What’s Your IBU?

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What’s Your
O?
ne of the most important contributions of
hops to beer is bitterness. Bitterness pro-
vides a counterpart to the sweetness of the
malt to create a balanced beer. If you’ve
ever made an IPA that turned out more like
a bock, you know that making an accurate
estimate of the amount of bitterness impart-
ed by the hops is paramount to success in
brewing. This article will compare several
methods used to estimate hop bitterness.
The bitterness of hops is derived from
the bitter resins in the yellow lupulin glands.
These resins, or crystalline weak acids, orig-
inally were categorized into alpha-, beta-
and gamma-fractions (De Clerck, 1957).
The alpha- and beta-fractions are collec-
tively known as the soft resins because they
are soluble in hexane. The gamma resin
fraction is now referred to as the hard resin
fraction because it is insoluble in hexane.
The alpha-fraction is composed of a
group of related chemicals called the alpha
acids. Alpha acid, often referred to in litera-
ture simply as humulone, is comprised of
the chemicals humulone, cohumulone,
adhumulone, prehumulone and posthumu-
lone (Fix, 1989). Each variety differs only by
what is present on a side chain of the humu-
lone molecule. The alpha acids will dissolve
in hot wort, up to 250 mg/L at a pH of 5 and
a temperature of 212 degrees F (100 degrees
C). They are not very soluble in beer, with
its lower pH and temperature, and will pre-
cipitate out if their concentration is higher
than 5 mg/L at a pH of 4 and temperature of
32 degrees F (0 degrees C) (Hough et al.,
1982). During the kettle boil, the alpha acids
undergo a molecular rearrangement called
isomerization. The resultant chemicals are
called iso-alpha acids, and there is a corre-
sponding version for each humulone (iso-
humulone, isocohumulone, etc.). The iso-
alpha acids are much more soluble in wort
and beer, and they are the primary source
of bitterness in beer.
The beta-fraction of the hop resins is
composed of the beta acids and many other
chemicals, including the oxidation products
of the alpha and beta acids that result from
aging (De Clerck, 1957). The beta acids are
known as lupulones and occur in varieties
similar to the humulones. The same side
chains of the humulone molecule applied to
the lupulone molecule give rise to lupulone,
colupulone, adlupulone, prelupulone and
postlupulone (Fix, 1989). The beta acids are
less soluble than the alpha acids (0.7 mg/L
at a pH of 4 and a temperature of 32 degrees
F or 0 degrees C) (Hough et al., 1982), but
they do contribute some bitterness to beer
through their oxidation products. The bit-
terness from oxidized beta acids, in beer
made from aged hops, has been described
as an unpleasant bitterness that is not as
refined as the bitterness derived from iso-
alpha acids (Fix, 1989; Garetz, 1994b).
The hard resins do not contribute to the
bitterness of the finished beer.
Quantifying Hop Bitterness
The simplest way to quantify hop bit-
terness in beer is by specifying the weight of
hops added to the wort. Many excellent
homebrews have been made with recipes
specifying simply “three ounces of hops,”
but repeating such a success can be difficult.
The main problem with this technique is it
doesn’t take into account the alpha-acid
IBU
By Michael L. Hall, Ph.D.
ILLUSTRATION BY AMY SMYTH
Finding the solution to balanced beer bitterness is all in the numbers.
CALCULATING BITTERNESS
content of the hops. Alpha acids make up
anywhere from 2 to 15 percent of the total
weight of the hops, depending on variety.
The alpha-acid content can therefore
account for a factor of 7 difference in the bit-
terness level.
Adding alpha-acid content to the calcu-
lation allows the brewer to exercise greater
control over the bitterness level. The Alpha
Acid Unit (AAU) was developed by Dave
Line (1985) and adopted by Charlie Papaz-
ian (1991) as the Homebrew Bittering Unit
(HBU). Both are equal to the weight of the
hops in ounces (Woz) multiplied by the
alpha-acid content as a percent (A%):
AAU = HBU = Woz A%.
A recipe calling for 15 AAUs or HBUs needs
five ounces of 3 percent alpha-acid hops or
two ounces of 7.5 percent alpha-acid hops.
Using AAUs/HBUs is better than using only
the weight of the hops, but it still allows for
wide variations in the bitterness level. There
are two main things missing from the formu-
la: the volume of the wort and the boil time.
You will achieve a much different bitterness
from 15 AAUs in five gallons than 15 AAUs
in 10 gallons. Similarly, 15 AAUs of hops
boiled for 60 minutes will impart more bit-
terness than those boiled for 20 minutes.
Many recipes sidestep this problem by spec-
ifying the volume and boil time explicitly.
There are, however, still some lurking
difficulties with the AAU/HBUmethod, even
if the volume and boil time are given. What
does a brewer do if she accidentally boils for
30 minutes instead of 15? What if he can’t
afford the time to boil for 90 minutes and
only boils for 60? What if the total volume
of wort cannot be boiled? What if the brew-
er lives at an elevation of 7,300 feet (like me)
where the boiling temperature is lower? In
general, how does a brewer estimate bitter-
ness levels under the changing conditions
of a homebrewing setup so favorite batches
may be duplicated?
The most precise way to define bitterness
levels is the International Bitterness Unit,
IBU (sometimes referred to as BU). The IBU
is defined in terms of the amount of iso-alpha
acid actually present in the beer, regardless
of how it got there. The definition is:
IBU = 1 ppm of iso-α-acid,
= 1 mg of iso-α-acid/liter of beer.
