FabLayout

Angled square to round calculator

For a square to round whose round end is not parallel to the base, tilted up to 45°: enter the rectangle, diameter, height to the centre of the round end, tilt and optional offsets.

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Enter your measurements

Your dimensions are measured to the

Export from the Trueflat app

1:1 PDF and DXF files of this flat pattern are made in Trueflat, ready for print, plasma, laser or waterjet. It works offline on site.

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1,160.0 mm698.3 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

469.9mm

Approximate, within ±3.1 mm

Cut length
In the app
Top edge (chords)
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.

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How to lay it out

  1. Draw the tilted end

    Draw the side view with the round end tilted by its angle about its centre at height H, and project the circle into plan.

  2. Find the tangent points

    On the A sides they are the lowest and highest points of the circle; on the B sides they move off the middle, so find them where the side and the circle's tangent lie in one plane.

  3. Take the true lengths

    For each point on the circle, combine its plan distance from the corner with its own height, which now changes around the circle.

  4. Lay out from the seam

    Start with the seam on the low side, then add corner fans and flat triangles in turn, each triangle from three true lengths.

  5. Close and finish

    End with the second seam line, curve the round edge through its points and add your allowances.

Good to know

  • This pattern is approximate; the result card shows how close it is.
  • Source: No published source checked for this shape. Method: outer envelope of the rectangle and the tilted circle (flat triangles and oblique cone corners), triangulated; checked against a separate reference implementation in Trueflat.

Method and formula

Here the round end is not parallel to the base: its plane is turned by α about an axis along the width, so one side rises and the opposite side drops. H is the height of the centre of the round end. The part is still four flat triangles and four oblique cone corners, all running from the rectangle's corners to the tilted circle. The seam is on the low side.

  • Tangent points: on the A sides, the low and high points of the circle. On the B sides the angle θ solves H sin θ + k cos θ = −r sin α, with k = (ex − A/2) sin α for one side and (ex + A/2) sin α for the other.
  • Tilt from 1° to 45°. Above that the opening faces sideways, which is branch work.
  • Clearance: H − max(r sin α, (B/2 + ey) tan α) ≥ max(A, B, D)/10, so the low side keeps a usable slope.
  • Accuracy: the round edge is drawn as chords; it is short by at most Σ rΔ³ ÷ (24 n²) over the four corner arcs Δ.

With sheet thickness and inside or outside dimensions, each opening is moved by one amount to the middle of the sheet. This is approximate: the calculator shows how far the opening can be off, and asks for middle-of-sheet dimensions if that is more than 1 mm.

Worked example

A = B = 400, D = 300, H = 300 mm, α = 30°, two sections per corner. The tangent point on one B side is at θ = 4.72° instead of 0°. The low point of the circle is 225 mm high and 129.90 mm from the centre, so the seam line is 235.67 mm and both seam edges total 471.33 mm. The low side stands 184.53 mm clear, well above the 40 mm minimum.

Questions

When do I use this instead of a plain square to round?

When the round end is cut at an angle instead of lying parallel to the rectangle, so the round pipe leaves at a slope. The tilt must be at least 1°; for a level round end use the square to round or the eccentric square to round.

What does H measure here?

The height from the base to the centre of the round end. The low side of the circle is lower than H and the high side higher.

Is the pattern exact?

The flat triangles are exact. The cone corners are drawn with chords, so the round edge is a little short of πD, by at most the sum of rΔ³ ÷ (24 n²) over the four corner arcs. Inside or outside dimensions with thickness are converted approximately and the deviation is shown.

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