FitUpGuide · Offsets
The 1.414 rule: how to calculate a 45 degree offset
The 1.414 rule: multiply a 45 degree offset by 1.414 to get the travel, center to center. The run equals the offset. Then subtract the take-out of each 45 and the root gap at each butt weld to get the cut. A 10 inch offset has a 14.142 inch travel; on 2 inch pipe with 45 LR elbows and 1/8 inch gaps, the cut is 11 1/8.
Travel = offset × 1.414
Run = offset
Cut = travel − 2 × take-out − 2 × gap
Why the multiplier is 1.414
With 45 degree fittings the offset and the run are the same length, so the offset triangle is half of a square, and the travel is that square's diagonal. The diagonal of a square is its side times the square root of 2, which is 1.41421. That is the whole reason behind the number on every fitter's cheat sheet. It is also 1 ÷ sin 45°, the same travel formula used at every other angle.
You can check it with the Pythagorean theorem. Offset² + run² = travel². With the run equal to the offset, that is 2 × offset², so the travel is the offset × √2. That is also why 1.414 × 1.414 comes out at 1.9994, which is 2 rounded: the multiplier squared is the 2 in that equation.
How to use the 1.414 formula
Measure the offset center to center
Square to the two runs, centerline to centerline, or the same side of both pipes if they are the same size.
Multiply by 1.414 for the travel
Use at least 1.414. 1.41 is close enough for a short offset and not for a long one (see the table below).
The run is the offset
At 45 degrees the second fitting sits one offset further down the line.
Subtract two take-outs
The center-to-end of your 45s: 1 3/8 inch for a 2 inch 45 LR butt-weld elbow, for example. Check your maker's chart or the take-out chart.
Subtract two gaps, then round once
For butt welds, two root gaps. Turn the final decimal into the nearest 1/16 only at the end.
1.414 chart: travel for common 45 degree offsets
Read the travel straight off for the offset you measured. These are center-to-center lengths; take off your fittings and gaps afterwards.
| Offset | Travel, decimal | Travel, mark |
|---|---|---|
| 2" | 2.828 | 2 13/16" |
| 3" | 4.243 | 4 1/4" |
| 4" | 5.657 | 5 11/16" |
| 5" | 7.071 | 7 1/16" |
| 6" | 8.485 | 8 1/2" |
| 8" | 11.314 | 11 5/16" |
| 10" | 14.142 | 14 1/8" |
| 12" | 16.971 | 17" |
| 15" | 21.213 | 21 3/16" |
| 16" | 22.627 | 22 5/8" |
| 18" | 25.456 | 25 7/16" |
| 20" | 28.284 | 28 5/16" |
| 24" | 33.941 | 33 15/16" |
| 30" | 42.426 | 42 7/16" |
| 36" | 50.912 | 50 15/16" |
| 48" | 67.882 | 67 7/8" |
Worked examples on 2, 4, and 6 inch pipe
| Pipe | Offset | Travel | Take-outs | Gaps | Cut |
|---|---|---|---|---|---|
| 2 in | 10" | 14.142 | 2 × 1 3/8 | 2 × 1/8 | 11 1/8" |
| 4 in | 18 3/8" | 25.986 | 2 × 2 1/2 | 2 × 1/8 | 20 3/4" |
| 6 in | 12" | 16.971 | 2 × 3 3/4 | 2 × 1/8 | 9 1/4" |
Line by line, the 4 inch example: 18.375 × 1.41421 = 25.986. Take off 2 × 2.5 = 5 for the elbows and 2 × 0.125 = 0.25 for the gaps, leaving 20.736, which marks as 20 3/4.
The 1.414 rule in plumbing
In drain, waste, and vent work a 45 is called a 1/8 bend, because it turns one eighth of a circle. The 1.414 rule is the same; what changes is the allowance. Soldered, glued, and threaded joints have no root gap, and the pipe slides into the fitting, so the allowance per fitting is the distance from the fitting's center to the bottom of the socket (or to where the thread stops), not to its outer end.
Say your 45s measure 1 inch from center to the socket shoulder. Measure yours; it varies by size, material, and maker. For a 16 inch offset: 16 × 1.414 = 22.627 center to center, less 2 × 1 = 20.627, marked 20 5/8. Without fittings the 10 inch offset is simply 14 1/8 center to center. How to figure allowances for each joint type is in take-outs and cut length.
Using the 1.414 rule backwards
When you know the travel and need the offset, divide by 1.414, or multiply by 0.7071 (sin 45°, the same thing). A 20 inch travel, center to center between two 45s, makes an offset of 14.142 inches, marked 14 1/8. If you are starting from a piece of pipe already cut, add both take-outs and both gaps back first to get the travel.
What rounding 1.414 costs you
The multiplier error grows with the offset. On a short offset 1.41 is within a sixteenth. On a long one it is not:
| Offset | × 1.41421 | Mark | × 1.41 | Mark | Short by |
|---|---|---|---|---|---|
| 12" | 16.971 | 17" | 16.920 | 16 15/16" | 1/16" |
| 24" | 33.941 | 33 15/16" | 33.840 | 33 13/16" | 3/32" |
| 48" | 67.882 | 67 7/8" | 67.680 | 67 11/16" | 3/16" |
| 96" | 135.765 | 135 3/4" | 135.360 | 135 3/8" | 13/32" |
With 1.414 the 96 inch travel is about 0.02 inch short, well under a sixteenth. Better still, let a calculator carry the full value and round only the cut.