Assuming the unrealistic circumstance that
all of the alpha acids in the hops are con-
verted into iso-alpha acids in the final beer,
we can easily calculate the ideal IBU num-
ber for a beer as:
Woz A% 7489
IBUideal = ———— x ——— .
Vgal
100
The factor of 7489 converts from oz/gal to
mg/L, and the factor of 1/100 converts the
alpha-acid percent into an alpha-acid frac-
tion. Vgal is the volume of the final beer
in gallons.
Reality, however, is much more compli-
cated than this simple equation. We will
add one more factor to the ideal equation to
account for all of the physical processes that
make the amount of iso-alpha acids in the
finished beer less than the amount of alpha
acids added to the kettle. This lumped fac-
tor is known as the hop utilization, and
will be denoted as a percentage by the sym-
bol “U%.” Here is the final equation, incor-
porating another factor of 1/100 for the uti-
lization percent:
Z Y M U R G Y S p e c i a l 1 9 9 7
CALCULATING BITTERNESS
5 6
twice as bitter as isohumulones (Hough et
al., 1982; Fix, 1989).
In addition to the problems associated
with undesired chemical pathways, the
main isomerization reaction is reversible. In
experiments starting with isohumulone in
wort, heating resulted in a quasi-equilibrium
of 10 to 15 percent humulone, before pro-
longed heating resulted in turning all of the
alpha acids and iso-alpha acids into
decomposition products. As a further com-
plication, it appears that the isomerization
process can be catalyzed by hop cones,
break material or even an inert surface
(Hough et al., 1982). A catalyzed reaction
will proceed at a different rate, translating
into a different utilization percentage. Sim-
ilarly, the pH of the wort will affect the uti-
lization, with higher pH values leading to
higher utilization rates.
Physical separations: At this point the
alpha acids have been isomerized and the
resultant iso-alpha acids are dissolved in the
wort. In the hot wort at the end of the boil
the utilization rate is about 50 percent.
Physical separation processes now take
0.7489 Woz A% U%
IBU = ————————— .
Vgal
This is the basic equation all IBU estima-
tion methods use. Everything in this equa-
tion is readily available, with the exception
of the alpha-acid utilization percent, U%.
The only difference between the various
IBU estimation methods, which are dis-
cussed later, is in the estimation of the uti-
lization percent.
Alpha Acid and Iso-alpha Acid
Loss Mechanisms
There are many ways for the alpha acids
to go astray on their circuitous path from the
lupulin glands of the hops to the iso-alpha
acids dissolved in your beer. Each of the
loss mechanisms chips away at the utiliza-
tion percentage until it reaches a value that
optimistically peaks at 35 percent. I will dis-
cuss the various loss mechanisms in
chronological order through the cycle of
beer production.
Storage deterioration: The first loss of
bitterness potential occurs during hop stor-
age. Before hops even hit the wort, alpha
and beta acids are subject to oxidation,
but it affects their bitterness in different
ways. Oxidation decreases the bitterness of
alpha acids and increases the bitterness of
beta acids. Some researchers have suggest-
ed that the gains and losses in bitterness off-
set one another, but other studies have
shown an overall decrease in perceived bit-
terness caused by hop deterioration
(Rehberger and Bradee, 1975). The amount
of alpha-acid deterioration is dependent on
age of the hops, storage temperature, hop
variety, amount of air present and hop form
(pellets or whole cones).
Chemistry: Once the hops make it to
the boil, the conversion of alpha acid to iso-
alpha acid is imperfect. Instead of isomer-
ization, the alpha acids can be oxidized to
make humulinic acids, isohexanoic acid
and isobutyraldehyde. There also is a com-
peting form of isomerization, referred to as
“reversed” isomerization resulting in anti-
isohumulones. The anti-isohumulones,
which account for about 10 percent of the
isomerization products, are reported to be
over to further limit the amount of bitterness
that makes it to your glass. Some of the
iso-alpha acids are adsorbed on the surface
of the hot and cold breaks and are precipi-
tated out of solution. About 7 percent of the
iso-alpha acids are removed with the
breaks, irrespective of the amount of the
break material. (Hough et al., 1982)
During the fermentation process, iso-
alpha acids are scrubbed by the rising CO2
and collect in the foam of the kraeusen. This
sticky foam can be blown off, skimmed off
or stuck on the sides of the fermenter, effec-
tively removing the iso-alpha acids from the
finished beer. Iso-alpha acids also are
bound up by the yeast cells and removed
when the yeast flocculates out. The amount
of time the yeast spends in suspension has
an effect on the utilization rate of about plus
or minus 5 percent. Filtration of the finished
beer also will physically remove some iso-
alpha acids. (Garetz, 1994b)
Staling reactions: Even when the iso-
alpha acids are safely ensconced in the fin-
ished beer in your bottle or keg, there can
be losses. There are oxidation reactions that
Z Y M U R G Y S p e c i a l 1 9 9 7
CALCULATING BITTERNESS
5 7
can reduce the bitterness of beer over
extended storage periods and create
“cheesy” aromas in its place.
Problems with
Estimating IBUs
There are many difficulties associated
with bitterness level estimation. First, all of
the processes previously mentioned occur
to different degrees and at different rates
under the varying conditions of the brew-
house. Quantifying their effect on hop uti-
lization can be a challenging task.
With whole leaf hops, variation of alpha-
acid content from the measured sample can
be a problem. Analyses can vary by as
much as 11 percent from bale to bale, and
the sampling rate can be as low as one out
of every 10 bales. (Hardwick, 1995; Ram-
sey, 1990) This is less of a problem with pel-
letized hops because several bales are
blended to achieve consistency.
