When I attended the Siebel Diploma Course in 1988, I asked the instructors if our class could brew a 5-gallon batch of beer. They said yes. It shouldn't be too surprising that only a handful of students were interested in the class brew - I was the only home brewer & craft brewer wannabee in the class. All of my fellow classmates, every one of them, came from large (mega) brand breweries from all parts of the globe.
I was put in charge of the project, and had fun educating my classmates about beer styles. None of them had ever heard of beer styles; they had only heard of beer brands. I wanted to make a lager because up to that point I had only homebrewed with ale yeast. Of course, to them the only difference between an ale and a lager was something the marketing department did with the label.
My project team was up for anything I suggested, including double bock, my first choice. I brought in a variety of imported lagers for them to taste. One fellow spat out the double bock and declared it tasted like goat piss. I calmly asked him when he last tasted goat piss. Jokes aside, it was clear that a lighter lager was called for. Since it was autumn, we settled on an Oktoberfest.
On the brew day, our instructor had us weigh out hops according to a 1/5th ratio: 2/5 went in at Beginning of Boil, 2/5 went in 20 minutes Before the End of Boil, and 1/5 went in at the End of Boil. I took mental note of that.
The following spring (1989) found me Brewmaster at my first paid brewing job: Golden Gate Brewing Co. in Berkeley, California. I was in over my head (that's another story) and trying to convert my old extract 5-gallon homebrew recipes to all-grain 10-barrel recipes. (They should have high school kids doing math problems like this - applied math would be so much more fun!)
I needed to come up with a formula for IBU, where the hop alpha could change from batch to batch, but my formula would compensate for that and keep my beers consistant. After going into "Math Brain Mode" for three hours, and using the 1/5th ratio I had learned at Siebel, I woke as if from a trance. There at the bottom following several pages of mathematical scribbles was my IBU Calculations formula. I have used this formula ever since.
How to Use the IBU Calculations:
= ounces to use for the batch.
The (f) factor starts out as an estimate and you will want to modify it as you taste your finished beers, or when you get your actual IBU levels tested. (Algebra is great, because if you know the values for three of the variables, you can solve for the fourth, which means you can work backwards to resolve for the factor if you have a firm IBU value from a lab test.)
Basic IBU Formula:
Oz. = [IBU x (f)] ÷ a
You'll need to solve for ounces separately for each of the three hop additions. For the final hop addition the answer would be divided in two in order to keep the 2/5, 2/5, 1/5 ratio. Of course, since the final hop addition doesn't add a lot of actual bitterness to the batch, I often round that up or down. Dry-hopping is not factored into this formula, so if I want to dry hop, I just dry-hop somewhere between 2-8 pounds per 10 barrels.
three hop additions that this formula are designed for are:
estimate for a 5-gallon
batch is that the factor (f) = about 0.4.
Disclaimer: It is my experience that calculated IBU is very logarithmic, and this formula doesn't account for that. You could make up a set of charts or tables with varying factors for each IBU level for a certain size batch (like my Schwartz Factors), but you would need a lab that could test IBU for you.
Then, you would work the formula backwards to solve for the factor at each of several IBU levels for your batch size. However, I suspect IBU calculations are more complex than that, as your starting gravity has a huge effect. To be completely accurate, the formula would probably need to solve for three dimensions because you would have varying gravity beers and varying IBU-level beers, and each combo would need its own factor.