Ok, here goes.
This is written in the sequence you would put into the windows calculator.
Let’s say you are putting a graphic on a beer mug with no taper.
The beer mug has a dia of 3 inches.
You are planning on 30% coverage. So…
360 X 30% gives you 108 degrees coverage. (Do not hit enter after the %)
Then you want 108 divided by 360 giving you .3 (remember that)
Now you want to multiply pi X 3 giving you 9.42 (pi X dia of mug) (pi=3.14 aprox)
Then .3 X 9.42 will give you 2.83.
That will be the width of your design. Scale you design (height and width locked) to that width and save that number.
That unfortunately will give you a design that looks taller (or narrower) than you want.
To fix that, we can figure out what the design should be changed to.
You need to divide your angle by 2 giving you 54.
In the windows scientific calculator punch this in.
54sin X 3 That will give you 2.42. That is what the design will actually look like for width.
So, take your first number and subtract the second number.
2.83 – 2.42=.41
Then calculate the percentage.
.41/2.83 X 100 = 14.5%
Subtract 14.5% from the height of your design without changing the width.
Close to what darcshadow said with way more detail that may not be needed.
You can change your numbers (dia and% of coverage) to reflect what you are actually designing.