title_body: by-volume/by-weight conversion formula
upvoted_answer: I'm a Chemical Engineer and it frustrates me that everywhere on the internet appears to be using this linear approximation. Yeah it's probably okay for hobby brewers, but for anyone actually interested in solving the problem for example use in software design or higher ABV products, this approximation is really not good enough. 
  
  This is actually a ridiculously complicated subject and it all boils down to the fact that at a molecular level, water and ethanol interact with one another with what are known as hydrogen bonds. Now you can just use an empirical lookup table or regress a tonne of data, but if you're interested in the root of this problem you should do some research into what are known as equations of state. In particular UNIQUAC for ethanol-water mixtures. It get's even worse when you realise that these equations of state describe gaseous behaviour remarkably well, but require additional thought to be applied to liquids. 
  
  People dedicate their entire lives into perfecting a generalised equation of state to describe the interactions between all chemical components. ANYWAY I digress... 
  
  I've done some number crunching myself using UNIQUAC and have come up with the following simple formula. Like yours above, it's only applicable to ethanol-water mixtures, and I've only validated this equation up to an ABV of 50% so be weary of going higher. This equation has an R-Squared value of 1. 
  
  ABW = 0.1893*ABV*ABV + 0.7918*ABV + 0.0002
  
  Try it yourself :)