Despite the amount of brew software that’s out there, it’s undoubtedly useful to be able to do your own brewing calculations.

I’ve been finding out how, and you can too if you want. All you have to do is keep reading!

Entering recipes into brewing calculators (like this or this) I’m never completely sure what I’m supposed to put where.

Volume, efficiency, gravity. These are ambiguous terms.

So after muddling along for long enough, I’ve spent the last few brews getting a handle on the numbers myself.

It turns out that basic brewing maths is not too tricky. And as with most things, spending time looking at it properly clears up a lot of doubts.

### Home Brewing Calculations

My idea here is to use an example recipe to describe calculations for water volume, gravity, alcohol, colour and bitterness.

I planned it as a series, but in the event decided there’s just too much overlap between each ingredient for that to make sense.

It’s more logical, I think, to look at everything in one lengthy hit.

Before I go any further, I should point out why I’ve put off learning about this until now. It’s because most of the information out there is in ounces, quarts and gallons.

Much preferring metric units myself, I’ve always found it difficult to follow along. I just don’t have an in-built understanding of, for example, what a cup is.

So this guide is largely for those of you who like metric units, although the principles are the same for everyone.

Apologies if you work in ounces and gallons but I think it’s fair to say you’re already well served elsewhere.

I’m also specifically using BIAB brewing as an example, but the concepts apply equally to other brewing methods. The main differences are in the water volume calculations.

### Starting at the End

In my opinion brewing equations are much more useful if they let you work backwards.

Instead of working out how much bitterness 40 g of Kent Goldings gives, it’s more useful to know how many hops you need to get 35 IBUs.

So that’s how I’ve presented the information where appropriate.

### Recipe Planning

OK. Let’s say you’re trying to brew a strong ale with these characteristics:

90% pale ale malt

10% crystal 60L malt

Hopped with Fuggles (bittering) and East Kent Goldings (flavour and aroma)

O.G. 1.085

80 IBUS

The rest of this page explains how to work out what you need of each ingredient.

In keeping with the backwards theme, the best place to start is with how much beer you want to end up with.

### How Much Beer To Make

Gravity and hop bitterness are both affected by final beer volume. The amount in the fermenter is what’s of interest in the calculations.

To account for spillages and siphoning losses it’s not a bad idea to add an extra litre to your finished target if you’re concerned about an exact volume.

So let’s make 15 litres of beer, planning for 16.

Target batch size: 16 litres

Before you can work out how much water to start with, you need to settle on the grain bill.

### Planning Malt and Fermentables

The gravity of beer is usually given as a decimal, 1.085 in the case of the example pale ale.

It describes the density of wort relative to pure water, but it doesn’t tell you how much malt you need.

For that there are **gravity points**.

### Thinking About Gravity Points

It took me a while to get gravity points, misguidedly focussing on gravity instead. Of course gravity is important, but once you shift to gravity points the various gravities (pre-boil, original, final etc.) make a lot more sense.

Gravity points describe the actual amount of sugar in your beer. Unlike gravity, which changes throughout brew day, gravity points stay the same. They are an absolute number that doesn’t change once you’ve extracted the sugar from the malt (unless you add raw sugar).

Here are some illustrations that explain the difference.

First, these two beers have the same gravity, represented by the density of the dots. Because of the different volume the total gravity points (the number of dots) is different.

The beer on the right has less sugar.

In the next example, the beers have the same number of gravity points. The different volume gives the one on the right a higher gravity.

The amount of sugar required to make both beers is the same.

It’s easy to work out how many gravity points you need, if you know your target original gravity and the target batch size:

So for the 1.085 strong pale ale:

### Extract Potential

Every fermentable you add to the mash contributes gravity points. How many is determined by the **extract potential**.

White sugar (sucrose) to all intents and purposes contributes 100% of its weight, and is the reference for all other ingredients. It has an extract potential of 100%.

Malt on the other hand, even after mashing, is not 100% sugar. This is obvious, of course, because you throw the husks away afterwards.

You can use a malt analysis sheet, like this one from Briess Malt, to find out the extract potential of a particular malt.

Looking at that chart, find the Extract % next to the malt you’re going to use. FG and CG stand for fine and coarse grain, and describe the size of the crushed malt the % represents.

