I have seen several questions lately regarding volume at various stages of brewing. I hope the following helps someone make sense of it all. It's long, but pretty thorough. I think it's comprehensive and easy to understand. If anyone has suggestions to make this better, I'm open to editing.
Understand brewing volumes.
The one thing that will generally stay the most consistent for every brewer is target volume. This is the volume you expect, after all the additions and subtractions, to end up going into your fermenter. How to arrive at this volume varies greatly among the extract brewer and the all grain brewer. Regardless of where you currently are, I'd suggest you read both outlines. They are long, but thorough.
I am an extract brewer:
As an extract brewer, your initial volumes will be more a product of your brew pot than your recipe. A good rule of thumb for brewing in general is the more you can boil the better. This ranges from the best option being to boil the full batch volume, to whatever volume you can handle with your equipment. Most extract brewers are probably starting out with a 5 gallon pot. Here, you will be limited in your initial volume by several factors including what volume can be safely boiled without boiling over. Mostly you'll be in the 3.5 4 gallon range. It is important to note at this point, one of the biggest fundamental differences between extract and all grain brewing is that as an extract brewer, you are typically not concerned with predicting volume changes with great accuracy during your brew. Regardless of where you end up after the boil, you'll be topping off to your target volume with water before fermenting. Still, understanding the following volume changes will help you to be a better brewer and will certainly aid you in your transition to all grain if you so choose that path.
You will begin your boil and the first change in volume you will experience will be a very minor one, but it is worth noting due to its similarity to one of great concern for all grain brewers. Steeping specialty grains in your pot is similar to mashing, but with much less grain and much less emphasis on temperature precision. Grain absorption will occur on some scale in both practices. When you remove the steeping bag, there will be some volume that is absorbed by the grains. There is some debate as to whether squeezing the bag to extract more of the flavor and impact of the grains and return more of the volume to the pot will extract tannins. Regardless of your procedure, there will be some loss of volume here, albeit a very small amount most likely. You don't have to do anything differently here per se, but understanding it is helpful. If you do transition to all grain, this loss to grain absorption will be significant and will need to be calculated during recipe formulation.
The second volume change you will encounter will be boil-off. This is the amount of volume lost to evaporation as the wort boils for a specific time usually 60 minutes for most extract brews. This is often calculated by a known rate, called the boil-off rate. The boil-off rate is generally considered to be 5% to 10%, but more accurately it is a function of energy input and time. Once you establish your boil-off, it will probably be helpful to think of it in terms of gallons per hour. Your boil-off will stay pretty constant with most things remaining equal, aside from volume. In other words, once you've established your rate, say .52 gallons per hour, you will boil off .52 gallons per hour regardless of what volume you start with within reason. Use the percentage as a guideline for what to expect, but learn your boil-off rate expressed in gallons per hours, and use that for future brews. Again, more important for an all grain brewer in practice, but understanding it is helpful. Note: Boil off is a good thing for brewers. It enables us to drive off certain unwanted compounds, things like DMS precursors. So remember to boil without a lid on!
After the boil is over, you begin to chill your wort down to pitching temps. The cooling of the liquid causes something called shrinkage loss. Shrinkage loss works out to be about 4% and is pretty consistent since we are all within the same general temperature range. This is obviously a small amount of your 2.5 gallons, but for the 5.5+ gallons the all grain brewer has at this point, it matters more.
The heating of the wort and cooling of the wort produces hot and cold breaks. Break material, as well as hop material and whatever else was put in the boil settles at the bottom of the pot and is known as trub. The trub will be your fourth volume loss whereas the material will absorb water similar to how the grain did. This loss will vary depending on your practice. Some brewers choose to throw everything, trub and all, into the fermenter. This approach doesn't change your volume at all...yet. But if you do this, realize that since you will not be bottling the trub you'll have to account for it later on. If you choose to deal with the trub later, then here even the extract brewer should account for loss because if you top up your fermenter to the 5 gallon mark with the entirety of the trub in there, you will not be getting 5 gallons of beer to bottle when the fermentation is done and you leave the trub behind before bottling. When I was an extract brewer, I always passed all of my cooled wort into the fermenter through a strainer. I left all the break and hop material behind that I could. With this approach, your trub loss will occur right away and when you top up into your fermenter, the 5 gallon volume will be much more representative of what you'll be bottling, with only the yeast cake left for absorption and the yeast cake is usually very tightly packed and absorbs very little volume. In fact, I never accounted for any loss to the yeast and if I got one or two fewer bottles on bottling day, so be it. You can adjust a little to say 5.25 gallons or so if you want, but realize that you are diluting you wort. So, unless your recipe was calculated for a target volume of 5.25 gallons, you will have changed the gravity and subsequently, the final beer.
