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# 1.414 Math, 45 degree offsets, a quick tutorial

Member Posts: 4,676
It occurred to me that lots of trades guys don't use this simple formula, I hope this sheds some light!

Gary Wilson
Wilson Services, Inc
Northampton, MA
[email protected]

• Member Posts: 21,844
I like his insertion math. I was taught to measure center to center and subtract to the bottom of the socket. This seems easier and more accurate.

On one of my plumbing licenses test you had to calculate two parallel offsets, then build with 1" copper and solder them.
They cut the solder joints apart to check for soldering skill also.
Bob "hot rod" Rohr
trainer for Caleffi NA
Living the hydronic dream
• Member Posts: 15,307
I have used 1.414 for years and it is absolutely accurate if measurements are accurate.

Most of my co workers wouldn't use it they just hold a fitting up there and guess

That is fine but if your using it for large size pipe 3," and larger steel pipe it becomes impossible to hold those heavy fittings in place to get a measurement. You have to use it by calculation.

I also have a method of measuring for using it with a rolling offset that is simple and works great

I can remember doing a rolling off set in a hallway with 3" threaded gas line. There was literally no play to move the pipes it worked great.

See attached

• Member Posts: 9,410
2^.5
• Member Posts: 6,506
I use the calculator I made, but also, I can't believe how much easier using a laser makes it.
steve
• Member Posts: 11,021
I do the trial and err method somewhat.
For me, most offsets are PVC piping. I dry fit the 45's and fit 2 short scraps between the fittings.

I only use the pressure type longer couplings and can telescope short pieces to get the 45's twisted to the correct angle. Then measure the temp length to get the correct cut and install the single new piece.

Use the same method to get one of the horizontal pipes to the correct length.

I save scraps that are 3" or longer, they eventually get used up for something.
• Member Posts: 4,676
JUGHNE dry fitting, totally cool, yet the guys that are doing this day in and day out, do not dry fit. (too much time)

Gary Wilson
Wilson Services, Inc
Northampton, MA
[email protected]
• Member Posts: 4,676
Ed I looked at that file last night, but now my phone cannot open it. Either my eyes are bugging on me: A squared plus B squared equals C squared”, ——you’re not supposed to add in 1.414 also. Did I read that correctly? That wouldn’t work very well
Gary Wilson
Wilson Services, Inc
Northampton, MA
[email protected]
• Member Posts: 983
edited December 2023
UGH! Your high school geometry teachers are rolling in their graves.
Yes, the 2 shorter sides of a triangle ( A and B ) squared does equal the longest side (C) squared.
And 1.414 has always been the square root of 2.
• Member Posts: 7,542
edited December 2023
MikeAmann said:

UGH! Your high school geometry teachers are rolling in their graves.
Yes, the 2 shorter sides of a triangle ( A and B ) squared does equal the longest side (C) squared.
And 1.414 has always been the square root of 2.

High school teachers rarely teach practical ways that math can be applied. This is one of the reasons we have such gaps in knowledge with people entering the trades. There is a huge need for the class "quick and dirty construction math" It just boils down to teaching in the real world rather than a textbook.

Ask any framing carpenter what angle they use for hip/valley rafters and they will tell you to just use the same rise on the framing square but use 17 instead of 12 for the run. <1% will tell you that the rise stays the same but the run should be 12x1.414=16.968, because the run is now the diagonal of a 12x12 square.

Great video, keep them coming! Maybe the class should be online with this group each teaching a section
"If you can't explain it simply, you don't understand it well enough"
Albert Einstein
• Member Posts: 6,506
Zman said:

Ask any framing carpenter what angle they use for hip/valley rafters and they will tell you to just use the same rise on the framing square but use 17 instead of 12 for the run. <1% will tell you that the rise stays the same but the run should be 12x1.414=16.968, because the run is now the diagonal of a 12x12 square… </p>

I remember wayyyy back being a carpenter and learning how to cut rafters. After learning the math and using/learning what all those marks mean on a framing square, I purchased a Construction Master calculator that was featured in Fine Homebuilding. I still have one over 30 years old.

steve
• Member Posts: 4,676
Who is it that you address? No math teacher can run pipe in a semi professional way (anyone can pipe an easy route), and make it look good
Gary Wilson
Wilson Services, Inc
Northampton, MA
[email protected]
• Member Posts: 15,307
@GW
I went back and looked and I am pretty sure the math is correct. I was trying to show 2 ways to get the answer and probably overcomplicated things. I tend to do that a lot my brain runs faster (or slower) than I type or draw.

One way is to think of the offset as a 45 degree triangle. A squared + B squared =C squared. C squared is what you need that is the length of the 45 degree pipe. Once you get C squared you x 1.414 and then make the fitting deductions as usual.

The other thing I was trying to show is how to figure out a rolling offset. If you can get a C-C measurement then you just treat it like any other 45 degree offset.

What I used to do when I couldn't get a C-C dimension easily is if you can picture two pipes heading for each other that need to be connected by a rolling offset is

1.get the center line measure for each from the floor or ceiling and subtract the two measurements to get the height difference. Then measure from a wall and get the two center line dimensions and subtract them as well to get the horizontal difference.