For the two malts we’re interested in:

Pale ale malt: 80%

Crystal 60 malt: 76%

The pale ale malt should give us slightly more sugar than the crystal, per weight.

Extract potential is a theoretical maximum that you’ll never get from a home brew set-up, nor probably would you want to.

This is where **efficiency** comes in.

### Efficiency

The percentage of potential extract you actually get from your mash is called efficiency.

A good working number is 70%, although as you brew more you start to know how your system works and can adjust the number accordingly.

Now if we go back to sucrose, 1 pound of it contributes 46 points of sugar when added to one gallon of water. Another way of saying this is that it gives 46 ppg (points per pound per gallon).

All else derives from this, so before going any further let’s convert it to pkgl (points per kilogram per litre) with the conversion factor 8.345.

So 1 kg of white sugar adds 384 gravity points to 1 litre of water.

Now you can calculate the pkgl of anything:

But let’s get back to planning the recipe. Combining the above (extract potential, efficiency and the white sugar reference point) you get the equation for gravity points from any malt:

The gravity points in a beer is the total of each malt’s contribution.

As I mentioned above, I prefer to work backwards so rearranging the equation I get:

All that’s necessary now is to work out the number of gravity points that each grain provides.

Of the 1360 total 10% are from crystal 60 malt and the rest are pale ale. That means:

Pale ale malt: 1224 points, 80% potential extract

Crystal 60L: 136 points, 76% potential extract

You can now work out the amount required of each:

**Pale Ale**

**Crystal**** 60L**

We now have a grain bill:

90% Pale ale malt: 5.69kg

10% Crystal 60L: 0.67kg

### OTHER MALT CALCULATIONS

At this point you can check what the likely beer colour is and how strong the beer will be.

Colour and strength don’t feed directly into the bitterness calculations, but you might as well get them right now. Then you can tweak the grains, if necessary, before going on.

### Predicting Beer Colour

I’m going to skim over this, because by all accounts predicting beer colour is approximate at best.

Personally, I’m not especially bothered as long as it’s roughly in the ball park of what I’d expect from a particular beer.

The metric unit of beer colour is EBC, but the equations are all based around the Standard Reference Measurement (SRM).

There’s a straightforward conversion to EBC which can be done at the end.

To predict beer colour you need to know how many Malt Colour Units (MCUs) you have. These’re similar to gravity points, in that they’re a function of the amount of malt and its colour potential.

The total MCUs are worked out like this:

2.205 converts kg to pounds, 0.264 litres to gallons. I looked at taking those factors out and running the equation through as metric but it seemed to make things more complicated.

If you know an easier way of doing it please let me know!

On the same malt analysis chart you used for the gravity points, get the colour rating in Degrees Lovibond.

Pale ale malt: 3.5°L, 5.69kg

Crystal 60L: 60°L, 0.67kg

Then calculate the MCUs.

**Pale Ale**

**Crystal 60L**

Simply add the contributions of each malt to get a total of 31 MCUs.

There are several ways of turning this into a prediction of colour. But cutting straight to the chase, here’s the Morey version:

Which for the strong ale gives:

To convert SRM into EBC multiply by 1.97:

At this point you might decide to change the crystal malt variety to lighten the beer, for example.

Bear in mind that there are so many variables in beer colour such as length of boil, amount of hops, age of beer, etc., that an approximation is the best you can hope for.

If you want to know more, it’s explained clearly and in more detail in an appendix of How To Brew.

### Predicting Alcohol Levels

This is a fairly straightforward matter, not worth spending much time on because of its approximate nature.

You can predict the final gravity, the amount of sugar left after fermentation, from the attenuation of the yeast. It seems reasonable to use 75% for every calculation, as this is a rough estimate anyway.

Let’s say our ale uses Windsor yeast:

So:

### Predicting Water Volumes

Before moving onto hop bitterness, you need to look at water.

From a practical point of view you want to know how much water to start with. But you also need an estimate of the boil volume to use in the bitterness calculations.

The basic calculation for starting volume is straightforward:

S=Starting volume (to be determined)

T=Target batch size (as explained above)

G=losses to Grain (rate of e.g. 1.1 litre/kg)

E=losses to Evaporation (rate of e.g. 2.1 litre/hour)

H=losses to Hops and break (e.g 1 litre)

You should determine these rates for your own brewing system, but I’ve put my current assumptions in brackets as an example.

