Beer Math – Hops and IBUs

The last couple of months we looked at the basics of some of the math of malt, and introduced the important concept of GU, or gravity units. This month we’ll look at hops and IBU calculations, and a better way to evaluate the bitterness of your beer by incorporating GU.

Before we get into the details, a few disclaimers – all these calculations are using the Tinseth formula; attenuation is not taken into account; and whirlpool hops will be a topic for another day!

Instead of starting off with how to calculate the IBUs of your beer, we’ll instead introduce the topic of BU:GU, which is just the ratio bitterness units (BU) to gravity units (GU) of your beer.  This is a better way to think about the bitterness of your beer instead of IBUs alone, as it takes into account the original gravity, which allows you to evaluate your recipe based on its perceived bitterness. For example, nobody would call an Imperial Stout hoppy or bitter, even though it most likely has a higher IBU than an IPA, but it’s much higher starting gravity helps to balance that out, reducing its perceived bitterness.

To help explain that further, the table below does a good job of how the final beer will be perceived (extra malty, slightly malty, balanced, slightly hoppy, extra hoppy) based on it’s starting gravity and total IBUs.

With this information in hand, let’s revisit our recipe and determine how many IBUs we should aim for.

Style – IPA
OG – 1.060
Efficiency – 72%
Volume – 20L
Ingredients
Pale malt – 80%
Munich 10 – 10%
White wheat malt – 5%
Caramel 60 – 5%

As we have a starting gravity of 1.060 (or 60 GU) and it’s an IPA let’s choose extra hoppy from the chart above, which would give us an IBU range of 40-50. The decision here is ultimately up to you and it’s been said that it’s impossible to tell a 5 IBU difference, so let’s choose 50.

Now that we know how many IBUs we want our beer to have, let’s look at the formula for calculating IBUs, which is actually mg of alpha acids/L:

g of hops – amount of hops needed in g (this is multiplied by 1,000 as the formula uses mg)
Utilization % – utilization of the hops, as a function of gravity and boil time, expressed as a decimal
Alpha acid % – alpha acid of the chosen hops, expressed as a decimal
Litres of cool wort – batch size in L

You might also come across Alpha Acid Units (or AAU), which is just your hops’ alpha acid % * weight of hops in ounces.

We can also rewrite this formula for calculating the amount of hops we need, based off a target IBU:

Before we can go any further with this, we need to know where to get our utilization % from. For this, we’ll use a table that’s available on John Palmer’s site (http://howtobrew.com/book/section-1/hops/hop-bittering-calculations), which I’ve condensed below. Palmer’s site also provides the formula used to populate this table if you’re interested. While this table isn’t perfect, it’s close enough for homebrewing purposes:

For our first example, let’s use one addition of Nugget hops (my package here has an alpha acid of 14.2%) at 60 minutes.

So, to get our targeted 50 IBUs, we’ll need 33 g of Nugget to be boiled for 60 minutes. Now, this wouldn’t make a very exciting beer, so let’s add some hops in with 5 minutes left in the boil – 42 g each of Strata (12.9%) and Citra (14%). We’ll start with these additions first, and then calculate how much nugget we’ll add at 60 to give us the final IBUs that we’re looking for.

Now that we’ve figured out how many IBUs our 5 minute additions of Strata and Citra contribute, we need to calculate how many grams of Nugget (14.2%) we’ll need to make up our remaining 27 IBU (50-11-12 = 27).

From all this, we can see that for our IPA with an OG of 1.060 and a target of 50 IBU, we need to add 18 g of Nugget at 60 to give us 27 IBU, and 42 g each of Strata and Citra to give us 11 and 12 IBU, respectively.

These formulas above can easily be adjusted based on the alpha acids of your particular package of hops, the gravity of your wort and boil time which changes the utilization, and batch size.

Overall this is a simplified version of what exists today which can also take into account mash hops, first wort hops, whirlpool hops, age of hops, etc, but can get you pretty much all the way there.

Next month, we’ll look at some basic water adjustments, to help dial in your recipe further!

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