# How do you calculate hop bitterness in beer?

This is the final question we need to answer in this short guide on how to create your own brewing recipes. I hope that you have stayed with me so far.

It has been a long journey but hopefully you are undaunted and have picked up the basics of calculating a brewing recipe. If you have missed anything it might be worth going back to the first article – How do you create a brewing recipe.

But if you are happy then the next thing that we need to consider is the bitterness of the beer that we want to brew and answer the question – How do you calculate hop bitterness in beer?

As you know the bitterness of beer is derived from the hops that we use. However there are a few things that we need to consider so that we can fully appreciate the complexities of hop bitterness. Apologies as this may all be familiar to you but I think it is worth just going over it and refreshing our minds.

**What are hops?**

Hops are hardy climbing herbaceous perennial plants growing rapidly during the spring and summer to a height of at least 16 feet (5 m). Although the plant itself is large the brewer only uses a very small part of it – the cone. For the brewer the important constituents of the hop, the resins and oils, are found in the lupulin glands at the base of the hop cone. The resins, and in particular the alpha-acids, are responsible for the characteristic bitterness. It is the oils which provide the wonderful hop aroma and are, for many, what defines the difficult to describe hoppiness of beer. The brewer will select hops on the basis of what they want them to do in their beer. Therefore hops fall into one of three groups depending upon whether they are high in alpha-acids and so good for bitterness, have a good oil composition so would be ideal for aroma or have a little bit of both. The three groups are defined as bittering hops, aroma hops and dual purpose hops. Therefore varieties such as Target and Admiral which contain high alpha-acid levels are classed as bittering hops whereas, East Kent Goldings which contains low levels of alpha-acids but has a good oil composition is an aroma hop.

The oil component of hops range from 0.03% to 3% of the weight of the hop cone, compared to the resins which can constitute up to 15%.

As mentioned above it is the alpha acids which give rise to the characteristic hop bitterness that makes beer so thirst quenching on a hot summers day. However, the alpha acids themselves are not bitter. For the bitterness flavor to occur the chemical structure of the alpha acids needs to be subtly altered in a process called isomerization and it is these iso-alpha acids that are bitter. As you know the process of isomerization is greatly enhanced when heat is applied and this is the reason why we add bittering hops in at the start of wort boiling.

However, the process of isomerization during wort boiling is not a precise science and there are many things that can influence the isomerization process. For example the pH of the wort can greatly affect isomerization with a lower pH (<5.3) reducing isomerization and a higher pH (__>__ 5.4) enhancing isomerization. Time in boil as well as the age of your hops and the actual alpha acid content can all give rise to wide variations in hop bitterness. Therefore once again when calculating hop bitterness please bear in mind that the number you calculate comes with a slight warning. That warning is that because of the imprecise nature of the brewing process that we are using the calculated bitterness value should be taken as a guide only. The only accurate way of calculating hop bitterness is via laboratory analysis but unless you have access to a fully equipped brewing lab a calculation will have to suffice.

With the warning out of the way let’s consider how we calculate the hop bitterness.

## Equations, equation and more equations!

As you have found out so far from this guide us brewers like our equations and this is certainly true for calculating hop bitterness.

If you do an internet search for how to calculate hop bitterness you will find references to a number of equations. The main equations, most often cited in home-brewing publications, were derived by Rager, Tinseth and Garetz. Each calculates hop bitterness in terms of International Bitterness Units (IBU) in subtly different ways. For example the Rager equation is most often used in extract and partial mash brewing and takes into account the original gravity of the wort. It also seems to give IBU values higher than the other two equations.

The Tinseth equation is favoured by all grain brewers, produces lower IBU values than Rager but is perhaps considered to be the most accurate. We will therefore be using the Tinseth equation for calculating hop bitterness.

So what does the Tinseth equation look like? Well it is a bit of a beast so prepare yourself, the equation is:

Now many home brewers will try and use this equation to get a figure for their IBUs but for me life is too short to worry about the 100% accuracy of the calculation. Therefore I would say please don’t worry about using the above equation because this can be greatly simplified as much of the calculation concerns working out the alpha acid utilisation. Please also bear in mind the only accurate way of determining the IBUs of your beer is by laboratory analysis.

Therefore for the purposes of our recipe I am going to use a much more simplified version of the equation which is:

IBU = (Weight of hops x Alpha acid % x Alpha acid utilisation) / (Volume of wort in gallons x 1.34)

Or to make it simpler:

IBU= (W x AA% x U)/(V x 1.34)

Where:

W = Weight of hops

AA% = Hop Alpha acid content in %

U = Hop utilisation

V = Volume of wort in gallons

The alpha acid utilisation is very much a moveable feast as there are a number of things that can affect it such as pH and type of hops used i.e. whole hops or hop pellets. Generally the conversion of alpha acids to iso alpha acids is not very efficient so the utilisation is generally quite poor. A typical value for whole hops is 23% and for pellet hops is 30% and it is therefore worth trying these figures in your calculations.

Bearing this all in mind I think it would be sensible to try an example calculation to show you how it works and hopefully answer our original question – how do you calculate hop bitterness in beer?

Let’s go back to our original recipe for an ale at 5% abv with an OG of 1.050. In this instance I might decide to use 2 oz of whole hops with an alpha acid content of 5%, a utilisation of 23% and I have 25 litres (6.6 gallons) of wort.

Therefore:

W = 2 oz

AA% = 5%

U = 23%

V = 6.6 gallons

Therefore IBU = (2 x 5 x 23) / (6.6 x 1.34)

IBU = 230 / 8.844

IBU = 26

This is all very well but usually we would like to do the calculation around the other way so that we can work out the weight of hops required to give a certain IBU value.

The equation therefore needs to be re-arranged to calculate the weight of hops.

Therefore the re-arranged equation is below:

Weight of hops = (IBU x Volume of wort x 1.34) / (Alpha acid % x Utilisation)

Or

W = (IBU x V x 1.34) / (AA% x U)

Now we have the re-arranged equation let’s try another example. This time I would like to go mad and achieve a bitterness of 100 IBUs in my finished beer. I still want to make 25 litres (6.6 gallons) of a 5% abv ale however, this time I will use a higher alpha hop variety with an alpha acid content of 13% but instead of whole hops I will use pellets instead.

For this example my values are:

IBU = 100

W = ?

AA% = 13%

U = 30%

V = 6.6 gallons

Therefore the weight of hops I require is:

Weight of hops = (100 x 6.6 x 1.34) / (13 x 30)

Weight of hops = 884.4 / 390

Weight of hops = 2.3 oz

This example also illustrates the benefit of using hop pellets and a high alpha acid hop variety for bittering. If I was using my 5% alpha acid whole hops that I used in the first calculation I would need 7.7 oz rather than the 2.3 oz that I have just calculated.

That is it, the fairly straightforward method to answer the question how do you calculate hop bitterness in beer?