Two different jobs get mixed up on this subject constantly, and I mixed them up myself for a long time.
3-4-5 does not size an offset. 3-4-5 finds square.
Those are two separate tools doing two separate things, and most of what you will read online runs them together. So there are two calculators on this page. One works out what to cut for an offset. The other gives you a square line to measure from. Use whichever one matches what you are actually standing in front of.
Duct offset calculator
Put in the horizontal room you have and the rise or drop you need. It gives you the travel, the cut length with your lap already added, and the angle you are asking the air to turn. Everything reads in sixteenths because that is what is on your tape.
No decimals. Tape-measure ready, to the nearest 1/16″.
Every figure here is geometry. Lengths are centerline, corner to corner — your own shop allowances win over anything this box says. It does not tell you what the offset costs you in airflow, because that needs the CFM, the duct size and a published loss coefficient for the fitting, and none of those are in here.
The duct offset formula
The travel is the long side of a right triangle. So it is the square root of the run squared plus the rise squared. Run 12 and rise 5 gives you a travel of 13. That is the entire formula and it has not changed in a very long time.
The number you actually cut to is that travel plus whatever lap you need on each end. The calculator adds it for you, but it is worth knowing what it is doing so you can check it against your own tape.
Word of the day: travel. The travel is the sloped length of the offset, corner to corner. Not the run, not the rise. It is the piece you are actually cutting.
What 3-4-5 is actually for
3-4-5 is a square check. Mark three units along a line you already have. Swing four units out from the same corner. When the diagonal between those two marks measures exactly five, that corner is square. If it does not, it is not, and you move it until it is.
The numbers themselves do not matter. What matters is the ratio. 6-8-10 is the same rule. So is 1.5-2-2.5. I have used all of them depending on how much room I had, and I never once cared what the actual dimension was. It is just the rule you follow to know the line is square.
Bigger is better where you can get it, because a small triangle scaled out over a long run multiplies whatever error was in it.
The 3-4-5 rule, at whatever size fits the space.
Any multiple of 3-4-5 works and the units do not matter, as long as all three use the same one. 6-8-10 and 1.5-2-2.5 are the same rule at a different size. Bigger is more accurate over a long run, so use the biggest one the space will take. Numbers are rounded to the nearest sixteenth, so where you can, pick a size that lands on clean figures. That is why everybody remembers 3-4-5 and 6-8-10.
How I use it on a duct job
Here is the only place I reach for it. I have a gap between two runs of duct and I need to know where perpendicular actually is, so I have something honest to measure the offset from.
Eyeballing square is fine right up until it is not. On a short piece nobody will ever know. On a long run, a corner that is a little bit out turns into a piece that will not land, and you find out after it is fabricated.
So 3-4-5 gets me the square line. Then I measure the run and the rise off that line. Then the offset calculator up top tells me what to cut. Two tools, in that order, doing two different jobs.
You can do most of this on the floor with a tape and a marker
I want to be honest about something, because every other calculator page you land on is going to pretend otherwise.
Most of the time I am not doing arithmetic for this. I mark the rise, I mark the run, I hook the tape corner to corner and I read the travel straight off the tape. It is faster than typing and it is just as right.
So use the calculator when you are not standing at the metal. Working out whether a piece will even fit before anybody orders material. Checking a number somebody handed you. Figuring a cut length at a desk instead of on a lift. Those are the times the math beats the tape.
When you are on the floor with the piece in front of you, use the tape.
What the numbers do not tell you
Everything on this page is geometry. Lengths are centerline, corner to corner, and your own shop allowances win over anything a box on a website says.
The angle readout is not a pressure loss figure and I am not going to dress it up as one. A real friction number needs the CFM, the duct size and a published loss coefficient for the fitting, and none of those are in here. What the angle does tell you is how hard you are asking the air to turn compared to a standard 45, which is the honest version of the same question.
And when the space is tight enough that the offset is getting abrupt, the answer is usually not a steeper offset. It is a different route, or a different shape entirely. There is a section on double offsets and pants in hanging duct from steel joists.
The short version
- 3-4-5 finds square. It does not size an offset. Different tool, different job.
- Any multiple of 3-4-5 works. The ratio is the rule, the dimension is whatever fits.
- Travel is the square root of the run squared plus the rise squared. Add your lap to get the cut length.
- Square line first, then measure the run and rise off it, then cut.
- On the floor with the piece in front of you, the tape beats the math.
Cutting an offset needs tools. See the ones you need. And once it is cut, now assemble the duct.