The characteristics of the boil can have
a great effect on the rate of hop utilization.
The isomerization and solution rate
depend directly on the temperature of the
boil, which varies with the altitude of the
brewery. How fast and to what extent the
iso-alpha acids go into solution depends
on the quality of the contact between
undissolved iso-alpha acids and unsatu-
rated wort. This is in turn affected by the
boil vigor, the boil gravity (via the viscosi-
ty) and the hopping rate.
The physical form of the hops also can
change the alpha-acid utilization. Pellet
hops have been observed to give a greater
utilization than loose leaf hops. Several rea-
sons have been postulated: pellet hops dis-
perse more easily in the wort; pellets retain
their alpha-acid content during storage bet-
ter than leaf hops and the pelletization
process ruptures the lupulin glands and
spreads the resins over the hop particles,
giving a larger surface area for isomerization
and solution. (Hardwick, 1995; Lewis, 1994)
Even if the level of iso-alpha acids in a
beer could be determined exactly, the per-
ception of bitterness can vary greatly. The
ionic composition of the brewing water can
accentuate hop bitterness; magnesium, car-
bonate, chloride and sulfate ions all increase
the perception of bitterness (Noonan, 1996;
Papazian 1994). Other compounds can
cause bitter tastes in addition to iso-alpha
acids. These compounds include the oxida-
tion products of beta acids, compounds pre-
sent in roasted grains and tannins extract-
ed from the grain husks.
Methods of Estimating IBUs
If you ever tell a commercial brewer that
you calculated the IBU level in your beer he
or she will think you’re crazy. The big brew-
eries are very different from homebreweries:
they make the same beer over and over
again, allowing for modification of the
recipe; they can blend different batches to
achieve a consistent bitterness level; and
they can afford to have the bitterness level
of their beers measured often. As a home-
brewer, you’re probably making lots of dif-
ferent beers, and even when you repeat a
beer it’s usually a little different from the last
time you made it. You can’t spend a lot of
money analyzing the last batch, and you
need to be able to predict the bitterness of
tomorrow’s batch. Calculation, rather than
measurement, is imperative.
But how is bitterness measured? The
American Society of Brewing Chemists has
adopted a standard method of measurement
that involves a centrifuge and a spec-
trophotometer (1992). Unfortunately, these
pieces of equipment are beyond the range
of the average homebrewer. You can, how-
ever, have your beer measured for bitterness
at various laboratories, for example the
Siebel Institute of Technology in Chicago,
for a fee of about $40. (Siebel, 1997) Mark
Garetz also describes a taste-titration
method for estimating IBUs at home using
dilutions of iso-alpha extract and your own
palate (Garetz, 1994b).
Before we get to the utilization factor
estimation techniques, a couple of caveats.
First, realize that estimating hop bitterness
is a rough science, and it doesn’t need to be
more exact. The human threshold for detect-
ing bitterness is about 4 IBUs (Kuroiwa et
al., 1973), so controlling bitterness levels
tighter than that tolerance probably won’t
be noticed. Also, the processes involved in
getting alpha acids from the hops into your
Z Y M U R G Y S p e c i a l 1 9 9 7
0
15
30
45
60
75
90
Kettle Boil Time (Minutes)
0%
5%
10%
15%
20%
25%
30%
35%
UtilizationRateRager
Garetz
Mosher
Tinseth
Noonan
Daniels
FIGURE 1. Utilization Rate as a Function of Boil Time
CALCULATING BITTERNESS
Utilization rate as a function of boil time for wort of SG 1.050, boiled at sea level, using low hopping rates, using
fresh leaf hops without a hop bag, with an average yeast flocculation rate, and with no filtration.
5 8
low hopping rates, using fresh leaf hops
without a hop bag, with an average yeast
flocculation rate and with no filtration. The
correction factors to account for situations
different from these will be discussed in
the next major section.
Ragermethod: JackieRager’sZymurgy’s
article (1990) was the first article in the home-
brew literature that attempted to estimate
hop utilization rates. It still is widely used
because of its accuracy and simplicity. His
method gives utilization values for different
beer involve many steps that are not well
known or are hard to quantify. You should
evaluate your need for precise bitterness
level knowledge and only do as many cal-
culations as you need to satisfy it.
The second caveat is that the following
descriptions constitute my versions of the
various authors’ methods. I have corrected
obvious errors in some cases and elucidat-
ed confusing areas in others. Sometimes I
have even added equations that should
have been included by the author. I have
tried to remain true to the original works, but
you should consult the references if you
have any questions.
Simple method: I’ll start off with a
bare-bones estimation of the IBU level in a
beer. For the kettle or bittering hops, which
are boiled for an hour or longer, use a uti-
lization of 25 percent. For the flavoring hops,
which are boiled for around 10 to 30 min-
utes, use a utilization of 10 percent. For the
aroma or finishing hops (or dry hops), use a
utilization of 0 percent. Using the Simple
method, the IBU equation becomes:
18.7 Woz A%
IBUkettle = ——————— ,
Vgal
7.5 Woz A%
IBUflavor = ——————— ,
Vgal
IBUaroma = 0.
Therefore, one ounce of a 1 percent alpha-
acid hop in five gallons gives 3.75 IBUs if
used for bittering and 1.5 IBUs if used for
flavor. This means that, for a five-gallon
batch, the Simple method can be used to
convert AAUs/HBUs into IBUs:
IBUkettle = 3.75 (HBUs or AAUs),
IBUflavor = 1.5 (HBUs or AAUs).
