The easiest way to work with hops is, of course, not to. Simply buy a can of pre-hopped malt extract and let someone else worry about the hops. But this convenience comes at a price: You are left brewing with the malt producer’s choice and amount of hops. This does not mean that you will be brewing inferior beer. But by selecting your own hops, you can experiment and expand your homebrew skills.

The key specifications on a hops package are quite easy to understand and calculating your own hops quantities from these specifications is a matter of applying one simple formula — the same formula the pros use. First, let’s look at what the active ingredients in hops do for your beer. Then we’ll delve into the math we need to master to control these ingredients.

The Anatomy of Beer Appeal: Bitterness, Flavor, Aroma
We’ll start with a bit of botany: Hops is a wild and prolific creeping vine that belongs to the hemp family.  Hemp, in turn, belongs to the order of nettles. There are only two species of hops, and only one of these species, humulus lupulus, contains the resins needed to brew beer.

Only female hops are useful to brewers. Male hops don’t have lupulin glands, and these glands are the source of hops’ all-important bittering substances. Because male and female flowers normally develop on separate plants and only the female plants develop hop cones (which is where the lupulin glands reside), the two hop genders are usually easy to tell apart.         

Brewers generally distinguish between three main contributions that hops make to beer: bitterness, flavor and aroma. Each of these terms describes different hop additions to the wort, as well as different active ingredients in the hops that are released during those additions. Simply put, the “bittering hops” addition gives beer its bitterness, the “flavor addition” adds flavor and the “aroma addition” adds aroma. Each of these additions balances the malty sweetness of the beer in a different way. Some of these ingredients are highly wort-soluble and even volatile — which means they  evaporate easily — while others are soluble only after much heat and agitation. In addition to influencing beer taste, hops also help preserve beer.

Hop Bitterness
Hop bitterness is largely an up-front sensation. It can be extremely mild, as in a typical light American lager, or it can be downright mouth-puckering, as in some northern German pilsners.

The hops’ bittering effect stems mostly from “alpha acids.” These are soft resins with such tongue-twisting names as humulones, cohumulones, and adhumulones. Part of the taste variations between different hop varieties — and between the same variety in different growing years — stems from the difference in the relative proportions of these alpha acids in the lupulin glands. In general, though, humulones are by far the most abundant of these acids.

The alpha acids in hops remain relatively stable, as long as the cones (or the pellets made from cones) are stored cold and vacuum-packed in an oxygen-barrier pouch. (If you can smell the hops through the package, don’t buy them.) Alpha acids only become wort-soluble after prolonged exposure to intense heat and physical agitation during the kettle boil. This process is called “isomerization.” It involves the rearrangement of the molecule’s atoms into iso-alpha acids.

When exposed to air instead of liquid, however, alpha acids oxidize over time, and this process accelerates in warm environments. Oxidized alpha acids are no longer wort-soluble and can, therefore, no longer contribute to the beer’s bitterness. To make good beer, it is essential to use the freshest hops you can find and store them properly, in the refrigerator or the freezer, which greatly slows oxidation.

There is a second group of soft resins, beta acids. These resins also contribute to bitterness, but only marginally, if you are using fresh hops. The names of these beta acids are analogous to those for alpha acids: lupulones, colupulones and adlupulones.

Beta acids are about as stable as alpha acids, but, unlike alpha acids, they become more (not less) wort-soluble as they get old and become oxidized. Oxidized beta acids are called hulupones. Generally, the perceived bitterness derived from oxidized beta acids is milder than that derived from unoxidized alpha acids, and there are ways to calculate the relatively small contribution that beta acids make to beer bitterness. Commercial breweries tend to pay quite a bit of attention to beta acids, but, for practical homebrewers, their bittering contributions may not be worth quantifying, especially if we stick to fresh hops.

Hop Flavor
Flavor is the middle sensation that you experience while the beer fills your mouth. Much of it comes from volatile, ethereal hop oils that are released by the second hop addition to the wort. Hop flavor components have such impressive names as myrcene, humulene, caryophyllene and farnesene. They survive in a short, but not in a prolonged, rolling kettle boil. (They survive even better if not exposed to heat at all; in other words, in dry hopping.) Myrcene especially escapes quickly or oxidizes under exposure to heat. Because hops flavor comes primarily from hops added to the wort near or at the end of the boil, the timing of the flavor addition is crucial.

Hop Aroma
Aroma is the “nose” of the beer. It also stems from volatile oils and their derivatives and stays in the beer only if not exposed to high heat for any length of time. Hop aroma thus comes from hops that are best added after the boil, when the temperature of the wort starts to drop or even when the wort is cool. Roughly 180° F (or about 80° C) is a great temperature for adding aroma hops: The wort is still hot enough to sanitize the hops, but cool enough not to drive all of the volatiles immediately into the atmosphere.

Polyphenols as Preservatives
The astringent component of the hop flavor spectrum comes mostly from polyphenols, such as oxidized tannins. These are great wort-soluble preservatives, but, in excess, they would make our beer undrinkable. Fortunately, enough of them precipitate out into the trub during a vigorous boil so that the beer remains palatable.

