Mad Alchemist: Relative Bitterness Ratio (RBR)

My belief--and the central purpose of this article--is that the Bitterness Ratio that many homebrewers use (myself included) can be easily made more accurate by focusing on more than Original Gravity and International Bitterness Units. If you are unfamilar with Bitterness Ratio (expressed as BU:GU), please see the BeerSmith BU:GU article linked below.

Some factors impacting beer balance are not numerically quantifiable in simple terms. Examples include the malt bill (e.g. 1 lb of Honey Malt contributes far more sweetness than 1 lb of Chocolate Malt--although I almost tried to factor SRM into the new calculation), adjuncts, yeast, mash schedule, and hop variety. You must use your judgment and experience with regard to balance in these areas, because numbers are limited in what they can express.

That said, one piece of data we have available to us is not figured into the standard Bitterness Ratio; attenuation. The more attenuated a beer is after fermenting, the fewer fermentable sugars--and therefore residual sweetness--are left behind. Without taking attenuation into account, the Bitterness Ratio is not quite as accurate as it could be in quantifiable terms.

For example: A beer that starts out at an OG of 1.050 at 25 IBU would be said to have a Bitterness Ratio of 0.5. If it were split into two batches and one had an apparent attenuation of 80% (Beer A), while another had an apparent attenuation of 60% (Beer B), Beer A would be perceived to be more bitter than Beer B, as the latter has considerably more residual sweetness.

The numbers in the tables and charts linked below reflect this theory that I have taken to calling the Relative Bitterness Ratio (RBR). The purpose of BU:GU and RBR are one in the same; to aid in properly balancing a beer against your taste expectations. Since balance expectations are set relative to all beers, we take into account a beer's Apparent Attenuation in comparison to the average beer, and increase the BU:GU if it is more attenuated than average or decreate the BU:GU if it is less attenuated than average.

Just like BU:GU, RBR is more bitter when the number is higher and less bitter when the number is lower. If you are used to BU:GU numbers, you will already have an understanding of RBR because the numbers are essentially the same (~0.5 is average balance--anything lower leans toward sweetness, and anything lower leans toward bitterness).

The numbers listed under "Relative Bitterness" should appear familiar to those who have been using BU:GU for a period of time. The Relative Bitterness Ratio can be determined with a fairly simple formula using data you likely already have if you know your BU:GU.

RBR = (BU:GU) x (1 + (ADF - 0.7655))

RBR = Relative Bitterness Ratio. ADF = Apparent Attenuation. 0.7655 is the average ADF of all beer styles. Since the Relative Bitterness Ratio takes into account balance relative to all beer styles, it uses this as a constant. You are comparing your beer's ADF against the average ADF (0.7655), then adjusting the standard Bitterness Ratio accordingly (it goes up if your ADF is higher than average, down if your ADF is lower than average). Just like BU:GU, higher numbers mean more bitter, lower numbers mean less bitter, and 0.5 is roughly average balance.

How do you use this formula? Here's an example.

Beer A has an OG of 1.050 at 25 IBU. The BU (Bitterness Units) is 25 and the GU (Gravity Units) is 50. Therefore, the BU:GU ratio is 0.5 (25/50)

The Apparent Attenuation of Beer A is 80%, or 0.8. So, the formula is as follows:

RBR = (BU:GU) x (1 + (ADF - 0.7655))
RBR = (25/50) x (1 + (0.8 - 0.7655))
RBR = 0.5 x (1 + (0.0345))
RBR = 0.5 x 1.0345
RBR = 0.51725

Since Beer A has a higher ADF than the average beer, it will be a little more bitter, relatively speaking. This means the Relative Bitterness Ratio (RBR) is slightly higher than the Bitterness Ratio (BU:GU).

Beer B has an OG of 1.050 at 25 IBU. The BU (Bitterness Units) is 25 and the GU (Gravity Units) is 50. Therefore, the BU:GU ratio is 0.5 (25/50)

The Apparent Attenuation of Beer B is 60%, or 0.6. So, the formula is as follows:

RBR = (BU:GU) x (1 + (ADF - 0.7655))
RBR = (25/50) x (1 + (0.6 - 0.7655))
RBR = 0.5 x (1 + (-0.1655))
RBR = 0.5 x 0.8345
RBR = 0.41725

Since Beer B has a lower ADF than the average beer, it will be a little less bitter, relatively speaking. This means the Relative Bitterness Ratio (RBR) is slightly lower than the Bitterness Ratio (BU:GU).

As you can see from the example above, the calculation is quite simple when you already know your beer's expected apparent attenuation, gravity units, and IBUs.

If you're not interested in calculating by hand, use this calculator!

Relative Bitterness Ratio Calculator
BU:GU Ratio
Apparent Attenuation (%)
Relative Bitterness Ratio
RBR = (BU:GU) x (1 + (ADF - 0.7655))
by Ryan "Mad Alchemist" Shwayder

The following links give more details and insight into how I arrived at this formula. The first is simply a whole bunch of data in a table. This is followed up by two charts that illustrate beer balance per style (the first using BU:GU and the second using RDR). Next is a table of the relative balance of beer styles to illustrate how BU:GU and RDR change the order of balance of beer styles relative to each other. The other two are useful links to external sources.

NOTE: If you wish to reproduce this information, you may do so if a link is provided to the original article(s) and credit is given to the author, Ryan Shwayder.