IBU Calculation

Hop

Let see some terminologies...

AAU - Alpha Acid Units

It is a measurement of potential bitterness in hops. The percentage of alpha acid in a given sample of hops multiplied by the weight in ounces of that sample. One ounce of hops with an alpha acid content of 1 percent contains 1 AAU, or .01 ounce of alpha acid.

HBU - Home-brew Bitterness Units

It is another method by which home brewers can determine how much hops to use. Home-brew Bitterness Units equals the percent alpha acid of hops multiplied by the quantity in ounces of hops used. If, for example, a recipe of a given volume of beer calls for 2 ounces of 5 percent alpha acid Cascade hops, it is equal to 10 HBU's.

If your Cascade hops are only 4 percent alpha acid you will know to use: 10 HBU ¸ 4% = 2.5 oz of hops. Or, if you wish to use another variety of hops, say Centennial hops at 10 percent alpha acid, you know to use: 10 HBU ¸ 10% = 1 oz of Centennial hops.

IBU - International Bitterness Units.

The term IBU is related to the end of the process with the final bitterness of production. One Bitterness Unit is equal to 1 milligram of isomerized alpha acid in 1 liter of wort or beer or 1 part per million isomerized alpha acid. This is a system of measuring bitterness devised by brewing scientists and is an accepted standard throughout the world. Home brewers usually do not have the sophisticated equipment to measure actual BU's and often use the system of HBU's to closely approximate the desired bitterness in their beer.

To define the IBU of a beer, we must take into account some factors such as:

The vigor of the boil: the Lupulin acts as an oil and, as such, depends on an intense boil for its perfect dissolution in the wort
Boiling time: the longer the wort boiling time, the higher the percentage of Isomerisation and the more bitter the beer will be
Wort thickness : the higher the wort thickness, the smaller the space for alpha acids to be isomerized

Hops can be divided into two general categories: bitterness and aroma (flavor).

Bitterness hops are rich in alpha acids, about 10 percent of their weight.
Aroma hops generally contain less, about 5 percent, and produce a more desirable flavor and aroma to beer.

How to define the intensity of bitterness?

In terms of IBUs, typical values, internationally used, are between 20 and 40 IBUs.

North American light beers, like Coors, have a bitterness of only 10-15 IBUs.
Soft beers like Heineken have a bitterness close to 20-25 IBUs.
American microbreweries like Samuel Adams Boston Lager have an approximate bitterness of 30 IBUs.
"Strong" beers like Anchor Liberty Ale and Sierra Nevada Celebration Ale have a bitterness of 45 IBU or more.

Calculation of the Hop Bitter - AAU

The first step is to calculate the alpha acid units (AAUs) for each hops.

The AAU formula uses weight in oz. To use in grams we need to dived the weight in grams by 28,35.

AAU (minutes) = Weight (grams) / 28,35 (oz) x % alpha acids

Ex 1: 1,5o z or 42,52 g of Perle Hop at 6,4% of alpha acid

AAU (60') = 42.52 (g) / 28,35 (oz) x 6,4 = 9,6 AAUs of Perle

Ex 2: 1,0 oz or 28,35 g of Liberty Hop at 4,6% of alpha acid

AAU (15') = 28.35 (g) / 28,35 (oz) x 4,6 = 4,6 AAUs of Liberty

Hop substitution - Let’s illustrate a practical use of this calculation

You’re brewing a basic American pale ale, and the recipe calls for a 60-minute addition of one ounce (28 grams) of Chinook hops with 12 percent alpha acids.

But you don't have Chinook , only Nugget instead. Your Nugget hops are 14 percent alpha acids, not 12 percent.

In order to do the substitution, you’d first calculate the number of AAUs that the original recipe called for with Chinook:

AAU = 1 ounce (28 gram) x 0.12 = 0.12 ounce

Now you want to deliver that same amount of alpha acid using your 14 percent Nugget hops, so just use the equation the other way around:

Weight (Nugget) = AAU ÷ Alpha acid percentage (Nugget)

Weight (Nugget) = 0.12 ounce (3.4 gram) ÷ 0.14

Weight (Nugget) = 0.85 ounce (24 gram)

So, in order to achieve the same level of bitterness using our 14 percent Nugget, we only need 0.85 ounces (24 grams).

