Determining the diameter of a circle for an array of circles


I was looking at another thread, and in trying to solve it for the poster, discovered it is rather difficult to form an array of circles of a given diameter to meet at just their tangents.

Yes, I’m aware that SketchUp doesn’t have true circles, so don’t preach that to me, please.

The diameter doesn’t really matter. So let’s say the circles have a 3’ diameter. I would like to create an array of 15, 12, 8 and 5 circles that only meet at their tangent points.

Every solution I’ve come up with has overlaps.




I won’t preach, but it’s kind of hard to reply when you rule out the technical explanation in advance…


Sorry, I’m not sure I would know how to do it in AutoCAD, which I’ve used for 17 years.

I was just trying to be specific, that I know SU doesn’t have true circles.

But I do know that a radius in SU will be correct point to point through the center, and I could make it with 1k sides.


Use a circle with the number of sides that are the same as the number of circles you want. The array of circles must have sides that are an even multiple of the number of circles desired.

For example, 15 circles with 30 sides each:

12 circles with 24 sides each:

5 circles with 30 sides each:

When done, scale the array to the diameter of the circle you need.

How to calculate volume of tires structure

Thank you jimhami, the scale at the end would do it.

How are you doing that using a multiplier at the end?

I mean, are you measuring the radius/diameter and scaling it to my hypothetical 3’ diameter?


looks like he made the circle radius to 1/2 the segment length.


That actually doesn’t work, that was my first shot at it, the circles overlap by a considerble amount due to the angles.

Sorry mics, the way he did it does. But only by the scale at the end.


I were just looking at (for me) some pretty complex calculators to figure out what you want. You could do the math that way but it gets pretty in depth!

The way Jim does it is a very simple and clever way.


one array does but will it work with the other 3 connected arrays?


I would be interested in those, that was my next stop. I knew there was a mathmatical aspect, I just had’t sought it out yet.


Good question, let me find the inital post I was talking about.

The OP, had a horrendous model, stacking tires. That’s where this started, for me anyway.


Okay, how about this, using the original radius of .52m.


I used the method described by Jim, then scaled the circle to size. For the other rings I copied one out and moved to “tangent” and copy/rotated. Then repeated for the other rings.

It works for this example, I didn’t try different sides…


you guys rock. preach at me anytime.
HOWEVER the OP wanted 4 arrays beginning with 15 circles then 12 then 8 and then 5…I’d guess that diameter of the array AND of the circles both would determine where to even start.


F’nking awesome!

Now for the math! LOL


I created arrays of 15, 12, 8, and 5 circles. Each is 240 edges and 3’ diameter:

stack_o_tires.skp (198.1 KB)


yes thats easy enough but…I assumed he wanted the sequential arrays to produce circles that joined the previous array the same way. I am dubious that it’s even possible with segmented circles


I believe that the arrays are in reference to this:



could be…I assumed the “stacks of tires” were a shipping calculation tied to another post about volume


If the OP wants those numbers, something tells me to make them nest inside each other “tangent” they would either all have to be odd or equal numbers…