So What’s “Nobility” In Hops?
Many beers — especially German and Czech lagers — are made with so-called “noble” hops. Noble hops are merely different from, not better than, other hops. Hops are considered noble if they contain a relatively small proportion of the alpha acid cohumulone and a relatively high proportion of the flavorful oil humulene. There are four traditional noble varieties: Hallertauer, Tettnanger and Spalt (from southern Germany) and Saaz (from the Czech Republic). Modern botanical science has produced new varieties of noble-type hops, such as Mount Hood, which is a triploid variation of Hallertauer. (Triploids are plants that do not develop seeds and thus cannot reproduce.) New noble-type varieties generally grow well in the Pacific Northwest.

Measuring Hop Additions
While bittering can be estimated relatively easily in a homebrew kitchen (and the formula is explained below), you would need complex lab equipment to measure flavors and aromas. But there are several practical rules of thumb that let you determine how much flavor and aroma hops you need to achieve a desired effect.

The mathematically elusive nature of hops flavor and aroma is probably part of the reason why some authors use the terms “flavor” and “aroma” interchangeably and thereby create confusion. For our purposes, it is best to simply rely on the timing of the hops addition relative to the start and the end of the boil to distinguish between the two. Flavor hops are added very late in the boil, and they still contribute taste components (but not much bittering) to the beer, while aroma hops added at the end of the boil or later contribute mostly components that you can smell. They give the beer bouquet.
 
Bittering Calculations
In commercial brewing, bittering in wort or in beer is measured in International Bittering Units (IBUs). Let’s get the technical definition out of the way, right up front: 1 IBU equals 1 milligram of dissolved iso-alpha acids in 1 liter of wort or beer.

Don’t worry: At home, you will never need to actually measure the IBU value of your wort or finished beer. You would need a fancy lab for that. Instead, you only have to calculate the amount of hops needed to achieve the target IBU value as specified in your recipe. It’s that simple.

To put IBU values for different beers in perspective, consider the following reference points: The common human taste threshold for bitterness is 4 IBUs in water and about 8 IBUs in beer. The upper solubility limit for iso-alpha acids in cold beer is roughly 100 IBU. The mildest American lagers may have an IBU level of 8, most ales and lagers have about 25 to 35 IBUs and IPAs, pilsners and barleywines may have 50 IBUs or more.

Many homebrew texts, including Brew Your Own, list hops in terms of Alpha Acid Units (AAUs). AAUs are the same as Homebrew Bittering Units (HBUs), which you also see in many homebrew books. The AAU was invented by Dave Line, the “father” of modern homebrewing, as a practical alternative to IBUs.

While working with AAUs has the advantage of simplicity, it also has the disadvantage of uncertainty, because AAUs do not relate to the volume of beer that you brew. One AAU is simply defined as 1 ounce (about 28 grams) of 1 percent alpha-acid hops. This is an easy way to express the amount of hops you add to your beer, but 5 AAU in a five-gallon batch will not lend the same amount of bitterness as 5 AAU in a ten-gallon batch. AAUs also do not account for any alpha acids lost during the brewing process. For these reasons, AAU does not relate the final bitterness of the beer. It is not possible, therefore, to construct a mathematical correlation or conversion between AAUs and IBUs.

Most recipes will contain a specification for the target bittering range in IBUs. If it does not, you can still use the formula below to calculate the bittering value you will actually get, but you can never be sure if this is the value the recipe author actually had in mind.

To hit target bittering values with the hops that you purchased, you need to know the hop’s “alpha-acid rating,” expressed in %AA. This is the minimum information that ought to be printed on any hops package and it is essential for working with hops.

The Formula
This is the only formula you will ever need to calculate your bittering hop additions to your kettle. If your recipe calls for two or more bittering hop additions, this formula tells you the total amount required for all additions. Note: Flavor and aroma hops quantities are in addition to the quantity calculated with this formula.

                                   (V x IBU)
Bittering hops (oz) =   ———————
                             (U x %AA x 7500)

To calculate kettle hops additions (in ounces), plug the target IBU value of your beer, your final batch volume (V) in gallons, the hop’s alpha acid rating (%AA) and the hop utilization coefficient (U) of your system and process into this formula. We’ll assume a hop utilization coefficient of 30% (0.3) for reasons I’ll explain in a minute. Note: Be sure to use the final volume of your batch, not the volume you boil.

Here’s a quick example. Say you brew a five-gallon (19 L) batch of beer with a target IBU of 25, and you use Mt. Hood bittering hops of 4.8% AA. You would use the formula as follows:

    (5 x 25) ÷ (0.3 x 0.048 x 7500) = 125 ÷ 108 = 1.16

For this batch of beer, you would need roughly 1.16 ounces of bittering hops to hit the target IBUs.

Explanation of Variables
For all practical purposes, you have to guess the hops utilization coefficient (U). In theory, of course, all the alpha acids contained in the hops should be usable in the wort. In practice, however, the boil can extract only a portion of them. The precise amount depends on many factors, such as the length and vigor of the boil, the geometry of your kettle, and even the elevation of the place where you live.

