Using a Hemocytometer
For those who have perfected their mash and boil, hitting their numbers every time, the next step in the adventure is yeast. We're going to cover the basics of using a hemocytometer, which, if you remember your Greek, "hemo" refers to blood, "cyto" is a container, or cell and "meter" is to count something. These devices were originally used to count blood cells, and still are, though I strongly advise against putting blood in your beer unless it's some kind of demon-summoning brew, in which case, you should probably question the life choices that led you to this point.
Believe it or not, the equipment required to count yeast cells is actually quite inexpensive, including the microscope. As far as cells go, yeast are large and you don't need a very powerful microscope to see them. 400x, or 400 magnification is all you need, which is what most children's microscopes are capable of.
Selecting a microscope
If you do a search on amazon, you're going to find that price varies wildly. Most of the features you won't actually need, though a couple are helpful and will make your day easier. 1. Having 10x removable eyepieces will allow you to clean them easier and 2. having a back light. Try to avoid getting one that doesn't have changeable lenses as they don't work particularly well. You're looking for 10x eyepieces and 40x lenses (which equals 400x). You can spend anywhere from $50 - $500 on it, though since you're only counting cells, I'd lean toward the $50 option.
Like any scientific equipment, the hemocytometer can vary wildly in price. What you're paying for on the higher models is straighter, clearer lines. I haven't found a significant difference between the $20 vs the $200 ones, though if you're counting cells all day, rather than a couple of times a week or month, you might want to spring for the higher end model.
Before you start
You're going to want a couple more pieces of sciencey equipment, namely glass beakers and some disposable droppers with 1 mL markings. Both of these, you can find almost anywhere and you shouldn't be paying through the nose for them.
Your hemocytometer should look like this.
It's a simple piece of glass with some grooves and etchings on it. If you look closely, you'll see a very tiny hashtag pattern on part of the raised area in the middle. This is called the Neubauer chamber and is standardised so that you can figure out how many cells are in 1 mL of your sample. Simply multiply the number of cells you have by 40 000 and you have an estimate of how many cells are in 1 mL. However, most people are lazier and they simply count the four corners plus the one in the middle and multiply by 5 first.
This highlighted part is the part you'll be counting.
You'll notice that it's demarcated by double lines with more double lines separating it into 25 squares. All the cells in these 25 squares x 40 000 = cells per mL. For the sake of clarity and making sure you get your math right, I'm going to be using the following terms:
Chamber = Everything in that red square
Block = the smaller squares bordered by double lines. There are 25 of them in the red square
The smaller squares inside each block are just used to help you keep your counting straight.
Place a slide cover over the middle of the hemocytometer and add a drop of yeast slurry.
The slurry will be sucked into the chamber. Then take a look.
As you can see, this is a hot mess. There are billions of cells here (it is slurry after all) and we need to dilute the sample. 1 mL of yeast slurry stirred into 99 mL of water usually gives you a countable amount. Anywhere from 5-50 cells per block is a countable amount. If you've got more than that, dilute it more.
Here you can see that the number of cells is around 30 per block.
You can also see that the cells are fairly evenly spread around. That's because this is an American Ale yeast strain. British and wheat strains tend to clump together, making them harder to count. For cells like this, you can get away with counting just the four corners and the middle block and then multiplying by 5 to estimate the amount in all 25 blocks. Because we diluted it, our formula is as follows:
(number of cells counted x 5) x dilution factor (100) x 40 000 = cells per mL. Estimating 30 cells per block, you get:
30 x 5 (the number of cells we counted in the four corners + the middle) = 150
150 x 5 (estimating the amount in all 25 blocks) = 750
750 x 100 (dilution factor) = 75 000
75 000 x 40 000 = 3 000 000 000 or 3 billion cells per mL.
Once you know how many cells you have per mL of slurry, you can figure out how many mL of yeast you need for your beer. You can read more about figuring out your pitch rate here.