Losses to grain and evaporation need a little work before you feed them in:

So for the ale:

Start volume: 26 litres

### Planning Hop Additions and Calculating Bitterness

While you could specify hops by weight alone (as in some old home brewing books), the chances are you’ll struggle to be consistent between batches, or to compare one beer with another.

That’s because alpha-acid content, responsible for bitterness, varies from hop to hop.

### AAUs

The first step up from a simple weight is the AAU. This takes into account the alpha acid content:

It’s usually in ounces but it works just fine as a metric value, so long as you don’t interchange without converting.

For example, 40g Nugget with 12% alpha acid content:

If you’re brewing to someone else’s recipe you generally try to match the AAUs. Say your Nugget hops only have 10% AAU, you can work out how many to use like this:

So:

48 g of 10% alpha acid hops is the same as 40 g with 12%.

That’s all very well, but what about when you’re deciding how many hops to use in a recipe built from scratch?

To match relative bitterness levels across a variety of beers you need to be more accurate.

Unfortunately, there’s no simple equivalent of extract potential for hops.

The amount of alpha acid (the main cause of bitterness) that wort gets from the hops is called **utilisation**. This is dependent on many things such as length of boil, gravity of boil, age of hops, format of hops and more.

Many of these factors don’t work in a linear way so calculation is complicated. In other words, brewing software’s so useful because bitterness is a pain to work out.

### Hop Utilisation and IBUS

Beer bitterness is measured in International Bitterness Units (IBUs). This can be predicted in advance if you know the alpha acid content, the amount and the utilisation of your hops.

The basic formula for IBUS is:

%A = Alpha Acid %

U = Utilisation (decimal)

W = Weight in grams

V = Volume (final) in litres

The good news is that the IBU is a metric unit, defined as 1 milligram of hop iso-alpha acid per litre of wort.

Utilisation is not completely understood and there are many proposals for determining it. This excellent article from Zymurgy runs through many of them.

Most often I see recommended the Tinseth method, which is what I’ve started using. It’s described here by Tinseth himself.

The important thing to realise is that for each combination of boil length and wort gravity the utilisation of the hops is different.

In a nutshell, utilisation increases with boil length…

…and decreases with wort gravity…

…although, as ever, advice is always changing and there’s now a theory that high gravity isn’t necessarily the cause of decreased utilisation.

You can use Tinseth’s formula to calculate utilisation manually, or look up the relevant combination in his table. It’s at the bottom of the description.

### Boil Length and Boil Gravity

Before we get back to the ale recipe, you’ll see in the table that you combine boil length with wort gravity to get utilisation.

Boil length is self-explanatory: it’s how long you boil the hops.

Gravity is *of the boil*. To work this out, we need to bring back some information from before: gravity points and boil volume.

I think John Palmer uses the volume at the start of the boil, but Tinseth says to use an average so that’s what we’ll do.

You can work out the average boil volume by going back to the water calculations.

S=Starting volume

G=losses to Grain

E=losses to Evaporation

For our ale:

With this we can get the boil gravity:

### Divide The IBUs

Before working out the weights, you need to make an executive decision about when to add the hops.

For the example, let’s say you decide:

Fuggles: 5% AA, 60 mins, 40 IBUS

Kent Goldings: 4.5% AA, 30 mins, 25 IBUS

Kent Goldings: 4.5% AA, 5 mins, 15 IBUS

Total 80 IBUs

Half the IBUS are added by the Fuggles at the start. The rest are spread between two additions of Kent Goldings that will give flavour and aroma as well.

Now we’re able to go back to the tables and look up the utilisation % for each addition.

Fuggles: 60 mins, 40 IBUS, 0.169

Kent Goldings: 30 mins, 25 IBUS, 0.130

Kent Goldings: 5 mins, 15 IBUS, 0.036

Note that 1.085 isn’t in the table, so I interpolated between the values given.

Rearranging the IBU equation we can work out the amount of each hop addition:

(V is target batch size, not boil volume).

**Fuggles 60 minutes**

**Kent Goldings 30 minutes**

**Kent Goldings 5 minutes**

Fuggles: 76g, 5% AA, 60 mins

Kent Goldings: 68g, 4.5% AA, 30 mins

Kent Goldings: 148g, 4.5% AA, 5 mins

### Correction For Pellets

These hop weights are for leaves.

