Most homebrewers measure the specific gravity of their beer at the beginning of fermentation and then at the end. They then use these numbers to calculate (usually using software) what the ABV of their batch of beer is. This can be very useful knowledge, especially when the brewer is asked the inevitable question, “How much alcohol is in this?” when they share the beer with friends.

While many recipes and software will provide predictions of what your ABV will be, these are rarely accurate. There are simply too many variables which cannot be taken into consideration until the beer is brewed. So, the only way to calculate the ABV with any accuracy is for the brewer to do it on their own beer.

Unfortunately, the truth is that homebrewers can’t really measure the alcohol in beer directly. To do this would require lab equipment well beyond the limits of the average home brewing budget. However, there is a measurement that can be taken which will help us calculate the ABV using a simple formula. That measurement is called the Specific Gravity.

## What is Specific Gravity?

Many homebrewers operate under the false assumption that they are measuring the sugar content of the wort when they measure specific gravity. While this is very close to the truth, it is not 100% accurate.

The Specific Gravity of a liquid is that liquid’s density compared to water. A liquid with a Specific Gravity of 1.030 is 1.03 times the density of water, for instance.

In the case of your beer, there are several factors which can contribute to the density of your wort before fermentation and of your beer when it is finished fermenting. Suspended in your beer, there are sugars, unfermentable starches, hop materials and oils, minerals, and other things that can all contribute to the density of the liquid.

If your gravity readings vary significantly from your recipe or your software’s prediction, there are many possible factors. It could be that your mash efficiency was higher or lower, that your starch conversion was more or less complete, or that your ingredients had a lower or higher yield during the conversion process.

In addition, your batch volume may be larger or smaller than expected, or your evaporation rate during the boil could have been higher or lower. As I said, there are many variables, which is why your recipe or software alone are not accurate predictors of ABV.

So, when you measure the Specific Gravity of your unfermented wort (often referred to as the “Original Gravity,” since it is before fermentation), you are measuring all of these things at once.

In the “Final Gravity,” you are still measuring all of these things, but the gravity will be much lower, as your yeast has eaten much of the sugar, which is more dense than water, and have left alcohol in its place, which is less dense than water.

So, while you are measuring the original and final gravity of the beer, you are actually using the overall change in gravity to calculate how much sugar has been changed into carbon dioxide and ethanol.

### How does the chemical reaction work?

When the yeast in your beer breaks down the fermentable sugars (glucose and fructose), it breaks them into alcohol molecules and carbon dioxide.

Here is the chemical formula for the reaction when your yeast makes booze:

Zymase is an enzyme used by the yeast to digest the sugar. As you can see from the equation, the sugar molecule on the left when combined in the reaction with Zymase, breaks into an even number of alcohol and carbon dioxide molecules.

When this chemical reaction is performed in your beer, it leaves the liquid far less dense than before, and that measurable changes is a consistent way to calculate the amount of alcohol in your beer.

As a bonus, you can also leverage this chemical reaction to carbonate your beer, which is essentially what you do when you add priming sugar to your beer before bottling. The yeast eat all of the sugar, converting it to more alcohol and carbon dioxide. The priming sugar calculations you see calculate the volumes of carbon dioxide that will be released into the beer based on the weight of the pure fermentable sugar being added to the batch.

### Doing the Math

Now that we know how the chemical reaction takes place, let’s discuss how we can calculate the change in alcohol based on the change in density.

If you’re going to go very far down the rabbit hole, you can look up Karl Balling, who pioneered calculating alcohol by weight using Specific Gravity. You’ll often hear of the Balling scale, which is a method for expressing the gravity of a liquid.

In order to keep it simple, we’ll use a few assumptions. The first is that your gravity readings are not being adversely affected by the air in which you’re taking your reading, and that you have allowed for any variation in temperature. The second is that your gravity is finishing at (or pretty close to) 1.010.

These assumptions are necessary in this case to eliminate the inclusion of them into the calculations. By using a constant instead of factoring in potential changes in atmospheric pressure and temperature, you can bring your ABV calculation down to a few simple steps.

You also will use the apparent extract of the fermentation to calculate this rather than the true extract, as the true extract is much harder to calculate.

##### To do the math, you’ll have to have the following pieces of information:

Your original gravity (OG), which is taken just before pitching your yeast and after the wort has chilled. Make sure you make any temperature adjustments to it before recording it. Follow the instructions for your hydrometer or refractometer for this.

Your final gravity (FG), which is taken just before packaging and before you add any priming sugar. Again, make sure you have adjusted for temperature if necessary.

##### To calculate ABV using specific gravity, you will then use this equation:

So, if you have a beer that has an original gravity of 1.050 and a final gravity of 1.010, this formula will give you the following:

ABV = 132.715 (.040)

ABV = 5.31%

This is the most practical way for the typical home brewer to estimate their ABV. It’s quick and relatively simple, and can be done with a pocket calculator or by hand in a pinch.

Ron Young says

Regarding % alcohol, You say the before and after hydrometer reading (corrected) plus math will not give a true value for alcohol. I agree but you never gave us an idea of how far off it could typically be. Are you talking 1%, 2% or fractions? Can you tie accuracy to brew styles like light, medium and dark brews? BTW, I never thought the amount of alcohol was that important anyway however I do understand it changes the taste.

Ben Stange says

It will rarely be off by a lot, and a hydrometer will serve for all practical purposes in the home brewing world. The color of the beer won’t affect a hydrometer reading, the hydrometer measures the density of the liquid, not the color, but I do wonder if the color could have an effect on a refractometer’s readings.

For the most part, you could only expect a few gravity points off on the hydrometer as far as alcohol %, so at the Homebrew level, it’s nothing to really worry about unless you’re a stickler (like me).

Art Glockler says

Very interesting,Will be tryin some of these.! Kuntz!

Eddie Wesselhoff says

Ben, I’m a real dummy when it comes to math so I do not understand where that 132.715 number comes from. Plus I don’t understand the formula ABV = 132.715. (0.040). I tried dividing, I tried multiplying but neither resulted in 5.31. The one formula that worked is OG – FG / ..00753. Why all the different formulas (like I said, I am math stupid).

Bryce says

Eddie, he didn’t provide the derivation for that number, however it’s a constant that makes several assumptions. Regarding the equation trouble, try 132.715 x 0.04.

Bryce says

Ben – great explanation and background, thank you! I did have a question about the equation’s second assumption (FG approximately equal to 1.010). I’m brewing a Belgian Quad with an OG=1.090 and an expected FG=1.028. How far off will my ABV appoximation be?

Zach says

Just brewed for the first time last week. I boiled and then I did not have a filter so I poured it all into my bottling bucket so I could pour it into my carboy from the spigot.

I took a sample from the spigot for the OG, I got 1.08 for an IPA, seems high. I wonder if I should have racked some from the middle of the batch instead of the sloppy bottom? Would that make any difference?