Boil-time-dependent methods: The
rest of the methods discussed in this article
give a utilization rate that is a function of the
amount of time the hops are boiled. All of
the methods apply one or more correction
factors to this rate to account for various
perturbations to the hop utilization rate. Fig-
ure 1 and Table 1 give the utilization per-
centages for all of the methods, with no cor-
rection factors used. These values should be
assumed to correspond to a wort of specific
gravity of 1.050, boiled at sea level, using
boiling times as well as a correction factor for
boil gravity. No other correction factors are
given. The plot has a stair-step form because
single values of utilization for ranges of tem-
peratures were given in the original article.
(Papazian gives a method for estimating uti-
lization [Papazian, 1991], but his method is
an abbreviated version of Rager’s method,
including the gravity correction, and will not
be discussed further here.)
Garetz method: Mark Garetz pub-
lished a relatively complex method to esti-
Z Y M U R G Y S p e c i a l 1 9 9 7
TABLE 1: Utilization Rates (%) as a Function of Boil Time (min.)
Boil Time
RAGER GARETZ MOSHER TINSETH NOONAN DANIELS
0.0
5.0
0.0
0.0
0.000
5.0
5.0
2.5
5.0
0.0
1.8
2.414
5.0
5.0
5.0
5.0
0.0
3.5
4.598
5.0
5.0
7.5
6.0
0.0
4.8
6.575
5.8
5.0
10.0
6.0
0.0
6.1
8.363
6.5
12.0
12.5
8.0
2.0
7.4
9.981
7.2
12.0
15.0
8.0
2.0
8.7
11.446
8.0
12.0
17.5
10.1
5.0
9.3
12.770
9.2
12.0
20.0
10.1
5.0
9.9
13.969
10.3
15.0
22.5
12.1
8.0
10.6
15.054
11.5
15.0
25.0
12.1
8.0
11.2
16.035
12.7
15.0
27.5
15.3
11.0
11.8
16.924
13.8
15.0
30.0
15.3
11.0
12.4
17.727
15.0
19.0
32.5
18.8
14.0
12.9
18.454
16.1
19.0
35.0
18.8
14.0
13.4
19.112
17.2
19.0
37.5
22.8
16.0
13.9
19.707
18.2
19.0
40.0
22.8
16.0
14.3
20.246
19.3
19.0
42.5
26.9
18.0
14.8
20.733
20.4
19.0
45.0
26.9
18.0
15.3
21.174
21.5
22.0
47.5
28.1
19.0
15.6
21.574
22.6
22.0
50.0
28.1
19.0
15.9
21.935
23.7
22.0
52.5
30.0
20.0
16.2
22.261
24.8
22.0
55.0
30.0
20.0
16.6
22.557
25.8
22.0
57.5
30.0
20.0
16.9
22.824
26.9
22.0
60.0
30.0
20.0
17.2
23.066
28.0
24.0
62.5
30.0
21.0
17.5
23.285
28.2
24.0
65.0
30.0
21.0
17.8
23.484
28.5
24.0
67.5
30.0
21.0
18.1
23.663
28.8
24.0
70.0
30.0
21.0
18.4
23.825
29.0
24.0
72.5
30.0
22.0
18.7
23.972
29.2
24.0
75.0
30.0
22.0
19.0
24.105
29.5
27.0
77.5
30.0
22.0
19.3
24.225
29.8
27.0
80.0
30.0
22.0
19.6
24.334
30.0
27.0
82.5
30.0
23.0
19.9
24.432
30.2
27.0
85.0
30.0
23.0
20.2
24.521
30.5
27.0
87.5
30.0
23.0
20.5
24.602
30.8
27.0
90.0
30.0
23.0
20.8
24.675
31.0
27.0
CALCULATING BITTERNESS
5 9
mate hop utilization rates in his book,
Using Hops. (1994b) The Garetz method
includes a table of utilization values for
different boil times, like the earlier Rager
method, but the new values are signifi-
cantly lower than the Rager values. The
correction for boil gravity given in the
Rager article is used, and new formulas for
correction factors for boil temperature and
hopping rate are developed. Rough ranges
for correction factors for yeast flocculation
rate, hop form, hop bags and filtration are
given. Also, a formula to predict alpha-
acid loss during storage is given (Garetz,
1994a, b).
Mosher method: Randy Mosher pub-
lished a method for estimating hop uti-
lization that was based on graphical
lookups (Mosher, 1994). Unfortunately,
this makes it difficult to precisely deter-
mine the utilization percentages, so the
values quoted in this article should be
assumed to have an error of at least plus
or minus 0.1 percent. The Mosher method
gives utilization values that are even lower
than the Garetz method values for long
boil times. The graphs in the Mosher
method give an effective correction factor
for boil gravity and hop form.
Tinseth method: As far as I know,
Glenn Tinseth has only published his
method on the World Wide Web to date
(Tinseth, 1997; Pyle, 1997). The Tinseth
method is the first to use a formula instead
of a graph or table for the relationship
between hop utilization and boil time. The
Tinseth formula is set up so the boil gravity
correction factor is unity at a specific gravi-
ty of 1.0557. Modifying it slightly so it is on
an equal footing with the other methods
(boil gravity correction factor of unity at
1.050), gives this relationship for the uti-
lization rate:
U%bt = 25.367715 (1 – e
−0.04 tboil)
where tboil is the boil time in minutes and
U%bt is the utilization rate that is only
dependent on the boil time, the uncor-
rected rate. Tinseth notes that this curve
corresponds to the solution of a chemical
first-order reaction. The Tinseth method
does not include any correction factors
except the boil gravity correction factor.
