Beer Color: How To Compute And Predict It

First, a sad story:

First we find out there's no tooth fairy. Next, we get the bad news about the Easter Bunny (Farmer McGregor blew him away, and he's gunning next for Peter Cottontail). Mr. Sandman, Jack Frost, Santa Claus, other cherished legends from our childhood ó gone! Then we have to pay our own dental bills, and sincerely wish there was a tooth fairy!

Phew! What a letdown! Perhaps we can take up a relaxing hobby, like homebrewing. The subject of our little anecdote has a color in mind for a brew, and wants to hit it just so . . . a nice coppery color, say about 10° Lovibond. Mmmm, he can picture it now.

He does as he's been told: Hmm, 5.5 gallons, times 10° L, is 55 color units. 9 pounds of a nice 2° L pils malt, and a little crystal, say about a pound. Ought to be tasty. How dark a crystal does our hero need? Well, he needs a total 55 units, and the pils malt contributes 18, so he's looking for the crystal to kick in 37 units. Ah! A 40° L crystal sounds just about right -- perhaps a tiny bit dark, but who cares? It will certainly be close enough!

So he brews a batch. "Looks a little light now, but it'll darken up when it's done fermenting," he thinks. Hope springs eternal! His nice coppery brew, pictured in his mind's eye, drives him forward.

But, alas! Our hero's hopes are dashed when he inspects the fruits of his labors. It's still quite nice in appearance, a deep golden color, but not that copper shade that was his heart's content. Another heartbreaking tale from the brew kettle!

Our intrepid hero bones up on the subject, and finds it a thicket. "Color is non-linear above a few degrees Lovibond," intones one pundit. "Beer's Law simply doesn't apply to beers," advises another, sounding somewhat contradictory. (Oh, the irony! If beer can't be expected to obey Beer's law, what can?) What's a brewer to do? Trial and error? Guess? Pray?

It doesn't have to be this way. You can predict color accurately from the color rating of your grains if you know your extraction efficiency. And that is a good reason to know your extraction efficiency!

ASBC Color, In A Nutshell

The American Society of Brewing Chemists has established a standard for assessing the color of worts, as well as the grains from which they are made. For a wort, a small sample is placed in a transparent rectangular holder called a cell. The wort-containing cell is then placed in a piece of apparatus known as a photometer (which means that it measures light). (Many photometers can measure the amount of light at many locations throughout the spectrum; these are then called "Spectrophotometers.") The amount of light transmitted through the wort in the Blue region of the spectrum (specifically, at a wavelength of 430 nanometers, or 4300 Ångstroms), compared to the amount of light of the same wavelength which can squeeze through a similar cell filled with nothing more harmful than water, is recorded. This quantity is referred to as the "transmittance" of the sample wort, and will be a number less than one. If we take its logarithm, it will be negative (the logarithm of a positive number less than one is negative, unless you use a number less than one as the base of your logarithms, but you wouldn't do that to me, would you?), so multiply it by minus one, to obtain a positive number. We refer to this quantity as "Absorption." (Aren't you glad this is a nutshell version of the ASBC color standard?)

One corrects the absorption for the thickness of the cell: most modern cells have a hollow area inside 1 centimeter thick, but the ASBC system was based on a half-inch cell, which is 1.27 centimeters just as sure as the day is long. So, if you used a 1 centimeter cell, you multiply by 1.27 so that you can pretend you used a half-inch one.

Finally, you multiply by 10, because when some brewing chemists did this ages ago with a half-inch cell, they got Absorptions which were very nearly one-tenth the rating of the Yellow Lovibond glass needed to best match the color of the beer. So that's what the ASBC decided they'd use.

For grains, you first make an extract, without boiling. You dilute the extract to a specific gravity of 1.0462, and then proceed as above for measuring worts. That's a nice middle-of-the-road sort of gravity, so it makes sense to call that the color rating which represents the grain ó it's going to be equivalent (or at least close) to the color rating of a beer with a gravity of 1.0462 made from that grain.

(For very dark grains, such as Chocolate and Black malts and Roasted Barley, the ASBC stipulates that the wort sample be diluted so its absorptance is in the most sensitive range of the photometer. The resulting absorptance is multiplied by the dilution factor, as well as the other multiplications mentioned above. But you don't have to worry about this, unless you've got a photometer of your own.)

