Can a 'chance to catch' percentage be calculated with the color of the circle?

Solution 1:

There is a correlation between the circle color and the catch rate of the Pokemon. No specific numbers are known, but a user has calculated approximate percentages for color thresholds in this post on the Silph Road reddit:

The colors seem to work like this: if the capture rate (remember the formula from the beginning) is less than ≈ 65% the color is yellow. I wasn’t able to test the exact boundaries but my tests showed that around 65 was when the circle turned yellow. Likewise, at ≈ 35% the circle would turn orange. I only encountered a red circle once and the % was 21% so I wasn’t able to even get an approximate value there and I’m not going to assume anything for that with only 1 value in my data set.

This is more of an aside, but based on the information in this post, the circle color is directly related to level, in addition to species.

Solution 2:

PokeAssistant's Catch Chance Calculator webpage does calculate percentages based on all the catch factors including a colored circle to help you compare.