method as well...nice and easy w/o a trig calculator. 

sometimes knowing the 30/60/90 triangle and associated side lengths is useful in layout work. 

http://upload.wikimedia.org/wikipedia/commons/1/15/Triangle_30-60-90_rotated.png


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