When using pellets, it’s usually agreed you need less of them but there’s no set correction factor.

Randy Mosher recommends reducing the quantity by 25% when using pellets.

Fuggles pellets: 57g, 5% AA, 60 mins

Kent Goldings pellets: 51g, 4.5% AA, 30 mins

Kent Goldings pellets: 111g, 4.5% AA, 5 mins

If IBU calculations are estimates, you may be thinking why bother?

Even if the beer doesn’t actually have 80 IBUS, or whatever (you’re not going to measure it), it is useful to know that it has 5 more than your last batch.

### The End

Now we have the final recipe:

Target batch size: 16 litres (to get 15 litres of beer)

Start volume: 26 litres

Pale ale malt: 5.69kg

Crystal 60L: 0.67kg

O.G.: 1.085

Fuggles: 76g, 5%, 60 mins

Kent Goldings: 68g, 4.5%, 30 mins

Kent Goldings: 148g, 4.5%, 5 mins

80 IBUS

Yeast: Windsor

These are home brewing calculations as I’ve come to understand them. Please bear in mind I’m a mere home brewer, far from an expert brewing mathematician or scientist.

Test them out and see if they work on your system. If not, tweak them!

Finally, I’ve built a spreadsheet based on these sums that works everything out automatically and can easily be changed.

Of course I could, and do, use brewing software instead. But doing it has given me a good feel for what’s going on when I adjust recipes.

If you can I’d highly recommend doing the same.

## Comments...

Good One!

This one is pretty good (and Free) and Units can be changed easily and recipes can be scaled etc.:

http://hbd.org/cgi-bin/recipator/recipator

Thanks for the link Michael. I’d not come across that before but it looks to be simple and effective.

Cheers!

Thanks to Niels R. who sent the following information by email:

About efficiency and extract potential you say that 1 kg of white sugar adds 384 gravity points to 1 litre of water. But using the HWE (Hot Water Extract) calculation method the common figure is 386 gravity point for 1 kg of white sugar in 1 litre of water. The difference is marginal, but I just wanted to let you know.

You sir, are a life-saver.

I’ve been fighting the Palmer book for months now. Not being a mathematician, I really struggle trying to convert everything to metric, plus I find the explanations there rather muddy.

I appreciate the time you have spent making this accessible.

Cheers.

Thanks for saying so and glad it was useful.

Cheers.

Hi, Really useful post, thank you for sharing. One query, on the example of the strong ale is the grain bill designed to get the og pre or post boil? Many thanks Niall

Niall,

It is post boil, just before you start fermentation.

Hi, I’m really thankful for your explanations as I continuously struggle with these pounds/cups/points etc..

However, as soon as I try to understand, I struggle again with some of the basics:

– you state that 1 pound of sugar in one gallon of water contributes 46 points – where does this number come from (did you measure or am I missing common knowledge)?

– you state that 8.345 is the conversion factor for converting ppg into pkgl – where did you derive this number from?

I would appreciate if you could elaborate on this.

Many thanks,

Bruno

With the help of https://homebrew.stackexchange.com/questions/9733/convert-us-to-metric-gravity-points I managed to figure the conversion factor.

My problem was that I calculated 1 lb = 0.454 kg and 1 gal = 3.790 l and got confused. The numbers seem more obvious with:

1 kg = 2.204 lb and 1 l = 0.2641 gal.

Then 2.204 : 0.264 = 8.345.

I hope this may help others.

Thanks for commenting, and for answering.

Re the conversions this has confused me previously but the explanation is that the gallon conversion here is to American gallons (3.78 litres) not UK gallons (4.544 litres). Hence 1 litre = 0.2641 US gallons used in the equation.

Thanks for clarifying – the two types of gallon can indeed cause confusion.

Many thanks for sharing this useful info in such a clear way.

One thing: your discussion of the difference between gravity and gravity points would be clearer if you emphasised that ‘gravity’ when used by brewers in fact means ‘specific gravity’ – which is a measure of density (of a sugar solution), while ‘gravity points’ are a measure of mass (of sugar) independent of the amount of water it is dissolved in.

Paul,

Thanks for the suggestion. Hopefully this will help others understand the difference.