Brewing efficiency is a topic fraught with unnecessary complications and various confusing definitions. One of the most cited and accurate article on the matter comes from Braukaiser.

## Mashing Efficiency

Mashing efficiency is best understood in terms of conversion efficiency and lauter efficiency. Most brewing software use “brewhouse” efficiency to also include further losses of liquid in equipment (pumps, hoses, mash tun dead space, etc…). For the brew in a bag brewer, brewhouse efficiency should essentially be equivalent to mashing efficiency. Assuming the entire kettle volume is transferred to the fermenter, there are no post-boil losses to speak of. We can also account for a bit of trub loss if desired, and we will revisit this later

Mashing efficiency can be defined as

Let's review each of the components separately.

## Conversion Efficiency

Conversion efficiency measures how well sugars were extracted from the grain. A good mash and a good crush should yield very close to full conversion of sugars (100% efficiency). The Braukaiser article describes factors that influence conversion efficiency in great details. In summary:

- Mash time
- Crush size
- Dough balls
- Mash pH, temperature

Braukaiser presents the following formula to calculate the maximum yield of a mash:

- FW
_{max}: theoretical maximum of extract (Plato) - e
_{grain}: weighted average of the laboratory extract of the grist. This is related to grain potential as the ratio of the gravity point potential of the grist over the potential of pure sugar (42). - m
_{grain}: weight of dry grain (kg) - V
_{water}: volume of strike water (liters)

As an example, let's say we will mash 12 lbs castle pilsner malt in 8 gallons water. From the data sheet, the moisture content is at most 4.5%. The dry weight is thus 12 X 0.955=11.46. Also from the data sheet, the laboratory extract for this malt is 82%. Converting to kilograms and liters and plugging into the above formula, we get

This corresponds to a specific gravity of 1.049.

We note here that 1.049 is the absolute most one can get out of this amount of grain mashed in the specified amount of water. 1.049 represents a conversion efficiency of 100%. While performing the mash, if one was to measure a 1.049 specific gravity, then conversion is complete and mash can be stopped. It would not be physically possible to measure any more than this. A measurement of less than 1.049 would indicate a conversion efficiency of less than 100%, according to the following formula:

It's worth noting that a more intuitive formulation of plato is simply the weight ratio of sugar to wort, as discussed in this post.

This formulation is basically what braukaiser by simply replacing the water weight by water volume assuming that 1L=1kg (hence the need to use metric units in his formula). The weight of sugar is the same as the weight of the grain multiplied by the potential ratio, and thus:

## Lauter Efficiency

Lauter efficiency is simply a measure of how well we extract the wort from the grain. an efficiency of 100% would mean that all liquid has been removed form the grain leaving nothing behind by dry spent grain.

In practice of course, 100% lautering efficiency is not possible. The least efficient way to extract wort from grain is to drain a full volume mash with no sparging. This however is also the simplest method and what many brew in a bag brewers including myself opt for. It can also be improved by actively squeezing wort out of the bag

A typical value for grain absorbions is 0.1-0.12 gallons per pound of grain. Note that brewers typically use what is called apparent grain absorption. That is the difference between the starting **water** and the resulting **wort** after the grain is removed. Note that the volume of water is smaller than the volume of wort as dissolved sugar take up some volume as well. Apparent grain absorption takes that extra volume under account. This makes sense because there’s not way to directly measure the volume of wort in the mash. However we readily have volume of strike water and volume of pre boil wort available to us.

This thread on HTB showcase some data from user doug293cz who simulated efficiency w.r.t to grain absorption and sparge steps.

note that lauter efficiency also depends on the mash thickness or the total amount of grain used. This should be obvious given that more grain will retain more liquid and thus generate more losses.

## Online Calculators

At this stage it's helpful to point out that the main online calculator for conversion efficiency gives the wrong results by a significant margin (as explained in this post). Brewer's friend efficiency calculator lets user calculate their efficiency.

