Flat Pattern Calculator Online: How It Works

A flat pattern calculator online works out the size and shape of a flat sheet needed to form a 3D part, such as a cone, cylinder, or duct transition. You enter the dimensions of the finished part (diameters, height, thickness, bend angle) and the calculator returns the flat blank dimensions, including developed length, width, and often a bend allowance. This is essential for sheet metal fabrication, HVAC ductwork, and any project where you cut metal or other material before bending or rolling it into shape.

Formula

For a truncated cone (the most common flat pattern), the formula uses the large diameter (D), small diameter (d), and height (h). First, find the slant height (l) of the cone: l = sqrt(h² + ((D-d)/2)²). Then the radius of the flat pattern for the large end is R1 = (D/2) * (l / ((D-d)/2)), and for the small end R2 = (d/2) * (l / ((D-d)/2)). The angle of the pattern is θ = 360° * (1 – (d/D)).

Variables:

• D = large diameter (mm or inches)
• d = small diameter (same unit)
• h = height of the truncated cone (same unit)
• R1 = radius of the outer arc on the flat pattern
• R2 = radius of the inner arc on the flat pattern
• θ = angle of the sector, in degrees

The calculator above uses the same logic but simplifies the intermediate steps. It assumes a perfectly sharp bend (no material thickness) and a straight-sided cone.

Worked Example

Using the default values: D = 300 mm, d = 200 mm, h = 400 mm.

1. Difference in diameters: 300 – 200 = 100 mm. Half of that is 50 mm.
2. Slant height: sqrt(400² + 50²) = sqrt(160000 + 2500) = sqrt(162500) ≈ 403.11 mm.
3. R1 = (300/2) * (403.11 / 50) = 150 * 8.0622 ≈ 1209.33 mm.
4. R2 = (200/2) * (403.11 / 50) = 100 * 8.0622 ≈ 806.22 mm.
5. Angle = 360 * (1 – (200/300)) = 360 * (1 – 0.6667) = 360 * 0.3333 = 120°.

The flat pattern is a sector of a ring with outer radius 1209.33 mm, inner radius 806.22 mm, and an angle of 120°. The calculator rounds to two decimal places, giving the same result.

When to Use a Flat Pattern Calculator

Use a flat pattern calculator whenever you need to cut a 2D shape that will be bent, rolled, or folded into a 3D object. Common applications include:

• Sheet metal cones for hoppers, funnels, or decorative pieces
• Transition pieces between round and rectangular ducts
• Pipe elbows made from segmented bends
• Chimney caps, rain hats, or roof flashings
• Any part that starts as a flat sheet and is formed by rolling or pressing

The calculator is especially useful for one-off or custom parts where you cannot rely on pre-made components. It saves material by giving you the exact shape before you cut.

How to Read the Results

The first output, R1, is the radius of the large arc on your flat pattern. R2 is the radius of the small arc. The angle tells you how many degrees of a full circle you need. To lay out the pattern on metal or paper:

1. Draw a horizontal line.
2. Mark a center point.
3. Draw an arc of radius R1 and another of radius R2 from the same center.
4. Measure the angle θ from the center and draw two radial lines.
5. The area between the two arcs and the two radial lines is your pattern.

Add a tab or overlap for welding or riveting if needed. For a full cone (pointed at the top), set d2 to a very small number, but not zero, to avoid division by zero.

Common Mistakes and Limitations

The biggest mistake is ignoring material thickness. The calculator assumes the sheet has zero thickness. In reality, bending stretches the outside and compresses the inside. For thin sheet metal (less than about 3 mm), the error is often acceptable. For thicker material, you need to use the neutral axis – the line inside the material that does not change length during bending. The neutral axis is typically at about 40–50% of the thickness from the inside surface, but it varies with the bend radius and material. Many professional calculators include a bend allowance field for this reason.

Another common error is mixing units. If you enter diameters in inches and height in millimeters, the result will be nonsense. Always use the same unit for all inputs.

Rounding too early can also cause problems. If you round the slant height to 403 mm instead of 403.11 mm, the final radius will be off by a few millimeters. Keep full precision until the end.

Finally, the formula assumes a perfectly straight-sided cone. If your part has curved sides (like a bell shape), this calculator will not be accurate. You would need a more advanced method, often involving CAD software or a specialized pattern development program.

Alternatives to an Online Calculator

If you do not want to use an online calculator, you have several other options:

• Manual layout using geometry and a compass – doable but time-consuming and prone to error.
• CAD software – most CAD programs have sheet metal tools that automatically flatten parts. This is the most accurate method for complex shapes.
• Spreadsheet formulas – you can build the same formulas in Excel or Google Sheets. This gives you a reusable tool that you can customize.
• Paper templates from pattern books – some old fabrication books include tables of flat patterns for standard cones and elbows.

For a simple cone, an online calculator is usually the fastest. For complex transitions with multiple pieces, CAD is better.

Safety and Accuracy Tips

When working with sheet metal, always wear gloves and safety glasses. Edges are sharp, and cutting tools are dangerous. Double-check your measurements before cutting – it is much cheaper to re-measure than to re-cut. If you are making a part that must fit precisely, add a small allowance for the joint and trim to fit. For critical structural parts, consult an engineer or use a verified CAD model. The calculator is a starting point, not a substitute for professional judgment.

Frequently Asked Questions

What is a flat pattern? A flat pattern is the 2D shape that, when bent or rolled, forms a 3D object. It is like the net of a solid in geometry, but for sheet metal it also accounts for material stretching.

Can I use this for a full cone (not truncated)? Yes, set the small diameter to a very small number like 0.1 mm. The calculator will give a very large R2 and an angle close to 360°. For a true point, you would need a different formula that does not divide by zero.

How do I account for material thickness? For accurate results, use the neutral axis dimensions. This means subtracting half the thickness (or the neutral axis factor) from the diameters. For example, if your material is 2 mm thick, use D-1 and d-1 for the diameters. The exact factor depends on the bend radius and material, but 0.5 is a common approximation.

What if my cone has a flange or hem? The calculator only gives the basic cone shape. Add the flange width to the outer radius or draw it separately. For a hem, you need to add the hem allowance, which is typically 2–3 times the material thickness.

Is the angle always less than 360°? Yes, for a truncated cone, the angle is always less than 360°. If you get a result greater than 360°, check your inputs – the small diameter must be smaller than the large diameter.

Can I use this for a cylinder? A cylinder is a special case where the small and large diameters are equal. The formula would divide by zero. For a cylinder, the flat pattern is simply a rectangle: width = circumference (π × diameter) and height = cylinder height. You do not need this calculator for that.

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in d1 | Large diameter | mm | 300 | 0
in d2 | Small diameter | mm | 200 | 0
in h | Height | mm | 400 | 0
out r1 | Large radius of flat pattern | mm | (d1/2) * sqrt(1 + (h/((d1-d2)/2))^2) | 2
out r2 | Small radius of flat pattern | mm | (d2/2) * sqrt(1 + (h/((d1-d2)/2))^2) | 2
out angle | Pattern angle | deg | 360 * (1 - (d2/d1)) | 2