Cone template generator (truncated cone)

Enter the top and bottom diameter and the height of a cone or truncated cone. You get its exact flat pattern at true size, with a glue tab, for lampshades, paper cones, party hats and planters. Set the top to 0 for a pointed cone.

01Measure the cone

Top diameterin Bottom diameterin Height top to bottomin

Top & bottom

Height

Top 0 = pointed cone · fractions work: 5 1/2

02Options

Glue tab along one seam; 0 = nonein

Print measurements on the pattern

03Download

Paper for the PDF

Flat patterntrue size

How the pattern is worked out

A truncated cone, or frustum, unrolls into part of a ring centred on the tip of the full cone. With top diameter D1, bottom diameter D2 and height h:

s = √(h² + ((D2 − D1) ÷ 2)²) side length R = s × D2 ÷ (D2 − D1) tip to the wide edge r = R − s tip to the narrow edge θ = 180° × (D2 − D1) ÷ s angle of the slice

The curved edges then measure exactly π × D1 and π × D2. For a lampshade 6 in across the top, 10 in across the bottom and 7 in tall, the side is 7.28 in, R is 18.20 in, r is 10.92 in and the angle 98.90°, so the pattern needs a piece about 27.66 × 11.10 in before the glue tab. Open this example.

Wider at the bottom, so the pattern’s tip sits above it and the long edge is at the bottom. Drawing not to scale.

Making it

Lampshades. Measure the top and bottom rings across and the height you want between them. Print the pattern on paper first, check it around the rings, then cut the shade material from it. Use the glue tab for the seam overlap.
Paper cones and party hats. Set the top to 0 for a point. To size a hat to a head, measure around the head, choose Circumference, and enter that as the bottom.
Thick card, felt or sheet metal. Use the diameters at the middle of the material’s thickness, so the inside and outside surfaces both fit.
Bigger than your printer. Download the PDF at template size for a print shop or plotter, or print it across several sheets with Pro.

Questions

How do I make a template for a full, pointed cone?

Enter 0 for the top diameter. The template becomes a sector of a circle whose radius is the cone’s side length.

What if my cone is wider at the bottom, like a lampshade?

Enter the measurements as they are. The template flips so the short curved edge is at the top and the long one at the bottom.

What diameters do I use for card, felt or sheet metal?

For thin paper, the outside diameters are fine. For thick card, felt or sheet metal, use the diameters measured at the middle of the material’s thickness, so the inside and outside surfaces both fit.

How do I print a cone template bigger than my paper?

Download the PDF at template size for a print shop or plotter, or with Pro print it across several Letter, Legal, A4, A3 or 13 × 19 in sheets with overlap and alignment marks.