However, the 25.367715 factor in front of
the equation represents the maximum
value of utilization that can be achieved
with extended boiling (at this boil gravity),
so a homebrewer easily can modify the
equation to fit his or her own circum-
stances. For long boils, the Tinseth method
gives utilization values between the Rager
and Garetz methods.
Noonan method: The first mention
I’ve seen of IBUs in the homebrewing lit-
erature was in the original edition of Gre-
gory Noonan’s Brewing Lager Beer (1986).
In his recent work Noonan provides a
method for calculating hop utilization
using tabular values (Noonan, 1996).
There are implicit corrections for boil grav-
ity and hop form, in addition to the stan-
dard boil time factor. The Noonan method
gives utilization values on the high side for
long wort boils.
Daniels method: Another recent
method was published by Ray Daniels
(1996). The Daniels method gives tabular
values for utilization rate versus boil time.
The boil gravity correction by Rager is
included in the method, as is the correction
Z Y M U R G Y S p e c i a l 1 9 9 7
CALCULATING BITTERNESS
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Z Y M U R G Y  S p e c i a l  1 9 9 7
1.030
1.040
1.050
1.060
1.070
1.080
1.090
1.100
Specific Gravity of the Boil
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
Boil Gravity Correction (Fbg)Rager
Mosher (scaled)
Tinseth (scaled)
Noonan (30 min)
Noonan (60 min)

CALCULATING BITTERNESS
FIGURE 2. Boil Gravity Correction Factor
for hopping rate from Garetz. Daniels also
provides some tables which can be used to
scale the utilization rate dependent on the
results from laboratory testing.
Modifications to the
Utilization Factor
The overall utilization rate is the product
of the boil time utilization rate (or uncor-
rected utilization rate) and all of the correc-
tion factors:
U% = U%bt Fbg Fhf Fhr Fbp Fst Fhb Fyf Ffil ,
where the Fs stand for correction factors for
boil gravity, hop form, hopping rate, boiling-
point temperature, storage losses, hop bags,
yeast flocculation rate and filtration, respec-
tively. All of the F variables are nominally
equal to unity, so you may omit any that
don’t seem necessary to you. Also, because
of the way I have structured the formulas,
any of the correction factors may be used
with any of the other correction factors, and
with any of the boil time utilizations given
6 1
Z Y M U R G Y  S p e c i a l  1 9 9 7
62
in the previous section. First, choose one of
the methods to determine the basic boil time
utilization (this may be a table lookup).
Then, pick and choose which of the follow-
ing correction factors to apply.
Boil gravity factor: All of the meth-
ods employ a boil gravity factor. Figure 2
and Table 2 show the behavior of several
boil gravity factor formulas. The most com-
mon formula for this correction was given
by Rager:
1
Fbg = ————————————    ,
1 + 5 (SGboil – 1.050)
where SGboil is the specific gravity of the boil
(which may differ from the original specific
gravity of the wort). This equation is only
used if SGboil is greater than 1.050; other-
wise, Fbg is equal to unity. This form for the
boil gravity correction factor is used in the
Rager, Papazian, Garetz and Daniels meth-
ods. The Mosher boil gravity correction fac-
tor seems to be based on the Rager method,
except it has been fit to a curve to smooth
out the rough transition at SGboil = 1.050.
Mosher only gives his correction factor
graphically, but after a little work the form I
developed for it is:
Fbg = 1.0526 [SGboil – 40 (SGboil – 1)2].
The Tinseth method gives another formula
for the boil gravity correction:
Fbg = 1.5673 [(0.000125(SGboil - 1))].
I’ve adjusted both the Mosher and Tinseth
formulas so they are equal to unity at SGboil
= 1.050, which makes them interchangeable
with all the other boil gravity factors. Lastly,
Noonan only gives his boil gravity factor
implicitly in table form, and it varies based
on boil time and hop form. I’ve given a cou-
ple of representative curves from his method
(30 and 60 minutes for leaf hops) in Figure
2 and Table 2, but if you want to use his
method it would be better to consult his
tables directly.
From the graph you can see there is a
certain amount of agreement. In general,
hop utilization rates decrease with increas-
ing boil gravity above 1.050. Below 1.050,
Rager and Noonan set the boil gravity fac-
tor to unity, while Mosher and Tinseth allow
higher values.
Hop form: Correcting the utilization to
account for the hop form also is common.
Leaf hops or hop plugs do not need a cor-
rection, but hops in the pellet form are
reported to have an increased utilization.
The Garetz method sets Fhf equal to 1.1 for
pellets boiled from 10 to 30 minutes, and
unity otherwise. The Mosher method sets
Fhf equal to 1.33 for pellets in general, inde-
pendent of gravity and boil time. Noonan
again uses a table, which gives Fhf between
1.0 and 1.5 for pellets, with maximum val-
ues centering around 15 minutes of boil
time and low boil gravities. Daniels does not
give a value for Fhf, although he recom-
mends using something between 1 and 1.25
for pellets. The other methods do not give
a correction factor for hop form, but any of
the above methods may be used with them.
TABLE 2:  Boil Gravity Correction Factors
SGboil
RAGER
MOSHER
TINSETH
NOONAN
NOONAN
(scaled)
(scaled)
30-min.
60-min.
