we use formulas like this all the time in airplanes because obviously, the plane goes where the wind goes.
For cycling though. I can't imagine that there is a formula or an algorhythm. There are simply too many variables.
I do have charts that will enable you to calculate wind components for every 10 degrees though if anyone is interested in that?
It basically would say that if you were riding on a heading of north (360) and the wind was blowing from a heading of 300@10kts, it will tell you what your headwind and direct (90) crosswind components are.
Then you could do simple math and get some form of a percentage like pinkrobe has found or come up with or estimated.