How to calculate BU:GU and Relative Bitterness Ratio (RBR)

The BU:GU ratio represents the bitterness value (IBU) divided by that of the original density (OG) of the beer. Many homebrewers ignore it or do not know it, but it is actually very useful when composing a recipe, because it estimates the perception of the bitterness that we will have in the finished beer. As we know, each style classified in the BJCP has ranges of values ​​within which each beer must be, for example an APA has from 30 to 50 IBUs and from 1,045 to 1,060 of OG. If we brew a beer close to the low initial density limit and the maximum IBU limit (BU: GU ratio of 1.11), we will have an unbalanced bitterness result. On the contrary, with few IBUs and too much OG (BU: GU = 0.5) we will obtain a beer that is not very bitter and less suited to the style.

This value is present in every Homebrewing program, in BrewFather we find it under the list of hops. In BeerSmith it is not shown by default, but it is possible to click “Select Fields” and make the “Bitterness Ratio” value visible, in order to make it appear at the bottom of the recipe.

In the following table we can see the BU: GU ratio range recommended for each style classified on the BJCP.

Click here to see the chart.

With these notions we already have an estimate of what the bitterness of the finished beer will be, but if we want to know more, there is another fundamental factor that this formula does not take into consideration: attenuation!

The more beer is attenuated at the end of fermentation, the less fermentable sugars, and therefore residual sweetness, we will have in our beer poured into the glass.

Without taking it into consideration, the formula is not as accurate as it could be.

Let's take an example: Let's take a beer with OG 1.050 and 25 IBU, so BU: GU ratio of 0.5. If we split this beer into two batches and ferment one with a yeast that attenuates at 80% (Beer A) and the other with one that attenuates at 60% (Beer B), we will obtain a beer (A) that is drier and therefore with a perceived bitterness much more intense than the other (B), which instead has a higher residual sweetness and therefore will have a much less perceptible bitterness.
If we introduce the apparent attenuation value to the BU: GU calculation formula we get:

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

Where is it:

RBR = relative bitterness ratio.

ADF = apparent attenuation.

0.7655 = average ADF of all beer styles

Since RBR takes into account the equilibrium for all styles of beer, we will use this value as a constant in the formula.

Just like the BU: GU ratio, the bitterness ratio increases as the value rises, decreases as it falls; 0.5 is an average value.

We then apply the formula to the previous example:

Beer A has an OG of 1,050 and 25 IBUs, so the BU: GU ratio is 0.5 (25/50)

The apparent attenuation of beer A is 80%, or 0.8, so the formula will be 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

As the RBR value is higher than the average (0.5), beer A will have a relatively higher perceived bitterness.

Beer B always has OG at 1,050 and 25 IBU, so the BU: GU ratio remains 0.5 (25/50)

The apparent attenuation of beer B is 60% or 0.6. So, the formula will be 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 the RBR value is lower than the average (0.5), beer B will have a relatively lower perceived bitterness.

As you can see from the examples, the RBR value will give us a more precise estimate of the perception of bitterness that we will have in our beer. It is very useful when creating the recipe, as we have seen that beers with the same BU: GU ratio value can actually give rise to completely different results.

The calculation is very simple, but if you want you can use this Tool 
(thanks to MadAlchemist)

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