Rectangular duct offset calculator
Enter duct width and depth, offset, run length, bend radius and pieces (0 for radius bends). You get the cheeks and the two equal wrappers of an S-shaped duct offset.
Enter your measurements
Seam
6,881.1mm
Exact geometry
- Cut length
- In the app
- Sheet size
- In the app
Every result is in Trueflat
The free web version shows the main result and the drawing. Trueflat gives you every mark and measurement, and exports a cut sheet. It is free to download.
How to lay it out
Draw the first bend on the cheek
From the first bend centre, swing the inner and outer cheek edges through the calculated bend angle (or draw the miter chords for a mitered offset).
Add the straight run
Continue both edges straight for the calculated straight run.
Draw the second bend
Draw the second bend as the first one turned through 180° about the middle of the offset, so the inner and outer edges swap sides. Close both ends square to the duct. Cut two cheeks the same.
Lay out the wrappers
Draw two strips, each as wide as the duct depth and as long as the calculated wrapper length. Both wrappers are the same length.
Form and seam
Roll or fold the wrappers to follow the cheek edges and seam them on, one on each side of the duct.
Good to know
- FabLayout runs the same code as Trueflat; the result is exact geometry.
- Source: No published source. Flat cheeks are drawn to true shape and the throat and heel wrappers are unrolled to their true arc or polyline length, in closed form on the middle of the sheet; checked against an independent reference implementation in Trueflat.
Method and formula
A duct offset shifts a rectangular duct sideways by δ over a run L, with two opposite bends and a straight piece between them. It uses the same solution as the round ogee offset. R is the centre-line bend radius.
- Bend angle α = 2 × atan t, with t = δ ÷ (L + √(L² + δ² − 4Rδ)).
- Straight run g = (L − 2R sin α) ÷ cos α.
- Largest radius R_max = (L² + δ²) ÷ (4δ), where g becomes zero.
The duct width A lies in the plane of the bends. Each cheek is a flat plate; the second bend is the first one turned 180° about the middle of the offset, so the inner and outer edges swap. That is why the two wrappers come out the same length:
- radius bends (pieces = 0): 2Rα + g;
- mitered bends (pieces 2 to 12): 4NR tan β + g, with N = pieces − 1 and β = α ÷ (2N).
The pattern is exact. Inside or outside sizes are converted to the sheet middle; the centre-line radius stays fixed.
Worked example
A = 100 mm, B = 100 mm, δ = 200 mm, L = 400 mm, R = 250 mm, 2 pieces per bend. R equals R_max, so α = 53.13°, g = 0 and tan β = 0.5. Both wrappers are 500 mm long and each cheek has an area of 100 × 500 = 50 000 mm².
The same offset with radius bends has wrappers of 2 × 250 × 0.9273 = 463.65 mm.
Questions
How is this different from the diagonal offset?
This offset moves the duct in one direction, the direction of its width, with curved or mitered bends. The diagonal offset moves it in two directions at once with three straight sections and two miters. Use the diagonal offset when the duct has to clear something both sideways and up.
Why is my bend radius rejected?
The bends must fit in the offset box: R must not exceed (L² + δ²) ÷ (4δ). The throat radius R − A ÷ 2 must also be at least 10 mm, and the bend angle must stay between 1° and 90°.
What does pieces = 0 mean?
Radius bends with rolled wrappers. Enter 2 to 12 for mitered bends, where the wrappers are folded at each miter corner.
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