The longer your boil, the better will be your hops utilization. In many commercial brew systems, hops utilization is about 28% for a 60-minute boil, 33% for a 90-minute boil and 38% for a 100-minute boil. The shape of your kettle may influence the amount of physical agitation during the boil. A rolling boil yields better utilization than does a placid one. Hops utilization is also greater at higher boiling temperatures. That’s why some breweries boil their wort in a closed system under pressure. In an open kettle, the barometric pressure and thus boiling temperature decreases as your elevation increases. So you get less out of your hops in the mountains than you do in the plains. (For a further discussion of hops utilization, see the sidebar at right.)

Because the factors that influence hops utilization are difficult to measure, simply assume for starters that your hops utilization is 30% (or 0.3). Then brew your first batch with this formula, taste the finished beer and adjust your utilization figure accordingly. Note that alpha acid ratings are often listed on the hop package as, for instance, 4.8% AA or 11.6% AA. In our formula, this translates into 0.048 or 0.116, respectively.

Some authors recommend more complicated formulas for calculating the desired amount of bittering hops. They may include such factors as gravity correction values and the declining contributions of second, third and subsequent kettle hops additions to the aggregate amount of bittering compounds in the finished beer. Now, it is true that hops utilization decreases as wort gravity increases. It is also true that hop additions even late in the boil still contribute small amounts of alpha acids to the wort. But such mathematical precision loses its relevance to brewers who can only guess at the true hops utilization coefficient at work in their brew setup.

However, if you want to walk the extra mathematical mile, you can get a rough idea of the bittering contribution that the different hop additions, including the later flavor and aroma ones, make to the overall bitterness of your brew. Just use the above formula separately for each addition, and use approximately 30% U for the first addition, approximately 15% U for the second and 2% to 5% U for the third addition. Then add up the three IBU values to get the total bittering value.

The above assumes a flavor addition at 30 minutes before the end of the boil and an aroma addition about five minutes before the end. For different times, make a guesstimate based on these values.  

Flavor and Aroma Hops
The alpha-acid strength of a given hops is generally no indication of its flavor and aroma potential, and the hop types for beer flavor and aroma naturally need not be the same as those used for bittering. In fact, many brewers use “high-alpha” hops for bittering (such as Chinook or Galena) only because this gives them a bigger alpha-bang for their hops buck. They then use noble hops (such as Hallertauer or Saaz) for the other two additions precisely because noble varieties have relatively high flavor and aroma potential, in spite of their relatively low bittering potential.

Volatile hop oils are the components that add aroma and flavor to the beer. The extent to which these oils and their derivatives stay in the wort and become part of the finished beer depends on many factors. Some of these factors are the timing of the addition, the quantity of hops and the variety of hops. Different varieties of hops provide different amounts of aroma potential for a given weight. For example, East Kent Goldings typically contains about 0.5 percent volatile hop oils, while Cascade typically contains one percent. It’s easy to see that for a given hop weight, the aroma potential may be vastly different.

There are a few simple rules of thumb that yield perfectly workable guidelines for flavor and aroma hops:

• For the average ale, calculate the amount of bittering hops as described in the formula above, then use about half that much in weight of whichever hops you choose for flavor. Then, for aroma, use the same amount as calculated for bittering.
• For a more delicately hopped beer, such as a Bavarian helles, use about a quarter of the amount of bittering hops, in weight, for flavor. For aroma, divide the calculated bittering amount in half.
• For an IPA or a Czech pilsner, both styles in which aroma must be pronounced, calculate your flavor hop as for ale. Then use up to one-and-a-half times the amount of aroma hops compared to bittering hops.
• If you want a truly simple approach, try this: For average ales, use about 4 to 6 grams per gallon of top-quality flavor hops near the end of the boil. Use about 8 to 12 grams per gallon of aroma hops after shutdown. For the average Bavarian lager, divide these ale quantities by two. For strongly aromatic beers, replicate the ale regimen, but be a bit more generous with the aroma hops.

Then, after a taste test of the fermented beer, adjust your hops amounts for your next brew, taking into account the flavor and aroma strength of the hops you use as well as your process choices. For your aroma yield, always consider the temperature of your wort at the last hop addition. The lower the temperature, the more volatile substances will stay in the wort and the less aroma hops you need.

Tasting the Result
The formula for bittering hops is fairly useful and straightforward within a certain margin of error. It is definitely much better than sheer guesswork. Use it to experiment with different hop varieties from different corners of the globe and see how the beer comes out. As homebrewers we should always emphasize the value of tasting and not get too hung up about theoretical analysis. If your beer has a flavor or aroma problem, simply keep careful notes of what you put into your brew, then take note of what your taste buds tell you, and adjust your quantities next time. After all, playing with ingredients is half the fun of homebrewing. The other half is drinking the fruits of your labor.

Horst Dornbusch is the author of “Altbier” and “Bavarian Helles,” two books in the Classic Beer Style Series by Brewers Publications. He lives in Massachusetts.