1.030
1.0000
1.0463
1.1969
1.0000
1.0000
1.035
1.0000
1.0379
1.1443
1.0000
1.0000
1.040
1.0000
1.0273
1.0940
1.0000
1.0000
1.045
1.0000
1.0147
1.0460
1.0000
1.0000
1.050
1.0000
1.0000
1.0000
1.0000
1.0000
1.050
1.0000
1.0000
1.0000
0.9333
0.9286
1.055
0.9756
0.9831
0.9561
0.9333
0.9286
1.060
0.9524
0.9642
0.9140
0.9333
0.9286
1.065
0.9302
0.9431
0.8739
0.9333
0.9286
1.065
0.9302
0.9431
0.8739
0.8667
0.8571
1.070
0.9091
0.9200
0.8355
0.8667
0.8571
1.075
0.8889
0.8947
0.7988
0.8667
0.8571
1.075
0.8889
0.8947
0.7988
0.8667
0.8214
1.080
0.8696
0.8673
0.7637
0.8667
0.8214
1.085
0.8511
0.8379
0.7301
0.8667
0.8214
1.085
0.8511
0.8379
0.7301
0.8000
0.7500
1.090
0.8333
0.8063
0.6980
0.8000
0.7500
1.095
0.8163
0.7726
0.6674
0.8000
0.7500
1.100
0.8000
0.7368
0.6380
0.8000
0.7500
CALCULATING BITTERNESS
Z Y M U R G Y  S p e c i a l  1 9 9 7
63
Hopping rate: As more hops are added
to the boil, the utilization factor decreases.
The Garetz method includes a factor, or
rather an equation, to account for this:
1
Fhr = ——————————————   ,
1 + (Vfinal / Vwort)(IBU/260)
where Vfinal is the final volume of the beer
(the same as Vgal above), Vwort is the volume
of wort in which the hops are boiled, and
IBU is the number of IBUs extracted from
the hops. Garetz suggests that an iterative
procedure should be used because this fac-
tor includes the IBU value that is unknown
at the start of the calculation. However, plac-
ing this factor into the original formula,
IBU =
0.7489 Woz A% U%*
1
———— —— — —— — — —— — ———————
,
Vgal
(Vgal/Vwort) IBU/260 + 1
where U%* is U% with all the factors except
Fhr (i.e. U%* = U% / Fhr), we can see this is
a quadratic equation in IBU. Quadratic
equations can be solved easily to obtain:
130 Vwort
IBU = —————— x [ -1 +
Vgal
√1 + 0.0115215 Woz A% U%*/Vwort].
Note that the hopping rate factor calculation
must be the last calculation, after all the
other factors have been determined. The
Daniels method is the only other method
that includes a hopping rate factor, and he
quotes the Garetz method, using the itera-
tive solution procedure instead of the qua-
dratic procedure given here. The hopping
rate factor is a function of the boil time uti-
lization rate and all of the other correction
factors, so it will change when they are mod-
ified. The hopping rate factor could be
applied to any of the methods.
Boiling-point temperature: The iso-
merization reaction rate depends on tem-
perature, so the boiling-point temperature
at your elevation can make a big difference.
At my elevation, 7,365 feet, water boils at
198 degrees F (92 degrees C) instead of 212
degrees F (100 degrees C). Garetz gives a
correction factor for this effect:
1
Fbp = —————————    ,
1 + Eft / 27500
months before use. If you do want to calcu-
late the storage losses, Garetz (1994a, b) pro-
vides a formula for the correction factor:
Fst = e
–k Mt Mst tst  ,
where k is the base rate constant, Mt is a
modification factor for the storage tempera-
ture, Mst is a modification factor for the type
of storage and tst is the storage time in
months. Mt is given by
Mt = 2 
(T – 20)/15 ,
CALCULATING BITTERNESS
where Eft is the elevation in feet. None of
the other methods correct for boiling-point
temperature.
Storage losses: The alpha acids in
hops deteriorate over time, reducing the bit-
tering power of the hops. It is unclear
whether or not the gain in bitterness from the
oxidation of the beta acids offsets this effect
to the extent that no correction is necessary.
The best solution for the homebrewer is to
buy only fresh hops in vacuum-sealed bags
and store them in a freezer for less than three
province of the Garetz method. Note that
the product of correction factors is much
lower for the Garetz method.
Combining the correction factors with
the boil time utilization factors from Table
1 and using the IBU equation gives the esti-
mates for the IBUs of the sample beer
shown in Table 4, which range from 24 to
57. The actual bitterness, as measured by
Siebel, was 45.5 IBUs.
So what does this mean? Are some meth-
ods better at predicting bitterness than oth-
ers? Keep in mind this is only a single data
point, and there are many intangibles in the
brewing process that can affect the bitter-
ness level. Some methods may be better for
certain brewers. Justifications aside, three of
the methods came very close to the mark:
Tinseth, Daniels and, surprisingly, the Sim-
ple method. The Simple method worked
well because the beer was close to an aver-
age brew; the correction factor product was
close to unity. The Tinseth and Daniels
methods have similar boil time utilization
factors (see Figure 1) and correction factors
• 2 oz (20 min.)
• 2 oz (five min.)
• 4 oz (dryhopped for five days)
%Loss:  0.45
Storage: Hops were used in the springtime,
right after receiving them via mail order, so
assume hops were stored at 32 degrees F (0
degrees C) for four months in airtight bags
at the supplier. 
Hop form:  plugs
Hop bags:  no
Filtration:  no
Elevation:  7,365 ft.