The shortest 45 offset two elbows can make
Two elbows and two gaps need room before any pipe fits between them. The smallest 45 degree offset is (2 × take-out + 2 × gap + the shortest piece you will accept) × 0.7071. With 45 LR elbows, 1/8 inch gaps, and at least 1/16 inch of pipe:
| Pipe size | 45 LR take-out | Shortest offset |
|---|---|---|
| 1/2 in | 5/8" | 1 1/8" |
| 3/4 in | 7/16" | 7/8" |
| 1 in | 7/8" | 1 1/2" |
| 1 1/4 in | 1" | 1 11/16" |
| 1 1/2 in | 1 1/8" | 1 13/16" |
| 2 in | 1 3/8" | 2 3/16" |
| 2 1/2 in | 1 3/4" | 2 3/4" |
| 3 in | 2" | 3 1/16" |
| 3 1/2 in | 2 1/4" | 3 7/16" |
| 4 in | 2 1/2" | 3 13/16" |
| 5 in | 3 1/8" | 4 11/16" |
| 6 in | 3 3/4" | 5 9/16" |
| 8 in | 5" | 7 5/16" |
| 10 in | 6 1/4" | 9 1/16" |
| 12 in | 7 1/2" | 10 7/8" |
Anything tighter needs a different fitting, a steeper 60 degree offset, or the fittings welded to each other.
Common mistakes
- Measuring on the slant. The offset is measured square to the runs, not along the angled piece.
- Cutting the travel. 14 1/8 is center to center. On 2 inch 45 LRs with gaps, the pipe is 3 inches shorter.
- Taking off one take-out. There is a fitting at each end of the travel piece, so there are two.
- Using 1.414 with other fittings. It belongs to 45s. 22.5s use 2.613 and 60s use 1.155; see the multiplier chart.
- Mixing pipe sizes. If the two fittings differ, subtract each one's own take-out instead of doubling one.
- Using 1.41 on a long offset. See the table above.
Questions about the 1.414 rule
What is the 1.414 rule in plumbing and pipefitting?
It is the shortcut for an offset made with two 45 degree fittings: multiply the offset by 1.414 to get the travel, the center-to-center length of the angled piece. The run, how far the offset moves along the line, equals the offset. In plumbing the 45 is called a 1/8 bend; the arithmetic is the same for drain, water, gas, and welded pipe.
Why is the 45 degree offset multiplier 1.414?
Because 1.414 is the square root of 2. With 45s the offset and the run are equal, so the triangle is half a square and the travel is the square's diagonal, which is always the side times the square root of 2 (1.41421). It is also 1 ÷ sin 45°, the same travel formula used at every angle.
What is 1.414 x 1.414?
1.999396, which is 2 for any practical purpose. 1.414 is the square root of 2 rounded to three places, so it squares back to almost exactly 2. That is the Pythagorean check: offset² + run² = travel², and with the run equal to the offset that is 2 × offset², so the travel is the offset × √2.
How do you use the 1.414 formula, step by step?
Measure the offset center to center, square to the runs. Multiply it by 1.414 for the travel. Mark the second fitting one offset further along the line, because the run equals the offset. Subtract the take-out of both 45s and, for butt welds, both root gaps. Round the result to the nearest 1/16 once, at the end.
Is the travel the length of pipe to cut?
No. The travel runs from the center of one fitting to the center of the other. The pipe stops at each fitting's end, so the cut is the travel minus two take-outs, and minus two gaps at butt welds. On 2 inch pipe with 45 LR butt-weld elbows and 1/8 inch gaps that is 3 inches shorter than the travel.
How do I find the offset if I know the travel?
Divide the travel by 1.414, or multiply it by 0.7071, which is the same thing (sin 45°). A 20 inch travel between two 45s, center to center, makes an offset of 14.142 inches, marked 14 1/8.
Does 1.414 work for 22.5, 30, or 60 degree fittings?
No. 1.414 belongs to 45s only. The travel multiplier is 2.613 for 22.5 degrees, 2.000 for 30, 1.155 for 60, and 5.126 for 11.25. See the offset multiplier chart and the 60 degree offset formula.
Is 1.41 close enough?
On a short offset, yes: on a 12 inch offset 1.41 comes up 0.05 inch short, under a sixteenth. On a 48 inch offset it is 0.20 inch short, more than 3/16. Use 1.414 or more and round only the final cut.
Does the 1.414 rule work for a rolling offset?
Yes, once you have the true offset. Find it as the square root of rise² + roll², then multiply that by 1.414 for the travel; the run equals the true offset. The rolling offset formula guide works an example.
Related guides
- The pipe offset formula for any angle
- 60 degree offset formula: 1.155 and 0.577
- How to do a 45 degree rolling offset
- The take-out of a 45 long radius elbow, by pipe size
Check one now
Type your offset into the pipe offset calculator with 45 selected and it shows each of these lines. In the FitUp app, 45 degree simple offsets are free with no limit, with the diagram and the formula on screen.
Verify measurements before cutting.