Our example has yielded a maximum gravity of 1.056. This is significantly higher than the 1.049 value we got from the Braukaiser formula. Brewer's friend seems to be making 2 mistakes.

### Grain Moisture

Malted grain is not 100% dry and contains a small amount of moisture. This value can be found on the datasheet but can generally be assumed to be around 4%.

This means that 4.5% of the grain weight is actually water (the following calculations use 4%). This has two consequences.

First the malt adds a small amount of water to the mash. This is almost negligible, but for completeness let's consider it. The water in our 12 lbs of malt will have a weight of 0.04*12=0.48 lbs. With water having a density of 8.345 lbs/gallon, we get an added water volume of 0.48 / 8.345 = 0.0575 gallons.

The second point to consider is that the weight of the dry grain is not 12lbs but rather 12 - 0.48 = 11.52 lbs. This is the actual amount of usable malt we have.

### A Gallon of Wort...

The grain potential is the specific gravity that would result from one pound of grain being used to create one gallon of **wort**, given 100% conversion. A gallon of wort is not the same as a gallon of water because dissolved sugars in water will increase the volume of the mashing water.

BH seems to be using the water volume entered rather than the wort volume resulting after the sugar from the grain is dissolved. From the datasheet, we know that 80% of the grain weight is sugar. That is 9.22 lbs or 4.18kg. Using the density of maltose (1.54g/cm^3) as a basis for our calculations, this then generates an added volume of 2.71 L or 0.71 gallons. This is a significant volume difference as compared to 8 gallons.

Adding the volume of the dissolved sugar and the grain moisture to the water volume, we end up with **wort** volume of 8 + 0.71 + 0.058 = 8.77 gallons. Plugging the dry grain weight and the actual wort volume into the BH calculator yields the expected specific gravity of 1.049.

It thus appears that BH ignores both the moisture of the grain and the added volume from dissolved sugar.

## Volumes

Having explained the expectation behind gravity measurements, let us turn to volumes. While the pre-boil gravity measured is independent of the collected volume of wort, the volume must be correct for the pre boil gravity to turn into the correct original gravity. For example, you may collect 7 gallons of wort at 1.050 or you may collect 5 gallons of wort at 1.050. The measured gravity depends on your grist and the amount of water you started with only, not on the volume of collected wort. However the original gravity will be different if you boil off 1 gallon from 8 gallons vs from 5 gallons.

Volumes in full volume mash BIAB are very straightforward to figure out. Let us work out an example. We will target 5.5 gallons into the fermenter. Starting with a fermenter target volume, let us work our way back. Let's say we expect to lose 0.1 gallon at the bottom of the kettle. This could be a some hop trub or just some volume that is below the dip tube and hard to drain. Then it means we need to finish the boil with 5.6 gallons.

Knowing our evaporation rate, say 1 gallon/hour, then we necessarily need to start with 6.6 gallons after the bag has been pulled out of the pot. Furthermore, if we know our apparent grain absorption (defined as the difference between the mash **water** volume and the pre boil volume), then we know how much water we need to start with. For example, if we use 10lbs of grain and apparent absorption is 0.1gallon/lbs, then we need to start with 7.6 gallons of mash water.

Note that all the volumes above are at room temperature. The following table summarizes the volume, along with heat expansion.

Volume | Room temp | Process temp |

fermenter | 5.5 | 5.5 (room temp) |

post boil | 5.6 | 5.82 (4% expansion at boil temp) |

pre boil | 6.6 | 6.80 (3% expansion at mash temp) |

strike water | 7.6 | 7.83 (3% expansion at mash temp) |

initial water | 7.6 | 7.6 (room temp) |

The volume calculation is as simple as that. The first 3 lines will be same for every brew. The strike water will change based on the size of the grist, as more or less water will be absorbed in the grain.

On brew day, we start with the initial water as calculated above and we mash-in. After pulling the bag, we let it drain and/or squeeze until we hit the calculated pre boil volume. From there, assuming accurate boil off numbers entered in calculations, we should end up with the desired volumes after boil and chill.