Now you have a height difference and a horizontal difference. See the new drawing attached
• Member Posts: 4,676
edited December 2023
Ed yes but if it’s a simple 45 then you just need the simple 1.414. You can’t do both. That’s a classic double entendre😀.

If you do the ABC method, that’s cool too.

Unless you’re doing some wizard math above my pay grade

If it’s not 45 then yes I see your math coming in handy. It’s ideal for multiple-way offsets on a sheet metal plenum

I guess we end up with the same result with different math. I like to stack the fittings together and do a C-C “offset”.
Gary Wilson
Wilson Services, Inc
Northampton, MA
[email protected]
• Member Posts: 4,676
Ed my rather costly iPhone won’t open the file. Can you screen shoot it?
Gary Wilson
Wilson Services, Inc
Northampton, MA
[email protected]
• Member Posts: 983
GW said:
Who is it that you address? No math teacher can run pipe in a semi professional way (anyone can pipe an easy route), and make it look good

Not directed at anyone.
• Member Posts: 15,307
@GW will try. It's just a PDF

My point is and was that if your installing steel pipe probably anything bigger than 2" and certainly in larger sizes like 3, 4, 6 etc it's impossible to hold the fitting in position to get a measurement. Has to be done by calculation.

Like the 8" insulated rolling offset I showed in my 3d picture down above. That is not a flat offset. From the pictures I don't see why I had to roll that down but I had to for some reason.
• Member Posts: 4,676
Ed yes I know see your point! I have always been able to know my centers, but good to know this math as well

Gary Wilson
Wilson Services, Inc
Northampton, MA
[email protected]
• Member Posts: 4,676
Im getting 19”

do you still need to draw it out?

Sq root of 181 is 13.45, x 1.414 is 19

Gary Wilson
Wilson Services, Inc
Northampton, MA
[email protected]
• Member Posts: 15,307
@GW
Answer looks right. So you can get the same answer 2 ways. The triangle method like you did A sq +Bsq=Csq etc.

Or draw it by marking the two pipe centers on the floor or on cardboard etc then draw the line between the two centers. Then measure the line you drew with a ruler take that measure ment and x1.414.

This is how I usually did it on the job just draw it out and measure the line and do the 1.414. Faster than the triangle measurements.

My drawing is not to any scale so you can't actually measure it it's just for show
• Member Posts: 4,676
Ed OK yes, I hung some cast-iron up in the air way back in the 80s, at my Boulangers Plumbing days. I recall dropping a Plumb Bob here and there to lay things out on the ground. I think it was just dinky 3 inch and 4 inch. I don’t recall anything bigger. I miss snapping the cast-iron, something primal about that snapping sound💯

Gary Wilson
Wilson Services, Inc
Northampton, MA
[email protected]
• Member Posts: 3,605
I don't understand all this 45° stuff. 1.4, 1.1, I mean just make your bends 30°, the math soooo much easier.
• Member Posts: 4,676
edited December 2023

@ratio do you speak in jest? If you run pipe for a living, you can be fast and well-fed, or slow and eating at McDonalds.

All kidding aside, the amount of time it takes to do the math and do it properly is a fraction of the time it takes to throw pipe up in the air and hope it looks good.💯

edit----darn voice to text is terrible on this phone

Gary Wilson
Wilson Services, Inc
Northampton, MA
[email protected]
• Member Posts: 3,605
Quite in jest, sir. My background is electrical. 1.1 is approximately the multiplier for a 60° offset, & the multiplier for a 30° offset is 2. But we use a bender to adjust the pipe, not so often fittings.
• Member Posts: 15,307
I didn't know you worked for Boulangers. Funny I used to run into some of their jobs occasionally. It was strange 1 job would be a perfect install and one would be a disaster. I assume the perfect installs were yours LOL!

I do remember a Christmas weekend call at the Holyoke post office this was about 28ish years ago. On a Saturday. They had renovated the boiler room. They had a huge storage tank for DHW and one of the unused tapings someone had put a black plug in it. Unlucky for me it let go on Christmas weekend. And it was a really cold weekend. The gas burner was down in a pit and the pit was full of water. The power to the burner was still on and the lights in the burner panel were lit even with the burner completely submerged!

We shut the power down and pumped the water out took the gas train apart and dumped the water out of it. Dried stuff off. I couldn't get parts or controls and was not going to trust the burner programmer.

So I disconnected everything electrically and hot-wired the burner motor and it ran then I hot-wired the pilot valve and ignition transformer and that worked so I hot-wired the gas valves and got main flame. Low -high fire wouldn't work as the mod motor was bad so I ran it on low fire and made steam and sat there for 4-5 hours till the building was warm. Then I shut it down and chopped all the wires so they couldn't restart it. Its a big brick building so once it was hot it was ok through Sunday. Monday morning I was back there with a truck full of parts.

It wasn't much fun and I pretty much missed Christmas but I made some good cash!
• Member Posts: 4,676
edited December 2023
Ed way to save the day 🎁

I worked at Boulangers, 1984 to early 1989. They had me running job at 19 years old. I wasn’t even licensed, yet. At the risk of sounded brash, I was pretty good for a young kid.
>>> Edit, I got my license at 19 years old, the exact dates are too foggy at this moment,
Gary Wilson
Wilson Services, Inc
Northampton, MA
[email protected]