Flat Cone Template Calculator

Calculator Inputs

Example Data Table

Example values are rounded. Your output changes with seam, edge allowance, basis, and thickness.

Formula Used

The calculator first converts the entered diameters into neutral line radii. This matters when the given size is an inside or outside diameter. For a centered value, the neutral radius is simply diameter divided by two.

The radius difference is: d = |R_large - R_small|. If vertical height is entered, slant height is: L = √(H² + d²). If slant height is entered, vertical height is: H = √(L² - d²).

For a cone or truncated cone, the outer development radius is: OR = L × R_large / d. The inner development radius is: IR = L × R_small / d. The core sector angle is: A = 360 × d / L.

Seam overlap adds angle by: A_seam = overlap / OR, converted from radians to degrees. The lateral area is: π × (R_bottom + R_top) × L. If both radii are equal, the flat pattern becomes a rectangle.

How to Use This Calculator

1. Enter the bottom diameter of the finished cone or frustum.
2. Enter the top diameter. Use zero for a pointed cone.
3. Choose whether your height value is vertical height or slant height.
4. Select the measuring basis for the entered diameters.
5. Add material thickness if inside or outside sizes need neutral line correction.
6. Add edge allowance for hems, trimming, or folding stock.
7. Add seam overlap for glue, welding, riveting, or stitching.
8. Submit the form and use the displayed radii and angle for layout.
9. Download the CSV or PDF for shop records.

Flat Cone Templates for Practical Layout

Why the Template Matters

A flat cone template turns a three dimensional cone into a cuttable two dimensional shape. This shape is usually a sector. A truncated cone uses an annular sector. A full cone uses one sector that closes at the apex. The right template saves material. It also reduces trial cuts. That is useful in sheet metal, cardboard, leather, foam, paper, and craft stock.

Neutral Line Planning

Thickness can change the final fit. Thin paper may not need correction. Thicker sheet material often does. The neutral line is the layer that keeps its length during bending. This calculator can shift inside or outside measurements toward that line. It gives a more useful pattern for real fabrication.

Allowances and Seams

A cone template is rarely cut only to the mathematical surface. Most projects need extra material. A seam overlap may be required for adhesive, rivets, welds, tape, or stitching. Edge allowance may be needed for a rolled rim or a clean trim. These additions are included separately. This keeps the base geometry clear.

Checking the Output

The most important values are the slant height, pattern radii, and sector angle. Mark the center point first. Draw the outer radius. Draw the inner radius when the cone is truncated. Then swing the angle between both radial edges. Divide the outer arc into tick marks for easier checking. Always test a small paper model before cutting costly material.

Workshop Use

The CSV file is useful for records. The PDF file is useful for sharing. The preview helps confirm the general shape. It is scaled, so it should not replace the numeric dimensions. Use a compass, trammel, large ruler, plotter, or CNC workflow for final layout. With careful measuring, the template becomes repeatable and easy to adjust.

FAQs