Pipe offsets and takeoffs
Pipefitting arithmetic: set, run and travel for 11¼° to 90° offsets, rolling offsets drawn as a box, parallel pipes through an offset or round a corner, cut lengths from centre-to-centre measurements less fitting takeoffs (copper, PVC/ABS DWV, threaded steel, PEX), drain slope over a run, and the volume and weight of a pipe full of water — in inches to 1/16 with millimetres.
Added
Works with
- Conduit bending US electricalthe same offset trigonometry for bending EMT and rigid conduit
- Plumbing sizing Building tradespipe sizes and minimum drain slopes to go with the cuts
- Gas pipe sizing Building tradessize the gas runs, then work out their offsets and cut lengths here
How to use it
The sums a plumber or pipefitter does on the back of a fitting box: how long the piece between two
fittings is, how far an offset runs, where each pipe in a bank starts its bend, and how much the run
falls. Type lengths the way you measure them — 8 3/16, 24-3/8, 4' 2 1/2 — and answers come back
to the nearest 1/16″ with millimetres underneath.
Typical values. The trigonometry is exact; the fitting takeoffs are typical of common patterns and vary between makers. Measure the fitting in your hand and type your own figure into the table.
How to use it
Offset — choose the fitting angle and give the set (how far the line moves over), the run (how far along it takes) or the travel (centre to centre of the two fittings); the other two follow. The table underneath lists the multipliers: travel = set × 1/sin(angle) (2.613 for 22½°, 1.414 for 45°) and run = set × 1/tan(angle). Pick a material and size and you also get the travel piece, the travel less a takeoff at each end.
Rolling — the line moves sideways (the roll) and up or down (the set) at once. The true offset is √(roll² + set²); treat that as a simple offset. The drawing shows the box method — run, roll and set as the sides of a box with the travel as its diagonal — and how far to turn the fittings off plumb. Choose Work it out from the run to find the angle a given run needs.
Parallel — several pipes through the same offset, or round a corner, kept evenly spaced. Pipe 1 is on the outside of the first bend; each pipe farther in starts its bend sooner by its distance from pipe 1 × tan(angle ÷ 2) — 0.414 × the spacing for 45°, the full spacing for 90°. Through an offset every pipe has the same travel; round a corner each pipe farther in is shorter by twice its advance.
Cut length — the measurement (centre to centre, end to centre, or end to end), the material and size, and the fitting at each end. The cut is the measurement less the takeoffs. For threaded pipe the takeoff is the fitting’s centre-to-end dimension less the thread that screws in, so the cut length includes the threads.
Takeoffs — the table behind the cut lengths, for soldered copper, PVC and ABS DWV, threaded steel with malleable iron fittings, and PEX crimp and expansion fittings. Edit any cell; your figures are kept in this browser and used everywhere in the tool.
Slope — the run (feet and inches), the slope (1/16, ⅛, ¼ or ½″ per foot, or 1 % or 2 %) and, if you like, the invert height at the high end. You get the fall, the grade in per cent and degrees, and a table of fall and invert at stations along the run. ¼″ per foot is 2.08 %; 2 % is 0.24″ per foot.
Volume — pipe, size and length give the volume (gallons and litres), the weight of the liquid and of the empty pipe, the weight full (what the hangers carry) and how long it takes to fill.
Where the numbers come from
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Offsets, rolling offsets and parallel offsets are plane and solid geometry: no rounding beyond the 1/16″ display.
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Threaded fittings: centre-to-end dimensions of 150 lb malleable iron fittings (ASME B16.3) less the usual hand-tight-plus-wrench thread engagement (½″ for ½″ pipe to ¾″ for 2″ pipe).
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Soldered copper (wrought fittings, ASME B16.22), PVC and ABS DWV (ASTM D2665 and D2661 patterns) and PEX (ASTM F1807 crimp, F1960 expansion): typical takeoffs of common fittings, rounded to 1/16″. They differ between makers, especially for DWV and PEX.
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Inside diameters: ASME B36.10 (schedule 40 steel; schedule 40 PVC shares its outside diameter and minimum wall), ASTM B88 (copper types K, L and M), ASTM F876 (PEX SDR 9). Empty weights are typical catalogue figures. Water is taken as 8.34 lb a gallon.
Limits
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Fittings are treated as points at their centres, the way the trade multipliers are. Long-radius bends, bent PEX and bent copper tube have a radius the tool does not model.
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The takeoff table holds typical values only. A few sixteenths matter on short pieces: measure.
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Minimum drain slopes by pipe size and the code’s other rules are in the plumbing sizing tool, not here.
Related: conduit bending (the same offset maths with bender marks), plumbing sizing, gas pipe sizing, pumps, tanks and hot water, angles and fractions.
Linking to an example
Lengths in links are inches and may be written as fractions (v=8%203/16); len is feet.
| Parameter | Meaning | Example |
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offset: fitting angle (11.25, 22.5, 45, 60, 72, 90), which length you know ( |
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rolling offset: roll, set and fitting angle ( |
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parallel: number of pipes, spacing, angle, |
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cut length: measurement, |
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slope: run, slope ( |
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volume: pipe ( |
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one of the presets below; other parameters override it |
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Presets:
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offset-45— 45° offset with an 8″ set -
offset-22— 22½° offset: 3½″ set to clear a flange -
rolling-45— rolling offset: 12″ roll, 16″ rise, 45° fittings -
parallel-3— three pipes 6″ apart through a 45° offset of 18″ -
corner-4— four pipes 5″ apart round a 90° corner -
cut-copper— ¾″ copper between two 90s, 24 3/8″ centre to centre -
cut-steel— 1″ threaded steel from a 90 to a tee, 36″ centre to centre -
drain-40— 40 ft of building drain at ¼″ per foot -
volume-pex— 120 ft of ¾″ PEX full of water
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