In this case it isn’t a big change, but it can be in case of different alpha acid concentration.

How to calculate the IBU?

IBU = AAU x U x 75 / V

AAU (Already explained above Alpha Acid Units)

U (Utilization factor)

For example: to calculate utilization factor for a wort gravity of 1,057 in 30 minutes. First look (in the table below) at the utilization factor values for 1,050 and 1,060. These values are 0,177 and 0,162 respectively (for 30 minutes).

The difference between both factors is 0,015, it means that between 1,050 and 1,060 we assume to have linearly 10 times 0,0015 (0,015 divide by 10) . The wort gravity, as already mentioned, is 1,057.

To calculate the utilization factor for this gravity, in this case, we need to multiply 0,015 times 7 (that equals to 0,011) and subtract from 0,177. Result is 0,166 of utilization factor.

Why subtract and not add? Because they are inversely proportional. As you can see in the table below, the bigger the gravity is, the lower the utilization factor.

75 - Conversion from English units to the metric system

It is a constant value. The unit for the IBU is milligrams per liter, so to convert "ounces per gallon" you need a conversion factor of 75.

To be precise 10 x 28,34952 (oz) /3,785412 (gal) = 74,892.

V - Wort Volume in liters (Self explained)

According to the table below, uses for 60 minutes and 15 minutes at a wort density of 1,080 are 0.176 and 0.087, respectively. Inserting these values in the IBU equations suggested above we have:

IBU (60) = 9.6 x .176 x 75/5 = 25 (round to the nearest whole number)

IBU (15) = 4.6 x .087 x 75/5 = 6

Which gives a grand total of 31 IBUs (25 + 6) = 31

Conversion curve - IBU Calculation - another way (based on the book "Designing Great Beers" and adaption)

As we see, the longer the hops stay at the boiling temperature, the more bitterness is acquired by the beer, by a process called isomerization of alpha acids. There are several techniques to perform this calculation depending on the time the hops are boiling and software such as Beersmith can help a lot in this process.

If you do not have software on hand, this table below, extracted from the book Desiging Great Beers, shows how much of the alpha acid is isomerized according to the time in contact with the wort in the boil. The data were obtained by observation, by the author Ray Daniels and can be used to obtain a rough approximation of the final value.

Total IBU calculation

To calculate the total IBUs in a beer, you will need to know some information about what can be assumed in the boil.

Hops - the weight, in grams, of the amount of hops to be used
Relative Bitterness% - the percentage of use of hops, based on the time, as seen in the table above
AA% - the percentage of alpha acids of the variety of hops used
Vol - the volume of wort, in liters, in the boil
Wort Gravity - Measured pre-boil
Corrected WG - the corrected gravity of beer (if it is higher tan 1,050)

Before continuing calculating, let's see what this corrected gravity would be. When we have a very dense wort in the boil, especially with very alcoholic beers, the isomerization will be reduced, and therefore we must apply an adjustment factor to the recipe. For beers with a gravity below 1.050g/ml there is no need for adjustment, but above that, we need to apply the following formula:

Corrected WG = 1,050 + ((Wort Gravity - 1,050) / 0,33)

In this case, the Wort Gravity should be measured before the boil. Thus, a wort with a gravity of 1.075g/ml after adjustment would have a factor of 1.126 to be applied in the calculation of the IBU.

Now, knowing how to correct the gravity, we can finally go to the IBU calculation.

IBU = (Hops x Relative Bitterness% x AA% x 10) / (Vol x Corrected WG)

For example, imagine that we are going to use 100g of Saaz hops (4% AA), in pellets, after 30 minutes of boiling for 22 liters of wort with a density of 1,075.

Substituting the values in the formula, we have the following result for the IBU of that use:

IBU = (100 x 24 x 4 x 10) / (22 x 1,126) = 38,8 = 39

Remember that if your beer has several additions of hops, this value must be calculated for each of the additions, adding all IBU values at the end, to find the total of the beer.

Reference: http://howtobrew.com/book/section-1/hops/hop-bittering-calculations

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