The last volume an extract brewer is concerned with is the difference between target volume vs what makes it into the fermenter from the boil. If you began with 3.5 gallons and over the course of boil-off, shrinkage, grain absorption, trub loss and everything else, you end up with 2.5 gallons into the fermenter, you simple make up the difference between your target volume and this. The easiest way to do that is to simply top off in the fermenter until you hit your target, usually 5 gallons. If you are doing any sort of water adjustment as an extract brewer, pre-boiling, treating for chloramine, using DI water or whatever else, you will want to be ready with this water. The best thing to do is have more on hand than you think you will need.
I am an all grain brewer:
If you are new to all grain brewing, hopefully you have at least a good foundation as an extract brewer. Whatever your level may be, it might be a good idea to read the extract brewing information above before getting started. One of the most pronounced differences between extract and all grain brewing is that with all grain brewing, we need to have good understanding of what our volumes mean and how they affect us. We also rely fairly heavily on the ability to predict our volumes - mostly our losses - and prepare for exactly what volume of wort we will be left with at each stage. There are several places throughout the process where can expect to leave volume behind. To comprise our volume with all grain brewing, we are usually talking about two separate additions of water, mash and sparge. The mash and sparge combine to form the volume we will need to go into the kettle, known as pre-boil volume. The most important thing to remember is that all of these volumes and losses will be specific to your brewery and no one else's. Your process and your equipment will be different than everyone else's, so it is important to learn what your volume changes are, and use them to predict volumes for your future recipes. It may take a few batches to learn and fully understand the volumes specific to your brewery, so take good notes during your brew day!
A good starting point to calculate volume for your brew day is to choose a water-to-grist ratio for your recipe. I'm not going to go into how to choose a ratio here, there's plenty of information available on that it's generally between 1 and 2 quarts-per-pound. For now, let's assume we've settled on 1.4 quarts-per-pound. If the recipe calls for 10 lbs of grain, that gives you 14 quarts or 3.5 gallons. This is the volume of strike water needed for your mash. As we said earlier, the other major addition of water you will make is the sparge volume. If you are batch sparging as we are in this example, it is important to know the volume of sparge water we need. Although it is at this point in the process that we need to know our sparge volume, we really cannot calculate it without knowing all future losses which is exactly why we need to predict our volumes before we start our brew day. Let's just continue through the process using the proper sparge volume and in the end it will be clear how we calculated that volume. Since we are using a batch sparge in our example, the sparge water here is going to be 4.47 gallons.
We begin our all grain process by doughing in. The first place we see a volume loss is grain absorption. We are dealing with a significant bed of grain here 10lbs. The grain will absorb a good amount of water, but how much will depend on a variety of factors like crush, equipment, practices, etc. It's usually between .1 and .2 gallons per pound of grain. For my brewery, I'll lose about 1.2 gallons in 10 lbs of grain.
Tun Dead Space
A second loss you will experience early on will be to the dead space in the mash tun. This is the space below which your tun can effectively drain and is very dependent on your equipment. I use a 10 gallon Rubbermaid cooler with a false bottom and I lose about .25g. If you use a cooler with a manifold or a stainless braid system, the dead space is much less, and becomes almost negligible if you tilt the tun when draining. You need to figure out the dead space of your tun and record it for future use.
Now that you have lost volume both to the grain and the dead space, 1.2 gallons and .25 gallons respectively, you can expect that of the 3.5 gallons that went into the mash, only 2.05 gallons will make it into the kettle when you drain the first runnings. Sparge water goes in next, and we said early that the volume need is 4.47 gallons. Because the grain bed is already saturated and the tun dead space is already full, we do not have to worry about either loss during our batch sparge. Once the sparge is complete and the lauter tun is drained into the kettle again, you will have added 4.47 gallons to the 2.05 gallons already in there for a total of 6.52 gallons. This is your pre-boil volume.
