hi vectorized,

Let's see if I can take you through this one step at a time.

Step 1. What shape do you need to make the label?

Have a look at my diagram below. It shows a large circle with a smaller one inside. And I've drawn two straight lines out from the centre. Two arcs plus the two lines make a sector of the circle. I've coloured the sector using red and pink. Try this with a bit of paper. Don't worry about sizes at the moment. Any size will do.

Cut out the sector (both bits, still joined). Fold it round until the straight lines meet. You should have a cone.

Cut off the pink bit. Re-fold. You should have a cone with the top cut off. (technical name: frustrum)

That's the shape you need.

Step 2. How big must the circle be to make the frustrum?

Now I'm assuming you will know the radius of the top and the bottom. Your values in the last post are correct.

You also need to know how far along the paper it is from the top circle to the bottom circle. This is the slant height along the pot. It is not the same as the vertical height.

I've shown these measurements in the second diagram

Now the distance from the centre to the small circle (L-s) as a fraction of the distance to the big circle is

The small circle is the same fraction of the large circle:

So these fractions are the same.

If that's starting to get confusing, try it with some numbers.

Suppose the small circle is 1/3 of the large circle.

But the distance L-s has to be one third of L. So

Let's say s = 10 inches.

If L-s is one third of L, then s must be two thirds of L. So

check: If L = 15 and s = 10 then L-s = 5 and 5 is one third of 15 tick.

So the formula for calculating L is

Now I've done some algebra to get L = something in this equation. Maybe that's too much for you so here it is with those numbers:

step 3.

So what fraction of the whole circle do we need to make this frustrum?The arc at the bottom is 2 x pi x R1

The whole circle is 2 x pi x L

So the angle is this fraction of a whole circle:

Now I multiplied that fraction by 360 degrees. If your software wants a percentage then I think you need:

Hope that does it.

Bob