Yeast:  Wyeast No. 1968 Special London Ale
Flocculation:  high
Table 3 shows the calculated utilization
correction factors for this beer for all of the
methods. With the exception of the Simple
method, all of the methods include a boil
gravity correction. Most of the methods
include a correction for hop form, but this
beer only used plug hops, so no correction
was necessary. The Garetz and Daniels
methods include a hopping rate calculation,
and the rest of the corrections are the sole
where T is the storage temperature in Cel-
sius. Mst is unity for hops exposed to air
(either unsealed or in polybags), 0.75 for
hops stored in airtight but oxygen-permeable
containers, and 0.5 for vacuum-packed
hops or hops stored under nitrogen or car-
bon dioxide. The base rate constant, k, is
dependent on the hop variety and can be
calculated from either the Hop Storage
Index (HSI) or the “% Loss” value for the
hop variety, which you can get from your
hop supplier or from Garetz (Garetz, 1994a,
b). If you start with the HSI, first calculate 
%Loss = 110 log (HSI/0.25),
which is actually the fraction (not the per-
cent) of alpha acids lost during storage at 68
degrees F (20 degrees C) for six months.
Now that you know the “%Loss,” the base
rate constant is given by
k = – ln (1 – %Loss)/6.
This corrects an error in the original work
and is somewhat simpler.
Other factors: There are many other
factors that affect the iso-alpha-acid uti-
lization in beer, but most of them are very
hard to quantify. The only method that even
attempts to quantify any other effects is
the Garetz method.
Garetz recommends Fhb = 1.0 for hops
loose in the boil, Fhb = 0.9 for hops in a hop
bag, and Fhb = 0.8 for hops in a hop bag
stuffed full. A yeast flocculation rate factor
(Fyf) of 0.95 is recommended for slow floc-
culation, 1.0 for average flocculation and
1.05 for fast flocculation. The filtration fac-
tor (Ffil) varies from 1.0 for no filtration to
0.975 for aggressive filtration.
A Sample Calculation
For this article I brewed a batch of my
standard hoppy pale ale (Jemez Pale Ale 5,
a.k.a. More Hops, Daddy!) and had the bit-
terness level measured by the Siebel Insti-
tute. This beer was brewed with the follow-
ing characteristics:
Batch size:  11.5 gal (full boil)
Boil gravity:  1.057
Hop schedule:  (all English Goldings at 5.1%
alpha acid)
• 5 oz (60 min.)
Z Y M U R G Y  S p e c i a l  1 9 9 7
TABLE 3:  Sample Beer Utilization Correction Factors
METHOD
Fbg
Fhf
Fhr
Fbp
Fst
Fhb
Fyf
Ffil Product
SIMPLE
1
1
1
1
1
1
1
1
1
RAGER
0.9662
1
1
1
1
1
1
1
0.9662
GARETZ
0.9662
1
0.9227[1]
0.7888
0.8881
1
1.05
1
0.6558
MOSHER
0.9758
1
1
1
1
1
1
1
0.9758
TINSETH
0.9390
1
1
1
1
1
1
1
0.9390
NOONAN
0.9286[2]
1
1
1
1
1
1
1
0.9286
DANIELS
0.9662
1
0.8842[3]
1
1
1
1
1
0.8543
[1] 20 min. = 0.9911.
[2] 30 min. = 0.9333, 15 min. = 1.0, 5 min. = 1.0.
[3] 20 min. = 0.9655, 5 min. = 0.9880.
TABLE 4:  Sample Beer IBUs
METHOD
60 min.
20 min.
5 min.
5 day
TOTAL
SIMPLE
41.52
6.64
0
0
48.16
RAGER
48.13
6.48
3.21
6.42[1]
57.82
GARETZ
21.78
2.34
0
0
24.12
MOSHER
27.55
6.03
2.07
0
35.65
TINSETH
35.97
8.71
2.86
0
47.54
NOONAN
43.18
6.71
3.32
6.64[1]
53.21
DANIELS
34.05
9.29
3.17
0
46.51
[1] Even though Rager and Noonan specify a utilization rate of 5 percent for hops that are not boiled, I don’t think
they meant to include dry hops, so these values are left out of the totals. Daniels specifically states a utilization of 0
percent for dry hops.
CALCULATING BITTERNESS
6 5
that pull them closer to each other – and to
the measured value.
The Garetz method, which didn’t fare as
well, started out with lower boil time uti-
lization values than most of the other meth-
ods and was pulled down even further by
the low correction factor for boil tempera-
ture because I brew at a high altitude. The
Mosher method, which has the lowest boil
time utilization numbers, was somewhat
higher than the Garetz estimate because it
had a high correction factor product. The
Rager and Noonan methods both came in
on the high side, which could have been
predicted because their boil time utilization
curves are the highest.
So which method should a homebrewer
use? I recommend brewing a batch as close
to your normal procedure as possible, and
taking good notes. Then, send a beer off to
be analyzed. Calculate the bitterness using
all of the methods to determine which one
fits your brewing style best. If you want to,
mix and match the formulas (in this article
only) to use your favorite boil time utilization
curve with your favorite correction factors.
Designing a Recipe
How does one go about determining the
hop bill for a new recipe? First, decide on
the hop varieties you will use for bittering,
flavor, aroma and dry hops according to
style or personal preference. Then check
with your hop supplier to see what the
alpha-acid percentages are for your cho-
sen varieties. Once again, use personal
preference or the requirements of the style
to set the amount of flavor, aroma and dry
hops. Calculate the bitterness contributed
by the flavor and aroma hops and subtract
this from the overall desired bitterness
level. Finally, work backwards to deter-
mine the weight of bittering hops to add to
your brew.
