# How do I create a cylinder with a taper at a specific angle?

I'm creating a cylinder in Blender and want to taper the top or angle the sides to a specific 75-degree angle. How can I achieve this by scaling the top horizontal face appropriately in Blender?

• I would say this is a maths question, not about Blender. Basically you have to look up triangle formulas, how long must one leg of a right triangle be so that the adjacent angle is 75°, then subtract this length from the radius of the cylinder and divide it by the radius. Then you have the scaling factor for the small face. This could be a Blender question if you would ask how to implement this in Blender. Like this it is just asking a maths question and so it's off topic here. Commented May 19 at 0:05
• @GordonBrinkmann I rephrased the question to make it more of a blender question rather than a math one. Commented May 19 at 8:31
• @HarryMcKenzie I just do not know how exact cable_pair needs the "specific 75-degree angle", because with scaling like in your answer it will most likely only be almost 75° and not exactly. So if were the OP I would prefer a mathematical solution. Without maths doing it just with editing in Blender, I would not use a cylinder at all to start with. Commented May 19 at 11:31
• @GordonBrinkmann yes I agree. I would definitely do it the math way if I needed to model this but since the OP asked how he can scale the top face, I just added that as the simple answer to their question :D Commented May 20 at 9:19
• @GordonBrinkmann yeah haha anyway what matters is we have some more "documentation" on this site to help the community learn how to do this in different ways :D Commented May 20 at 11:42

Just in case you want a mathematical formula to get a scale factor (although, as I said, that's just maths and not a real Blender question - scroll to the bottom to find out how you can use the maths in Blender):

If you look at the desired cylinder's cross section, there are some things we know: the height $$h$$ of the cylinder and the radius $$r$$ (with a height of 2 m and a radius of 1 m for the default primitive object).

Apart from that, the border edges going upwards should be angled by $$\beta=75°$$ and the height is of course orthogonal, so we can build a right triangle with a remaining angle of $$\alpha=15°$$.

What you now need to find is the length $$a$$ which is how much the lower radius exceeds the desired upper radius to build the triangle. The new radius $$b$$ is then just the radius $$r$$ minus $$a$$, and to get $$b$$ you have to scale the original radius by a factor of $$\frac{r-a}{r}$$, which in case of a default radius of 1 m comes down to simply $$1 - a$$.

And because we have all angles and the value for the height, you can easily calculate the value for $$a$$ with the following formula:

$$a=h\cdot\frac{\sin{\alpha}}{\sin{\beta}}$$

With the given values this results in:

$$a=2\cdot\frac{\sin{15°}}{\sin{75°}}\approx 0.535898$$

So the upper radius has to be scaled by a factor of

$$\frac{1-0.535898}{1}=1-0.535898=0.464102$$

to get a cylinder (or actually a frustum) with the sides angled at 75°. I hope all the variables did not confuse too much, I thought if you wanted to do this with cylinders of other heights and radii and maybe have different angles as well, it would be better to not only give you formulas with fixed values.

Basically, the whole operation can be written in a single line formula:

$$\text{upper radius }= \text{lower radius}-\text{height}\cdot\frac{\sin{15°}}{\sin{75°}}$$

which can help you since Blender accepts mathematical formulas in value fields. It gets a little bit more complicated since you have to convert the angles in radians:

$$\text{upper radius }= \text{lower radius}-\text{height}\cdot\frac{\sin{\pi\frac{15°}{180°}}}{\sin{\pi\frac{75°}{180°}}}$$

Unfortunately, you cannot enter this complex formula as a factor while you are scaling, but here is the solution:

## Now to the part how you can use maths in Blender

Okay, this looks a bit complicated now. But as I mentioned above, this is not a cylinder you are talking about, but a frustum or truncated cone. So what you can actually do instead of creating a cylinder and scaling down the upper face to get the desired angle, just do the following:

Press Shift+A > Add > Cone. Then open the properties at the bottom left of the viewport and just enter

1-2*sin(pi*15/180)/sin(pi*75/180)

into the value for Radius 2, that is Radius 1 subtracted by the Depth multiplied by the angle calculations. And the result is the angled cylinder.

Under Mesh Edit Mode Overlays you can enable Edge Angle and see the angles when scaling using S to scale and Shift+Z

You could as well, just make a single edge, rotate it by the angle you want(I randomly used 25° in the GIF), move it away from the center(object space origin) by the length of your desired radius and then use Screw modifier to make the cylinder out of it:

• ... if you are lazy like me and prefer to avoid maths at all costs. :D Commented May 19 at 19:57
• +1 That's exactly what I had in mind when writing my comment under the question: "Without maths doing it just with editing in Blender, I would not use a cylinder at all to start with." 😁 But since I'm not avoiding maths at any costs I gave my mathematical answer 😉 The only problem would be if a specific height was to be achieved as well (I would then make it larger and just cut it at the desired height). Commented May 19 at 22:18
• Might be easier to cut the single edge at the start with Auto Merge and Split Edges and Faces enabled since one can easily move a vert to the correct height and then just extruding and edge to intersect is really easy. I don't know, might just be my thing, I do things like that quite a lot and might just be used to that. Not sure if that makes sense to do for newer users. Commented May 19 at 22:54
• Yes, I said I would cut it, too. How or when in the process does not really matter. I was just pointing that out because if a cylinder should also have a specific height and a beginner is already struggling to find a way to get the angle, it might not be so obvious how to get or preserve the correct height as well. Again, I'm thinking way too much ahead because I learned that people often do not automatically know what I assumed or it turns out they want more or different things than given in the question. Just my usual overthinking, sorry 😆 Commented May 20 at 7:16