Since I received the VST Coffee Lab III refractometer thanks to Vince Fedele’s generosity, I started logging the concentration (in % TDS) of every coffee I brew. This allows you to calculate the average extraction yield of your brew, which represents the fraction of your coffee beans by mass that was dissolved in your brew water. This is a super useful measurement because it correlates very well with taste. Many of you might know that finding a good brew recipe is like navigating a thick forest at night – I would argue that using a refractometer is as useful as having a compass in that situation. I discuss coffee concentration and average extraction yield a bit more in this post.

I often compare the average extraction yield of my brews with other coffee geeks. While it’s an extremely useful measurement, I came to realize that we need to be careful when we compare numbers, because people use several different methods to estimate it. I’d like to review some of those methods here, and discuss precautions I think we should take when communicating our measurements.

A summary of this post is available for download here in the form of a cheat sheet with the relevant equations only. I also added it to the *resources* menu.

VST labs provides phone and computer applications to calculate extraction yields, which takes away the need to do the calculations yourself, but even in this scenario it’s really useful to understand how to properly use it, and to understand what the calculations rely on when you use different modes in the application. If you compare your numbers with people not using the VST application, one immediate difference will be that the application accounts for moisture and CO_{2} contained in the bean. Those using simpler approximations of average extraction yield will most likely not be including these correction factors, and as a result your average extraction yields will seem approximately a full percent higher than those of others.

Because of this, I like to set moisture and CO_{2} to zero in the application when I compare numbers with other people. It’s important to keep in mind that this makes the calculation less realistic, but it’s also important to compare apples with apples when you communicate with someone not using the app.

Coffee brews can generally be split between two big categories: percolation and immersion. We’ll discuss these two categories separately, and then we will discuss mixed methods last.

## Percolation

In a percolation brew, fresh water is being continuously added on top of a coffee bed, resulting in an aggressive extraction because fresh water is a great solvent. The coffee bed also acts as a filter, which prevents a lot of very fine coffee particles to end up in the beverage, and therefore results in a brew with less body and more clarity of taste. Brew methods such as the V60, the Kalita Wave, the Chemex, the moka pot, espresso and batch brewers fall in this category. Espresso is the only one among these where it is not just gravity that is forcing water through the bed of coffee, but it is still a percolation brew.

Calculating the average extraction yield is most straightforward for percolation brews, but it requires an additional measurement on your part if you want to be precise. Typically, brew recipes are designed with a coffee dose in grams (we’ll call it *D* below), and a mass of brew water also in grams (we’ll call it *W*). A refractometer allows you to measure the concentration of coffee in %, let’s call this *C*. This is often referred to as the *total dissolved solids*, or TDS. The concentration of your brew is by definition the amount of coffee mass that made it into your beverage (we will call this *M*_{bev}), divided by the total beverage mass (we’ll call it *B*):

There are two reasons why we divided by *B*, and not by the mass of water *W* which was poured over the coffee. First, this quantity *B* also includes the mass of coffee compounds. But most importantly, a lot of water actually never made it into the cup of coffee, and instead remained trapped in the spent coffee bed. The mass of water in grams that each gram of coffee can retain is called the *liquid retained ratio* (often called LRR, we will call it just *L*). Typically, a coffee particle retains twice its weight in water, so in other words its liquid retained ratio is approximately two. By now, we can write the relation between the total beverage mass *B* and the other variables:

The first term on the right hand is the total amount of water poured, to which we subtract the amount of water retained in the spent coffee bed, and to which we add the mass of dissolved coffee solids. In this discussion, we will ignore the effects of CO_{2} and moisture in the coffee bean.

The quantity we want to measure is the average extraction yield (we will call it *E*), and from its definition you might have foreseen that it will be given by:

If that’s what you expected, you are *kind of* right. In reality, we should include the coffee compounds that were dissolved in *all of the water* at the exact moment where the brew ended, because this is the quantity that informs us on the profile of chemical compounds that were extracted from the beans. Whether these compounds ended up in the cup of coffee or in the spent coffee bed, we must count them if we want the average extraction yield to correlate with flavor profile as best as it can.

I know this is counter-intuitive, so let me offer a thought experiment to settle this. Imagine you brew yourself a V60, place the spent bed in a glass, and immediately pour half of your coffee cup in the spent bed. This will artificially bump up your liquid retained ratio artificially, and half both *M*_{bev} as well as *B*. Did you just change the flavor profile of your cup ? You didn’t, but the equation above would tell you that you just halved it, so we know it’s wrong.

The reason why I called this extraction equation *kind of right* is because we ** assume** the water retained in the coffee bed

**in a percolation brew**has almost no dissolved coffee solids in it, at the moment where the brew ended. The key words here are

*in a percolation brew*, because you are constantly pouring fresh water on the coffee, and near the end of the brew there won’t be a lot more stuff that comes out from the coffee particles and into the fresh water. What happens if you wait 15 more minutes bears no impact on the flavor profile of your cup, this is why we are worrying about the concentration of retained water

*at the moment where the brew ended*. The complete equation for the average extraction yield should be:

where *M*_{ret} is the mass of coffee solids dissolved in the retained water exactly when the brew ended. But as we just discussed, *M*_{ret} is approximately zero in a percolation brew.