A Glimpse Ahead
In this first article I have given a survey
of the methods available in the home-
brewing literature for estimating the hop
bitterness level in beer. In a future article
I will develop a new method for bitterness
estimation based on research I am doing
in the professional brewing literature. I
hope you will be able to enhance your
brewing process with the formulas con-
tained in this article.
Nomenclature
AAU Alpha Acid Unit, = Woz A%
A% alpha acid content as a percentage
Eft elevation or altitude in feet
Fbg hop utilization rate correction factor for
boil gravity
Fbp hop utilization rate correction factor for
boil point temperature
Ffil hop utilization rate correction factor for
filtration
Fhb hop utilization rate correction factor for
hop bags
Fhf hop utilization rate correction factor for
hop form
Fhr hop utilization rate correction factor
for hopping rate
Fst hop utilization rate correction factor for
storage losses
Fyf hop utilization rate correction factor for
yeast flocculation rate
HBU Homebrew Bittering Unit, = Woz A%
HSI Hop Storage Index
IBU International Bitterness Unit, = 1 ppm
of iso-alpha acid = 1 mg of iso-alpha acid /
liter of beer
IBUaroma IBU number contributed by the
aroma hops
IBUflavor IBU number contributed by the fla-
voring hops
IBUideal IBU number for a beer assuming
100% utilization (not realistic)
IBUkettle IBU number contributed by the
kettle or bittering hops
k base rate constant for bitterness loss dur-
ing storage
%Loss fraction (not percent) of alpha acids
lost during storage at 68 degrees F (20
degrees C) for six months
Mst a modification factor to the storage loss
rate for the storage type
Mt a modification factor to the storage loss
rate for the storage temperature
SGboil specific gravity of the boil, which
may differ from the original specific gravity
of the wort
tst hop storage time in months
U% hop utilization rate as a percentage
U%bt hop utilization rate (as a percentage)
that is only dependent on the boil time; the
uncorrected rate
U%* hop utilization factor, U%, with all the
factors except Fhr; i.e. U%* = U% / Fhr
Vfinal final volume of beer in gallons, = Vgal
Vgal final volume of beer in gallons, = Vfinal
Vwort volume of wort that the hops are
boiled in, in gallons
Woz weight of the hops in ounces
Z Y M U R G Y  S p e c i a l  1 9 9 7
CALCULATING BITTERNESS
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Z Y M U R G Y  S p e c i a l  1 9 9 7
CALCULATING BITTERNESS
Hough, J.S.; D.E. Briggs; R. Stevens and
T.W. Young. Malting and Brewing Sci-
ence, Chapman and Hall, 1982.
Kuroiwa, Y.; E. Kokubo and N. Hashimoto.
“Advanced Hop Chemistry in Connec-
tion with Beer Flavor,” MBAA Technical
Quarterly, 10:4, pp. 215-219, 1973.
Lewis, Gregory K. “Kiss of the Hops,” The
New Brewer, pp. 10-19, 11:4, July/Aug.
1994.
Line, Dave. The Big Book of Brewing, Argus
Books Ltd., 1985.
Mosher, Randy. The Brewer’s Companion,
Alephenalia Press, 1994.
Noonan, Gregory J. Brewing Lager Beer,
Brewers Publications, 1986.
Noonan, Gregory J. New Brewing Lager Beer,
Brewers Publications, 1996.
Papazian, Charlie. The New Complete Joy of
Home Brewing, Avon Books, 1991.
Papazian, Charlie. The Home Brewer’s Com-
panion, Avon Books, 1994.
Pyle, Norm. Hops FAQ, http://realbeer.
com/hops/FAQ.html, as of June 1997.
T hop storage temperature in Celsius
tboil boil time in minutes
References
American Society of Brewing Chemists,
Methods of Analysis (8th Edition), 1992.
Daniels, Ray. Designing Great Beers – The
Ultimate Guide to Brewing Classic Beer
Styles, Brewers Publications, 1996.
De Clerck, Jean. A Textbook of Brewing,
Chapman and Hall Ltd., 1957.
Fix, George. Principles of Brewing Science,
Brewers Publications, 1989.
Garetz, Mark. “Hop Storage: How to Get –
And Keep – Your Hops’ Optimum
Value,” BrewingTechniques, pp. 26-32,
2:1, Jan/Feb 1994a.
Garetz, Mark. Using Hops – The Complete
Guide to Hops for the Craft Brewer,
HopTech, 1994b.
Hardwick, William A., ed., Handbook of
Brewing, Marcel Dekker Inc., 1995.
Rager, Jackie. “Calculating Hop Bitterness
in Beer,” Zymurgy Special Issue 1990
(Vol. 13, No. 4), pp. 53-54.
Ramsey, Michael. “Factors Influencing Hop
Utilization or Where Does It All Go?”
Zymurgy Special Issue 1990 (Vol. 13,
No. 4), pp. 46-52.
Rehberger, A.J. and L.H. Bradee. “Hop
Oxidative Transformations and Control
of Beer Bitterness,” MBAA Technical
Quarterly, 12:1, pp. 1-8, 1975.
Siebel Institute of Technology home page,
http://www.breworld.com/welcome/, as
of June 1997.
Tinseth, Glenn. The Hop Page, http://
realbeer.com/hops/, as of June 1997.
Michael L. Hall, Ph.D., is a computational physi-
cist at Los Alamos National Laboratory in New
Mexico. He has been brewing for eight  years, is
a BJCP Certified judge and was one of the found-
ing members of the Los Alamos Atom Mashers.
Michael is a member of the AHA Board of Advis-
ers and can be reached at hall@lanl.gov via E-mail.
© 1997 Michael L. Hall
6 7