Cone Flat Pattern (Template) Generator

The Cone Flat Pattern Generator computes the 2D developed surface (unrolled template) of a 3D cone or truncated cone (frustum). Enter the base radius, top radius (for frustums), and height or slant height, and instantly obtain the outer radius, inner radius, and sweep angle needed to cut the flat pattern from sheet metal, cardboard, fabric, or paper.

What Is a Cone Flat Pattern?

When you "unroll" or "develop" a cone onto a flat surface, you get a circular sector. For a full (pointed) cone, the flat pattern is a simple pie-slice shape. For a truncated cone (frustum), the pattern becomes an annular sector — the area between two concentric arcs. These three values define the template:

• Outer Radius (R): The distance from the virtual apex to the outer arc (base edge)
• Inner Radius (r): The distance from the virtual apex to the inner arc (top edge) — frustums only
• Sweep Angle (θ): The angular span of the sector in degrees

Formulas Used

Full Cone

Truncated Cone (Frustum)

Where r₁ = base radius, r₂ = top radius, h = vertical height, s = slant height.

How to Use This Tool

1. Choose cone type: Select "Full Cone" for a pointed cone or "Truncated Cone / Frustum" for a cone with the top cut off.
2. Select input mode: Choose whether you are entering radii or diameters, and height or slant height.
3. Enter dimensions: Fill in the base size, top size (frustum only), and height or slant height.
4. Choose unit: Select millimeters, centimeters, inches, meters, or feet.
5. Add seam allowance (optional): Enter extra material for welding, gluing, or sewing overlap.
6. Click Generate: View the flat pattern diagram, exact dimensions, and step-by-step calculations.

Real-World Applications

Sheet Metal Fabrication

HVAC ductwork, industrial hoppers, reducer transitions, ventilation funnels, and chimney caps all require accurate flat patterns. Sheet metal workers use these templates daily to cut galvanized steel, aluminum, or stainless steel sheets before rolling and joining.

Paper Crafting & Cardboard Models

Making party hats, lamp shades, gift boxes, architectural models, or science project volcanoes requires precise cone templates. This tool calculates the exact cutting pattern including optional glue tab allowance.

Sewing & Fabric Work

Conical skirts, teepee covers, sail-making, and upholstery projects use developed cone patterns. The seam allowance feature helps calculate the extra fabric needed for stitching.

3D Printing & CNC

While 3D printers create cones directly, CNC plasma/laser cutters need flat patterns to cut sheets that are then rolled into cones. This tool provides the exact dimensions.

Understanding Seam Allowance

Seam allowance adds extra material around all edges of the flat pattern. Recommended values:

• Sheet metal welding: 5-10 mm overlap
• Sheet metal riveting: 10-15 mm for rivet spacing
• Paper/cardboard gluing: 10-15 mm glue tabs
• Fabric sewing: 10-15 mm standard seam
• Soldering (thin metal): 3-5 mm

Tips for Accurate Results

• Measure the actual outside dimensions of your cone, not inside dimensions
• For existing cones, measuring the slant height directly is more accurate than calculating from height
• Use a beam compass (trammel) for large radii that exceed a standard compass
• Score fold lines for tabs before cutting
• For sheet metal, account for material thickness — use the neutral axis (mid-thickness) radius
• Mark the straight edge and label it "SEAM" for easier assembly

Frequently Asked Questions

What is a cone flat pattern?

A cone flat pattern (also called a developed surface or unrolled pattern) is the 2D shape you get when you "unwrap" a 3D cone onto a flat surface. It forms a sector of a circle for a full cone, or a sector of an annulus (ring) for a truncated cone (frustum). This flat template is used to cut sheet metal, paper, or fabric that can then be rolled into the desired cone shape.

How do I calculate the flat pattern for a truncated cone (frustum)?

For a frustum with base radius r₁, top radius r₂, and slant height s: First find the outer radius R = s × r₁ / (r₁ − r₂) and inner radius r = s × r₂ / (r₁ − r₂). The sweep angle θ = 360° × r₁ / R. The flat pattern is the area between two concentric arcs of radii R and r, spanning angle θ.

What is seam allowance and how much should I add?

Seam allowance is extra material added around the pattern edges for joining (welding, riveting, gluing, or sewing). For sheet metal, 5-10 mm is typical for overlap joints. For paper crafts, 10-15 mm glue tabs work well. For sewing fabric cones, 10-15 mm seam allowance is standard.

Can I use this for HVAC ductwork transitions?

Yes! HVAC round-to-round reducers and transitions are frustum shapes. Enter the large duct diameter as the base, the small duct diameter as the top, and the transition length as the height. The tool will generate the exact flat pattern needed to fabricate the transition piece from sheet metal.

What units does the calculator support?

The calculator supports millimeters (mm), centimeters (cm), inches (in), meters (m), and feet (ft). All output dimensions use the same unit you select for input, so there is no need for unit conversion.

Additional Resources

• Cone - Wikipedia
• Frustum - Wikipedia
• Developable Surface - Wikipedia