Where We Lost Our Way

Somewhere along the way, some smart boy (or girl) scratches their chin and says, "1.0462, eh? Isn't that the SG of a wort with one pound of extract per gallon? So all I should need to do is multiply the number of pounds of extract I get from my grains by their respective color ratings, and then divide the total by the number of gallons of wort I made. Then, I can predict the color of my wort!"

This is great, and the bright boy (or girl) is quite happy. Life (to say nothing of their beer) is good. Unfortunately, some not-so-smart boy (or girl) gets wind of this formula, and attribute great mystical properties to it. Because the formula is mystical to them, they don't try to understand it; they just want an answer. Instead of looking at the amount of extract gleaned from each grain, they use the amount of each grain they put in the mash tun. "My color calculations came out wrong," they lament. (Refer to the story above for more details.) "I have to make an adjustment to the #@$%&*!! formula!"

Experimenting further, they find that the formula seems to work fine for worts with predicted color ratings at about 5 or 6 ASBC and below. "This complicates matters ó we need the formula to have unit slope below one level, then have its derivative drop as the number of color points per gallon increases." Much pulling of hair, wailing, and gnashing of teeth follow. Finally, a spiffy formula emerges, probably created by an aspiring Nobel Laureate with an old copy of Cricket Graph, which would do least-squares fits the whole live long day. (Isn't there a category of Nobel Prize for fitting polynomials to data?)

Unfortunately, this new formula casts aspersions on a long-cherished law of physics (viz and to wit, the aforementioned Beer's Law, or, as we color scientists prefer to call it, the "Beer-Bouger-Lambert Law.") As the ramifications of this are discussed, much finger pointing and name calling abound, in addition to more wailing and gnashing of teeth.

Of course, the problem is that one needs to know the amount of extract contributed by each grain, not how much of each grain was actually used. One must examine what is coming out of the lauter tun, not what is going in!

For this reason, I like to think of the color rating of worts as being expressed in degrees Lovibond, and the colors of grains in ° L gallons per pound. That's a dopey looking unit, but the scientist in me keeps on insisting on it, so I'll keep it in this page. You can ignore the units, if it makes the scientist in you feel better!

Back to Reality (or a reasonable facsimile of it, anyway)

If we know the following:

1. The ASBC rating of each grain
2. The number of pounds of extract contributed by each grain
3. The final wort volume

4. The color pick-up in the kettle

Step Zero

Step One:

Step Two:

Step Three:

Step Four:

We see right away that this color rating is significantly lower than the 10° L that the brewer in the story was aiming for. The factor, after accounting for the color pick-up in the kettle, turns out to be an aggregate measure of the brewhouse yield! Coincidence? I think not!

Working It The Other Way

In the anecdote at the top of the page, we started out with a wort color rating, and computed the color rating required for a specialty grain. Can we apply this technique in that direction, as well? The answer, happily, is yes.

The desired color (minus the color imparted by the boil) is multiplied by the wort volume, and the contribution of the base malt is subtracted. Subtract 1 °L for kettle pick-up from our target of 10 °L to obtain 9 °L; multiply 9 °L by 5.5 gallons to obtain 49.5 °L gallons. Again, we multiply the 5.31 pounds of extract from the pils malt by its 2 °L gallons per pound to obtain its contribution of 10.62 °L gallons, and see that, by subtraction, the crystal must contribute 38.88 °L gallons. One pound of it will yield 0.54 pounds of extract, so we divide 38.88 °L gallons by 0.54 pounds to obtain a color rating of 72 °L. An 80 °L crystal malt should get us close enough (to about 10.8 °L).

Symbolically, we may write:

Color Rating of Specialty Malt = (Wort Volume x (Color Rating of Wort - Kettle Pick-Up) - Extract from Base Malt x Color Rating of Base Malt) / Extract from Specialty Malt

We can also determine how much of a specialty malt is needed to obtain a particular color. This is particularly helpful when adjusting the color of a wort with a small amount of a so-called Farbmalz, or color malt, like Carafa I, which is a dehusked Chocolate malt made by Weyermann. It has a color rating of about 350 °L gallons per pound. (They also produce Carafa II; it is like a black patent malt, also dehusked.)

Suppose we're determined to make the beer using a pound of 40° L crystal (perhaps that's what we've got on hand), and make up the difference with some color malt, like the Carafa I. The 49.5 °L gallons for the finished wort should be familiar by now, as should the 10.62 °L gallons contributed by the base malt. One pound of crystal malt is assumed to contribute 0.54 pounds of extract, and that will, in turn contribute 21.60 °L gallons to the color. This leaves 17.28 °L gallons to be provided by the color malt.

