It's simple to roll paper into a cone but what if you want to make a cone that's a specific radius and height? What if you want the base to sit evenly on a flat surface?

This will teach you how to make custom-sized cones for craft and home projects. I like using math in crafts BUT I know some people's eyes glaze over when confronted with it so you only have to do one simple calculation. You can also find these instructions and some uses for paper cones on my blog: Craftastic World.

Paper cones are versatile for crafting.
- tip down, they serve as hanging vases
- holiday paper cones can represent trees
- they make great party hats

You need:
paper or cardstock (either for a paper cone itself or to be used as a template)
protractor (there are printable ones on the web)
compass (helpful to have but I give directions for a substitute)

Step 1: Calculations

  • Decide on the radius of your base (r) and the height you want. You'll use this to find the "slant height" which will be necessary for the rest of the cone's dimensions. This online calculator will do it for you: http://www.analyzemath.com/Geometry_calculators/pythagorean.html. Just enter the radius of the base and the height as the sides. The result (hypotenuse) is your slant height: S.

(Or, If you are familiar with the Pythagorean Theorem, you can calculate this yourself. The slant height is the hypotenuse and the height and radius of the base are the sides.)

  • Determine the angle of the wedge shape you'll need to cut from paper. This another simple calculation: Angle=360r/s
(r is the radius of the base, s is the slant height from the previous step)

Step 2: Draw the Angle

Now you will be drawing the angle of the wedge on your paper. To do this, select a point for the vertex of the angle. Draw one line that starts at the point and is length S.

Using a protractor, mark a point that makes the angle you determined from this point. Draw a line that connects the point to this line and extends beyond it for length S.

At this point, you should have an angle with two legs of equal length on your paper.

Step 3: Draw the Arc

To draw the arc which will be the edge of your cone's base, you will need a compass*. Adjust your compass so the distance it spans is the same as the slant height, s. Place the point of your compass on the vertex of your angle and sketch the arc.

Substitute Compass: Cut a narrow strip of scrap paper a little longer than S. Place the paper to be cut onto cork board or some other surface you can pin into. Mark a line on the strip that is the same length as S. Make a small hole in one end of the line. Then pin the other end of the line through the vertex of your angle. Place a pencil into the hole and make your arc line.)

Step 4: Assembly

Make a tab along one side of the wedge, as shown. This will be the gluing tab. I added the red lines to this picture to show the details. Notice, I cut the tab short on the point side.

Cut out the wedge, roll and glue together.
<p>Hi</p><p>How can i make a cone with slant angle 52 degree from base line?</p>
I really don't know how to make the math simpler than I have stated. <br>1. Use the Pythagorean theorem to get the slant height (plug the dimensions you want into the online calculator to reduce the arithmetic). <br>2. Multiply the radius by 360 and divide by slant height to get the angle. <br>That's it. I hope it turned out well for you. <br>I still haven't made standard templates because I'm not really sure what people want but there are many online. <br>Sorry.
I think there are some cone templates on the web for crafters.&nbsp; One of these days I'll put together some precalculated cone templates or instructions for making such but I won't be altering this Instructable for it it--I'll make a new one.&nbsp; The point of this instructable is to make &quot;modular&quot; cones so geeks who want cones of specific sizes for their own purposes can put some together.&nbsp; <br /> <br /> Truly, there are many ways to use your cone.&nbsp; I found that if i&nbsp;wanted to make a really tall cone-shaped hat as a gag or large volume cones from standard sheets of paper, there were no instructions out there, thus this Instructable.<br />

About This Instructable




Bio: I'm a Renaissance woman. I love to create things with a fantasy, medieval, or geeky edge. I'm also a math/science nerd. I ... More »
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