We already know the dose of coffee because that’s something we specify when we build a brew recipe and (hopefully) actually measure before brewing. What we must now deduce is this mass of coffee dissolved in the brew water, *M*_{bev}. The clue we have to figure it out is the concentraction *C* which we measured with the refractometer. If we combine the first two equations in this blog post, we get:

and we now want to revert this equation to obtain *M*_{bev} as a function of the concentration *C*. This takes a bit of algebra, which I’ll spare you. The result is this:

And we can now directly calculate the extraction yield, by substituting *M*_{bev} using the equation above:

The 1/(1-*C*) factor on the right-hand side of the equation has a very small effect on the calculated extraction yield for filter coffee, typically smaller between 0.2% and 0.4%. What this term represents intuitively is the contribution of extracted coffee mass to the beverage weight, so it is more important when *C* is high.

The equation above is useful if you know the *liquid retained ratio*, or want to approximate it. But in practice it’s more precise and easier to actually weigh the mass of your brewed coffee *B* (just note the mass of your empty mug before brewing). Look how much easier the extraction yield equation becomes, and it’s not an approximation:

Measuring the mass of your brewed coffee makes the calculation of average extraction yield much easier, and more precise ! It’s a win-win, so I really recommend that you always do it. I recommend this even if you use the VST application, because then you don’t need to assume any liquid retained ratio. Make sure the application is in percolation mode, and then you can directly adjust your beverage weight to your measured *B* in the application, instead of adjusting the amount of brew water (which we called *W* here).

Unless you use an unusually fine grind size and filter papers with unusually large pores, syringe filters should not be needed when you measure the concentration of a percolation brew, with the very important exception of espresso (see a recent awesome experiment by Mitch Hale about that). If you want to be sure your particular set-up does not require syringe filters, I recommend measuring your concentration with and without for a few brews, and determine whether they affected the measurement.

In my first blog post, I made the mistake of ignoring water retained in the spent coffee bed when I build a *coffee control chart* that is useful for V60 brews. As a result, my *fixed ratio* (*W*/*D*) curves were offset (this should now be corrected in the post).

Here’s an updated coffee control chart that assumes a liquid retained ratio of 2, which is much more appropriate for percolation brews than the one I had posted in my first blog post:

## Immersion

An immersion brew consists of plunging coffee beans in water (or the reverse) and leaving the same water with the coffee until the end of the brew. Extraction happens a bit more slowly because as water becomes more concentrated, its power as a solvent goes down. The spent coffee is then typically gently separated from the water to avoid drinking it, but typically a lot of fine coffee particles end up in the beverage, resulting in more body and less flavor clarity. Cupping and the french press fall in this category. You may be tempted to think that other brew methods like the aeropress, vacuum pots (also called siphons or syphons) and the Clever Dripper also fall in this category, but they don’t exactly – we’ll discuss these in the next section.

In an immersion brew, most of the technical discussion we already had in the *Percolation* section still holds. The main difference is that you cannot ignore the mass of coffee solids dissolved in water retained by the spent coffee bed anymore, and the approximation that the liquid retained ratio is near 2 can become very inaccurate depending on the brew method. Let’s go back to our full equation for the average extraction yield *E*:

We must now calculate *M*_{ret}, and to do this it is useful to recall that, at the precise moment where the brew ended, the concentration of coffee that will end up in the cup or in the spent coffee bed is the same. We can therefore calculate *M*_{ret} with the following equation:

which can also be inverted with a bit of algebra:

Now if we put together our equations for *M*_{ret} and *M*_{bev} in the extraction yield equation and do a bit more algebra, we end up with:

As you can see, all terms with the liquid retained ratio *L* disappeared ! This means you do not need to weight your beverage or make a supposition about *L*, which makes it easier to calculate the average extraction yield of an immersion brew. Again, the term in 1/(1-*C*) on the right-hand side of the equation is a small correction that has an effect of 0.2% to 0.5% on the calculated extraction yield.

The fact that beverage weight disappeared in the equation above should tell you something about how to use the VST application in immersion mode: you’ll want to adjust “BW” directly (here we call it water weight *W*), rather than the beverage weight, to achieve a better precision.

Syringe filters are needed to measure the concentration of an immersion brew. They all let enough fine coffee particles in the beverage which cannot be dissolved in water, so you will get very imprecise and inaccurate measurements if you don’t use syringe filters in this scenario.

The coffee control chart appropriate for immersions doesn’t need to assume any liquid retained ratio:

## Mixed Phases Methods

There are a few methods that cannot be simply categorized as percolation or immersion, and that are instead better described by an initial immersion phase, followed by a percolation phase where the already concentrated brew water passes through the partly spent coffee bed and typically also a filter to end up in the cup of coffee. Coffee brewed with these methods shares the properties of both: extraction is a bit more aggressive than an immersion brew alone because of the final percolation phase, but not as aggressive as a pure percolation method, because the percolation phase is done with water already concentrated with coffee, that is therefore a worse solvent. Depending on the details of where the filter is placed and what force pushes the coffee through the filter, a varying amount of fine coffee particles, smaller than typical immersion brews, ends up in the cup. Similarly, the *liquid retained ratio* will strongly depend in this force. The brew methods that fall in this category are the aeropress, the siphon and the Clever Dripper.

