What the Hydrometer Knows
A weighted glass float and two readings are all it takes to know how strong your beer is. The trick is understanding what the numbers actually measure.
The hydrometer is the least glamorous tool in the shed and the one I would give up last. It is a sealed glass float with a weighted bulb and a paper scale inside the stem. Drop it in your wort, read where the liquid crosses the scale, and you know something you could not otherwise see: how much sugar is dissolved in the liquid.
Density is a proxy for sugar
Sugar is denser than water. Dissolve a lot of it into your wort and the whole liquid gets denser, which makes the hydrometer float higher. The scale reads that buoyancy as specific gravity, the density of your liquid compared to pure water, which sits at 1.000 by definition. A wort reading 1.050 is five percent denser than water, and that extra density is almost entirely the malt sugars the yeast is about to eat.
That first reading, taken before you pitch yeast, is your original gravity, or OG.
Fermentation is visible as a falling number
Yeast eats sugar and produces, among other things, alcohol and carbon dioxide. Alcohol is less dense than water. So as fermentation proceeds, two things happen at once: sugar leaves the solution, and alcohol enters it. Both push the density down. Over a week or two the hydrometer sinks lower and lower, then stops.
When the reading holds steady for a few days, fermentation is done. That final number is your final gravity, or FG, and it usually lands somewhere between 1.008 and 1.015 for a typical beer, because yeast cannot ferment every last sugar.
The math is almost too simple
Subtract final gravity from original gravity, and multiply by 131.25. That gives you alcohol by volume, near enough.
ABV ≈ (OG − FG) × 131.25
A beer that started at 1.052 and finished at 1.012 ran a drop of 0.040, which works out to about 5.25 percent ABV. The constant 131.25 is an empirical fudge factor that bundles up the chemistry of how much alcohol a given drop in gravity represents. It is not exact, but for homebrew it is closer than your palate will ever need.
Why bother reading it at all
Two reasons. The first is that you cannot taste alcohol percentage reliably, and guessing leads to a session beer that flattens a party or a "small" beer that is secretly nine percent. The second is diagnostic: if the gravity stalls high and will not drop, fermentation is stuck, and that tells you to check your temperature or rouse the yeast before you bottle a batch that is not finished. A bottle of unfinished beer keeps fermenting on the shelf, builds pressure, and occasionally explodes.
The hydrometer is how the shed talks back to you. Learn to read it and the whole process stops being a leap of faith.