Dividing the color rating of the color malt into this figure gives us 0.0494 pounds. This is the amount of extract it must provide. In order to obtain the amount of malt to use, we must divide this by its brewhouse yield. Assuming a brewhouse yield of 50% for this malt, we compute the quotient 0.0988 pounds, or just a touch over an ounce and a half.

Again, symbolically:

Extract from Color Malt = (Wort Volume x (Color Rating of Wort - Kettle Pick-up) - Extract from Base Malt x Color Rating of Base Malt - Extract from Crystal Malt x Color Rating of Crystal Malt) / Color Rating of Color Malt

and divide:

Amount of Color Malt = Extract from Color Malt / Brewhouse Yield of Color Malt

Why the wrong way seemed to work for light-colored worts

"Why, then," I hear a voice asking, "did the other approach come up with the correct prediction for worts with color ratings less than 5° L, if it assumed a brewhouse yield of 100%?" Allow me to offer a theory, unproven, but plausible. Perhaps you can think of others. If so, I'd love to hear about them.

ASBC grain colors are based upon unboiled extracts of the grains. But our worts are boiled when we evaluate beer color. The boiling process, no matter how delicately, tenderly, even lovingly executed, will invariably result in some color increase in the kettle. Further, under identical boiling conditions, the amount of coloring material produced during the boil will depend more upon the gravity of the wort, and less upon the color of the grains from which the wort was extracted. After all, more sugar, under otherwise identical conditions, will result in more caramel; more sugar and more amino acids (and other small protein fractions) would be expected to result in more melanoids. The resulting effect on color will be additive (remember, ASBC color ratings are already logarithmic), rather than multiplicative. And a 1 °L increase for a 3 °L wort is a large chunk of the difference between using a multiplier of one and a multiplier equal to the aggregate brewhouse yield.

Why did the malts in the example have different brewhouse yields?

Another voice asks, "Why was our brewhouse yield 59% for the pils malt and only 54% for the crystal?" Another good question. I offer a more concrete answer for this one. We have defined here brewhouse yield to be the product of your extraction efficiency and the grain's extract content (As-Is, Coarse Grind, or AICG on the analysis sheets). The grains have different amounts of extract in them. The AICG content of a two-row pils malt is in the neighborhood of 80%, but it may be 71% for a six-row crystal malt. With an extraction efficiency of 76%, we obtain the brewhouse yield values of 59 and 54 percent, respectively.

Why is it important to know the extraction efficiency?

Here we make an assumption: We assume we can get out about the same fraction of the available extract from each grain ó those with more extract available will give us more; those with less will give us proportionally less. Not an unreasonable assumption.

In other words, we say that the extraction efficiency is invariant with respect to the type of grain being mashed. This is probably an over-simplification, but is still quite reasonable. This is why it is helpful to know your extraction efficiency: it permits you to compute your brewhouse yield from the extract content of a grain.

If all you're interested in is gravity prediction (". . . if I get 25 point gallons per pound, and want 5 gallons with an SG of 1050, I'll need 10 pounds of malt"), knowing your aggregate brewhouse yield (in either percent or in point gallons per pound) is good enough. If you use 10 or even 20 percent specialty grains, any difference between their extract content and that of your base malt will be attenuated by a factor of 10 or 5, respectively. So, any gravity error attributable to a lower extract content in your specialty grains may be lost in the noise.

However, if you want to apply the color prediction technique outlined above, a small difference in the brewhouse yield amongst the grains can have a profound influence on the computed color. Instead of multiplying by relatively close numbers, such as 37 and 34 point gallons per pound, in the color prediction method we multiply by very different numbers, sometimes differing by a factor of 200 or more. When predicting gravity, most of the gravity comes from your base malt, so it's important to know your brewhouse yield for your base malt. On the other hand, most of a wort's color often comes from the specialty grains, so it is important when predicting color to know your brewhouse yield for the specialty grains. And extraction efficiency is the best way to determine what your brewhouse yield will be for any grain whose AICG extract content is known.

The Moral Of Our Story

Like those timeless fables of the Greek raconteur extrodinaire Æsop, ours, too, has a moral. If you don't understand a formula, but blindly apply it because "all you want is an answer," you are more likely to get burned. There are no mystical formulae. Thinking there are can lead you astray.