The main difference between these mixed methods and regular immersions in how they affect the calculation of extraction yield lies in the fact that the concentration in the spent coffee bed is not necessarily the same as in the coffee cup, but it is not zero either. Instead, it is somewhere in between, and will be close to the concentration of water at the end of the immersion phase, just before the percolation phase. Accurately measuring the extraction yield of these methods is more cumbersome and twice as expensive if you use a brew method that allows enough fines in the beverage that syringe filters are needed. Basically, you need to measure the weight of your beverage *B*, the concentration of your beverage (let’s call it *C*_{bev}), and the concentration of your spent bed (let’s call it *C*_{last}). You can measure the latter by keeping the few last drops of your brew in a different container. Make sure to keep at least a dozen drops if you need a syringe filter.

You can calculate *M*_{bev} and *M*_{ret} with the exact same equations as those in the sections above, by just replacing the concentration *C* with the respective *C*_{bev} and *C*_{last} concentrations. There is just one step that is easy to miss, where you estimate the total weight of retained water (let’s call it *W*_{ret}) from the water and beverage weights, make sure you don’t forget the contribution of coffee solids that were dissolved in the beverage:

This will allow you to properly write down the equation linking the concentration to the dissolved mass in the retained liquid:

Add to this a little bit of algebra, and you get the following equation:

Note how setting *C*_{last} = *C*_{bev} will simplify it to the immersion equation, and setting *C*_{last} = 0 will simplify it to the percolation equation, as it should. In other words, the equation above is more general, and includes both of the immersion and percolation cases.

If you are interested to view the detailed calculations leading to this more general equation, you can find them in PDF format here.

This particular equation is not currently supported by the VST application. The closest you can do is assume that *C*_{last} = *C*_{bev} and use the immersion equation. In fact, there are some recipes for which this approximation will be very good; I encourage you to verify this for your particular recipe, and see the difference you get from this equation versus the immersion equation. If you find out that the difference is small, then just use the immersion equation for that particular recipe.

This equation is a bit large, and clumsy to use, so Mitch Hale gracefully created a web tool so that you can use it way more easily ! Please have a look at it here.

Here’s a way to tell if the immersion equation is accurate enough, in one equation:

If that constraint is verified, then you can just use the immersion equation.

Determining whether these mixed brew methods require syringe filters or not will require experimentation on your part. Try measuring your concentrations with and without them for five or six brews, and notice if the syringe filters had an effect or not. With my very limited trials, it seems that a regular aeropress method requires a syringe filter, even if you use two filters. With the siphon, I noticed syringe filters were also needed, at least with the relatively fine grind size I tested and the Hario paper filters. Combining aeropress with the thick aesir filters and the prismo valve with a grind size slightly coarser than typical V60 brews did not seem to require syringe filters. Do not take these as absolute recommendations, but more as an illustration that whether syringe filters are required will depend on several parameters.

## Sharing Extraction Yields

As Mitch Hale pointed out recently on his Instagram account, when using a scale precise at 0.1 grams or worse to measure your coffee dose, it doesn’t make sense to report average extraction yields with more than one digit. This is true because effect of your 0.1 grams measurement error on your coffee dose will impact your calculated average extraction yield by about 0.1%, depending on your exact recipe.

When sharing extraction yields, I recommend that you also report all the variables that are required to use the relevant equation, plus the water/dose ratio. In the example of a percolation brew, this means reporting your coffee dose, brew water ratio, beverage weight and beverage concentration.

## Some Parting Thoughts

While this blog post summarizes the concepts behind equations currently used for calculating extraction yields, it is likely not the final answer to how we should calculate them. More than a year ago, Scott Rao posted a very interesting discussion about the limitations of our current assumptions, and how he thinks that the retained liquid in percolation brews are in fact not completely devoid of dissolved solids. I really recommend you read his post, especially if you just went through all of this blog post with a fresh memory of how things are currently calculated. I’ll definitely do some experiments in the future and think about how we can implement Scott’s and Dan Eil’s suggestions.

[EDIT 2019 March 25: I wrote a follow-up discussion to this post here].

*Disclaimer:* I was offered the VST Coffee Lab III refractometer for free by Vince Fedele, but I do not have any financial interest related to any coffee equipment.

This might be really daft and show a lack of comprehension…

With immersion methods, if you measure the setup pre- and post- “adding water”, should it not give you the bev weight inclusive of the all the dissolved solids?

That’s measured right before you pour the coffee of course

Thanks

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I’m not sure I understand your question well. When you pour the beverage outside of the immersion container, what you weigh is the output water + dissolved coffee solids indeed.

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