FabLayout

Flat oval to round transition calculator

For a flat oval duct (two half circles joined by straight sides) going into a round one: enter the oval's overall length and width, the diameter and the height. One-piece pattern.

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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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1,258.7 mm1,099.1 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

707.1mm

Approximate, within ±3.7 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. Divide both ends at the same angles

    Divide each half circle of the oval into equal angles, and divide the matching half of the round end at the same angles.

  2. Find the true lengths

    Join each oval point to the round point at the same angle and work out the true length of that line and of one diagonal per piece from the plan distance and H.

  3. Draw the first flat side

    Start with the seam from the middle of a straight side to the round end, then the triangle that takes in the rest of that half side.

  4. Lay out the curved end

    Add the four-sided pieces of the end one after another, each from its two joining lines, its two chords and the diagonal.

  5. Repeat and close

    Add the second flat triangle and the other end, finish on the second seam line 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 two openings (flat triangles and oblique truncated cones, points joined at parallel tangents), triangulated; checked against a separate reference implementation in Trueflat.

Method and formula

A flat oval has two straight sides and two half-circle ends. Its transition to round is two flat triangles standing on the straight sides, and two oblique truncated cones linking each half-circle end to half of the round end. Points on the oval and on the circle are joined where their tangents are parallel, so each end piece is a true cone that unrolls without stretching.

  • Sizes: A is the overall length, B the width. The straight sides are A − B long and the ends have radius B/2.
  • Oval perimeter = 2(A − B) + πB.
  • When B equals D, the end pieces are oblique cylinders.
  • Accuracy: both curved edges are drawn as chords, each short by at most π³ × max(D/2, B/2) ÷ (48 n²).

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 = 600, B = 200, D = 200, H = 300 mm, one section per quarter. B equals D, so each end is an oblique cylinder. Each flat triangle has a 400 mm base and is 300 mm high, 60 000 mm². The four end pieces are parallelograms of 46 904 mm² each, so the whole pattern is 307 617 mm². Both seam edges total 600 mm and the oval perimeter is 800 + 200π = 1428.32 mm.

Questions

What is the difference between flat oval to round and oval to round?

A flat oval has straight sides and half-circle ends. Oval to round is for a true ellipse with no straight part. Measure your duct: if the sides are straight, use this page.

Is the pattern exact?

The flat triangles and the cone ends unroll exactly, but both curved edges are drawn with chords. Each edge is short by at most π³ × max(D/2, B/2) ÷ (48 n²). Inside or outside dimensions with thickness are converted approximately and the deviation is shown.

Can the oval be a circle?

No. The overall length must be more than the width, and at most 20 times it. With A = B both ends are round and the part is a concentric reducer, which the truncated cone calculator covers.

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