Home / Plate work & forming

Plate layout development

Choose the part, enter sizes and thickness, and get the dimensioned flat layout, the ordinate table by division, the plate size and the weight, all at the neutral line.

Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.

Pre-sizing
Part
Layout

The drawing, ordinate table and plate size change with the part type. X and Y coordinates start at the lower-left corner of the rectangle that encloses the layout.

—Plate required (enclosing rectangle)
—

Dimensioned flat layout

To scale, seen from the outside. Dashed lines: layout lines numbered as in the table. Dimensions in the chosen units.

Ordinates and layout lengths

Value at each division of the table, from point 0 to the last.

Tap the chart to see the values.

Ordinate table by division

Next step

Take this page’s results to another calculator with the fields already filled in.

The calculation report gathers this page's inputs, results, equations, assumptions and references, with fields for project, engineer and revision. The full report also includes the charts and interpretations, in color. In the print dialog, choose Save as PDF.

Method, assumptions and references

Equations used

Neutral line: D_m = D_out − t/cos α (or D_in + t/cos α), α = cone wall angle; for cylinders α = 0
Cone frustum: s = √(H² + ((D₁ − D₂)/2)²); R₁ = s · D₁ ÷ (D₁ − D₂); R₂ = R₁ − s; θ = 360° · D₁ ÷ (2 R₁)
Eccentric cone and square to round: triangulation; each triangle is laid flat with true lengths L = √(Δx² + Δy² + H²) and the round-end arcs
Gore: β = total angle ÷ (N − 1); half gore h(ψ) = (R + r cos ψ) · tan(β/2); full gore = 2h; x = girth · i/n
Branch saddle: s(φ) = [√(R² − r² sin²φ) − r cos φ cos θ] ÷ sin θ; cut height = L − s; hole: x = s cos θ − r cos φ sin θ, arc = R · arcsin(r sin φ ÷ R)
Area by the polygon (shoelace) formula on the outline with 8 subdivisions per division; weight = area · t · ρ

Assumptions and limits

  • Constant-thickness plate with no stretch during rolling; the neutral line is at mid-thickness. In tight bends the neutral line shifts: use the press brake bending calculator.
  • Eccentric cone with parallel ends and concentric square-to-round; on the eccentric cone and the transition, the thickness correction ignores the slope of each wall.
  • Branch saddle with intersecting axes (no lateral offset). No root gap, bevel or cutting allowance included: add them per the welding procedure.

Standards and technical documents

  • Pipe Fitters Blue Book. W. V. Graves, Graves Publishing, 2001
  • The Pipe Fitter’s and Pipe Welder’s Handbook. T. W. Frankland, Glencoe/McGraw-Hill
  • Meyer, L. A. Sheet Metal Layout, 2nd ed., McGraw-Hill
  • ASME B31.3: Process Piping, item 304.2.3 (miter bends)
  • ASME B16.9: Factory-made wrought buttwelding fittings (dimensões de reduções e curvas de referência)

U.S. regulations

  • OSHA 29 CFR 1910.212: general requirements for all machines (guarding of plate rolls and shears)
  • ASME Boiler and Pressure Vessel Code, Section VIII, Division 1, and state rules for pressure parts
  • ASME B31.3: process piping, miter bends

Frequently asked questions

What does laying out a plate part mean?

It means drawing on flat plate the outline that becomes the part once rolled or bent. The calculator does this for cone frustums, eccentric cones, square-to-round transitions, mitered elbows and branch saddles, and gives a dimensioned drawing and an ordinate table to mark on the plate.

Why use the neutral line instead of the outside diameter?

When rolling, the outer face stretches and the inner face shrinks; only mid-thickness keeps its length. In the default example (40 in outside diameter, 1/4 in plate), the neutral-line girth is about 124.8 in; laying out by the outside diameter would give 125.7 in, about 0.85 in too long, and the part would not close.

How do I read the cone frustum result?

With 40 in and 24 in ends, 20 in high and 1/4 in plate, the sector has an outer radius of about 53.5 in, an inner radius of about 31.9 in and an angle of 133.7°. Strike both arcs from the same center and open the angle; the whole part needs a plate of about 98.4 × 40.9 in and uses 53% of it, which is why large cones are often made in 2 or more segments.

Where do I get the inputs?

From the assembly drawing or the equipment: diameters at both ends, height between them and plate thickness. State whether dimensions are outside, inside or mean. For pipe, use the outside diameter from the pipe table (for example, 12.75 in for NPS 12).

How many divisions should I use?

Twelve divisions are enough for small parts; above about 40 in diameter, use 24 or 32 so points are less than about 6 in apart. The calculator works with 8 internal subdivisions per division, so girth and area are already accurate; divisions only set how many points you mark.

Does it include weld gap and bevel?

No. It gives the part at the neutral line, with no root gap, bevel or extra stock. Add what the welding procedure requires and make a trial piece in thin sheet or cardboard when the shape is new.

When should I call an engineer?

For pressure vessel, boiler and pressure piping parts, geometry is only the start: wall thickness, branch reinforcement and miter bends need design per the governing code (ASME Section VIII, B31.3) by a qualified engineer.