A cone or a frustum (a cone with its tip cut off) is a developable surface: its curved side can be unrolled flat onto a sheet of paper without stretching or tearing anything, unlike a sphere. That flat shape is always a circular sector, possibly with a smaller sector cut out of its point, and the tool above computes and draws it directly from the three measurements that define the solid - the bottom radius, the top radius and the height - so you can print it, cut it out and fold it back into the 3D shape it came from.
Using the Generator
Enter the bottom radius R and height h of the cone or frustum you want to build. For a frustum, also set the top radius r; for a plain cone that comes to a point, check "Full cone", which fixes \(r=0\). The preview updates immediately and always shows the correct aspect ratio, but it is scaled down to fit the box above - the actual printed size at 100% scale is reported underneath it, in millimeters, so you know which paper size to use before you print.
The optional glue tab adds a narrow flap along one straight edge of the sector, separated from the main shape by a dashed fold line. Cut along the solid outline, fold the tab under along the dashed line, roll the sheet into the cone shape, and glue the tab underneath the opposite straight edge to close the seam.
The Geometry Behind the Template
Slice the frustum along its axis and you get a trapezoid: two parallel sides of length \(2R\) and \(2r\), and two slanted sides connecting them. Continue those two slanted sides past the smaller parallel side and they meet at a single point - the apex the frustum would have if it weren't cut off. This apex is the center of the circular sector we are about to unroll, and everything below follows from properties of that one trapezoid.
Let \(m\) be the length of the slanted side between the two rims, and let \(M\) be the full distance from the apex to the outer rim. The slant \(m\) is the hypotenuse of a right triangle formed by the height \(h\) and the difference in radii \(R-r\):
\[ \boxed{m=\sqrt{h^2+(R-r)^2}}. \]To find \(M\), look at the two right triangles formed by dropping a perpendicular from the apex onto the axis: the larger one has legs along the axis and the outer rim, the smaller one has legs along the axis and the inner rim, and both share the same apex angle. That makes them similar, so their radii and apex distances are in the same ratio:
\[ \frac{R}{r}=\frac{M}{M-m}, \qquad\text{equivalently}\qquad \frac{r}{M-m}=\frac{R}{M}. \]Cross-multiplying gives \(rM=R(M-m)=RM-Rm\), so \(Rm=M(R-r)\), and solving for \(M\):
\[ \boxed{M=\frac{mR}{R-r}}. \]This is exactly why the top radius has to be strictly smaller than the bottom radius: for \(R=r\) the frustum is really a cylinder, whose lateral surface unrolls into a plain rectangle rather than a sector, and the apex distance \(M\) would have to be infinite for that to still count as a sector. Setting \(r=0\) is no problem at all, though - the apex is simply reached at distance \(M=m\), and the "inner" sector radius \(M-m\) collapses to \(0\), which is precisely the point of a plain cone.
The Sector Angle
Unrolling the lateral surface keeps every length on it unchanged - that is what "developable" means. In particular, the rim of the base circle, a circle of circumference \(2\pi R\), becomes the outer arc of the sector, an arc of radius \(M\) and some central angle \(\alpha\). Since the arc length has to match the circumference it came from,
\[ \frac{\alpha}{360^\circ}\cdot 2\pi M = 2\pi R, \]and solving for \(\alpha\) gives
\[ \boxed{\alpha=360^\circ\cdot\frac{R}{M}}. \]If \(\alpha\) is measured in radians instead, the outer arc length is simply \(\alpha M\). The same circumference condition therefore reads \(\alpha M=2\pi R\), giving the equivalent form
\[ \boxed{\alpha=2\pi\cdot\frac{R}{M}}\quad\text{(radians)}. \]The same argument applied to the top rim, a circle of circumference \(2\pi r\), lands on the inner arc of radius \(M-m\) sweeping the very same angle \(\alpha\) - which is exactly why one shared angle at the apex produces both arcs correctly, and no second angle needs to be computed. Substituting \(M=\frac{mR}{R-r}\) shows that \(\alpha\) never reaches \(360^\circ\) for any real cone or frustum with \(h>0\), and it only approaches that limit as the shape gets flatter and flatter.
Drawing the Sector
With \(M\), \(m\) and \(\alpha\) known, the outline is four pieces stitched together into one closed path: the outer arc of radius \(M\) sweeping from \(0^\circ\) to \(\alpha\), a straight radial edge inward to the inner arc, the inner arc of radius \(M-m\) sweeping back from \(\alpha\) to \(0^\circ\), and a final straight radial edge back to the start. The optional glue tab is built the same way, just with the sector extended a little further by a small extra angle so that a fixed physical tab width is preserved along the outer edge, with the original edge kept as a dashed fold line.
Because the whole sector is generated directly from \(R\), \(r\) and \(h\) instead of a fixed pre-made pattern, the download always matches the exact solid you asked for, sized precisely in millimeters, ready to print at 100% scale.