Over the duration of your boil, you will experience another loss called boil-off. This is the amount of volume lost to evaporation as the wort boils for a specific time usually 60 minutes for most beers. The calculation is found with a rate known as boil-off rate. The boil-off rate is generally considered to be 5% to 10%, but more accurately it is a function of energy input and time. Once you establish your boil-off, it will probably be helpful to think of it in terms of gallons per hour. Your boil-off will stay pretty constant with most things remaining equal, aside from volume. In other words, once you've established your rate, say .52 gallons per hour, you will boil off .52 gallons per hour regardless of what volume you start with within reason. Use the percentage as a guideline for what to expect, but learn your boil-off rate expressed in gallons per hours, and use that for future brews. Again, more important for an all grain brewer in practice, but understanding it is helpful. Note: Boil off is a good thing for brewers. It enables us to drive off certain unwanted compounds, things like DMS precursors. So remember to boil without a lid on! Realize that not only equipment, but boil vigor factors here as well. To be a consistent brewer, try to keep these process-related aspects the same from brew to brew. My boil-off rate is about about .52 gallons per hour, so when boiling a 6.52 gallon volume as in our example, this would make the post boil volume around 6 gallons.
When the boil is over you begin to chill your wort down to pitching temps. The cooling of the liquid causes something called shrinkage loss. Shrinkage loss works out to be about 4% and is pretty consistent since we are all cooling within the same general temperature range. The 4% of the 6 gallons works out to be about another .25 gallons, leaving you now with 5.75 gallons.
The heating of the wort and cooling of the wort produces hot and cold breaks. Break material, as well as hop material and whatever else was put in the boil settles at the bottom of the pot and is known as trub. Trub loss is the volume that gets absorbed into the trub when you transfer the wort from the kettle to the fermenter, and will vary depending on your practice. Some brewers choose to throw everything, trub and all, into the fermenter. This approach doesn't change your volume at all...yet. But if you do this, realize that since you will not be bottling or kegging the trub, you will have to account for it later on. Personally, I leave as much of the break and hop material behind as I can. With this approach, trub loss will occur right away and what goes into the fermenter will be roughly the target volume for bottling, minus a small amount lost to the yeast cake post fermentation. I generally do not calculate any extra volume for the yeast cake loss, as it is insignificant to me in most beers that brew. A ball park idea of how much is usually lost to trub is .4 gallons to .8 gallons, but you really need to figure out what it is for your brew house. Because I usually leave behind as much as possible, my loss to trub is usually about .75 gallons.
At this point, I'm sure you can see that the goal of our calculations was to ensure we had 5.75 gallons post boil, so that a clean 5 gallons goes into the fermenter. You may lose a little more volume to gravity samples and the yeast cake from this point on, but not enough to be of any concern a bottle or two of beer maybe. If the loss to trub was going to be .5 gallons, we would have made sure the post boil volume came to 5.5 gallons instead.
Sparge Water Calculation
Back to the sparge calculations, we can now see why we work backwards. In reality, we work backwards up to the point where we converge with our water-to-grist ratio, since that is a design of the recipe and remains constant independent of our equipment. If we know our water-to-grist gives us a strike volume of 3.5 gallons, the difference between that and our target volume of 5 gallons is 1.5 gallons. The 1.5 gallons is what we would need to have left over from our sparge water after all of the losses are accounted for. If we go back and add all of the losses to that 1.5 gallons, we will find the volume we need to batch sparge with. Doing the math, 1.5 + .75 (trub) + .25 (shrinkage) + .52 (boil-off) + .25 (dead space) + 1.2 (grain absorption) = 4.47... Hot damn if that isn't our batch sparge volume! Please note, If you are fly sparging, the volume situation simplifies a bit in that you can really just work backwards to what your pre boil volume needs to be, and simply sparge until the kettle volume is equal to that.
Happy Brewing. Hope this helps someone!