Angled offset trouser piece calculator
Set the legs by their angle instead of mouth spacing, then shift both mouths by an offset. Enter main and leg diameter, height, leg angle, offset and direction to get both legs.
Enter your measurements
Seam
3,535.5mm
Approximate, within ±2.0 mm
- 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
Find the mouth spacing
Work out the mouth spacing c = 2H tan θ and place the two mouths at ±c ÷ 2 in plan.
Apply the offset
Shift both mouths by the offset e in direction ψ.
Divide and draw generators
For each leg, divide its seat on the main pipe, its crotch arc and its mouth at matching angles and join them with generators.
Mark crotch points and true lengths
Mark where each crotch-side generator meets the crotch plane, then find the true lengths of the generators and diagonals.
Triangulate both legs
Lay out each leg from its outer seam line. With an offset the legs lean by different amounts, so mark each pattern for its side.
Good to know
- This pattern is approximate; the result card shows how close it is.
- Source: Derived from first principles: each leg is the oblique cone between the main-pipe circle and the leg mouth, the crotch lies in a plane, so every facet is flat and the leg is laid out by triangulation on the middle of the sheet. Checked against an independent reference implementation in Trueflat.
Method and formula
This version takes the leg angle θ instead of the mouth spacing. θ is the lean of each leg from the main pipe axis before any offset. The spacing follows from it:
- c = 2H tan θ.
The two mouths, both of diameter d, are then shifted together by e in plan direction ψ, as on the offset trouser piece. Once the offset is applied, the two legs no longer lean by the same angle. One leans more and one less; the calculation works out the true angle of each. Use this page when the drawing gives a branch angle and an offset rather than the outlet positions.
Each leg is a slanting cone from the main pipe circle to its mouth. The two cones meet on a plane, so the facets are flat and each leg is triangulated without twist. The only error is drawing the curves with chords: the mouth is short by at most r(w³ + (π − w)³) ÷ (12n²).
Limits: θ from 5° to 60°; e ≤ (Dg − d) ÷ 2; neither true leg axis above 60°; mouths at least 5 mm clear of the crotch plane. Inside or outside sizes are converted approximately and rejected above 1 mm of mouth deviation.
Worked example
Dg = 500 mm, d = 200 mm, H = 450 mm, θ = 25°, e = 60 mm, ψ = 30°, n = 6. The spacing is c = 419.68 mm. After the offset, one leg leans 19.65° and the other 30.35°, with areas of 366 160.33 and 373 731.34 mm². The middle crotch point sits 312.64 mm up, the shortest generator is 166.67 mm and the chord error bound is 1.79 mm.
Questions
Why do the two legs lean differently?
The leg angle sets the mouth positions before the offset. Shifting both mouths sideways tilts one leg further out and brings the other back, so their true angles differ: 19.65° and 30.35° in the example.
How is this different from the offset trouser piece?
The geometry is the same; only the input differs. The offset trouser piece takes the mouth spacing c directly. This page takes the leg angle and works out c = 2H tan θ.
Is the pattern exact?
The layout is exact up to the chords that draw the curves. In the example at n = 6 the leg mouth comes out at most 1.79 mm short of its true length. Raise the curve samples if you need it closer.
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