# Beer math

## Recipe Calculation

### Predicting Original Gravity

```GU = (lbs of grain x points) / Total Volume in Gallons
```

So for this calculation let say I'm using 2 row pale malt with a gravity of 1.030 which would be gravity 30 points. Take the amount of pounds of grain and multiply it by the gravity points then divide by the total volume in gallons. Here is an example below:

```GU = (10 lbs of grain x 30 points) / 5 US gallons = 60
```

To convert GU (Gravity Units) to specific gracty, divide by 1000 and add 1: 60 would be 1.060. What I do on my brew sheet is add the gravity for each grain then divide that by the total volume in gallons.

```(10 lbs of grain x 30 points) = 300
(5 lbs of grain x 10 points)  = 50
(300 + 50) / 5 US Gallons = 70 or 1.070
```

### International Bitterness Units (IBU)

```IBU = ((Alpha Acids AA% x Quantity in oz's) x % Utilization) / 7.25
```

Note: This does not account for utilization differences due to gravity of the wort

Multiply Alpha Acids of the hop by the amount of hops you are using. Then take that calculation and multiply it by the total utilization based on the amount of time you plan to boil these hops. Take that calculation and divide by the constant 7.25 to get your final IBU.

Utilization Chart:

Time Utilization
00-05 minutes 5.0%
06-10 minutes 6.0%
11-15 minutes 8.0%
16-20 minutes 10.1%
21-25 minutes 12.1%
26-30 minutes 15.3%
31-35 minutes 18.8%
34-40 minutes 22.8%
41-45 minutes 26.9%
46-50 minutes 28.1%
51-60 minutes 30.0%

Example:

```((8.8 AA% x 0.75 oz ) x 30) /  7.25 = 27.31 IBUs
```

### Standard Reference Method (SRM)

```SRM = (lbs Grain x Deg Lovibond) / Total Volume in US Gallons
```

So if you used 10 pounds of 2 row grain that is 1.9 Lovibond then you would multiply lbs of grain by Lovibond to get your SRM. Then add all the SRM's and divided by total batch volume by total US Gallons. Here is an example below:

```(10.00 lbs x 1.9 Lovibond) = 19.0 SRM

(0.50 lbs x 10.0 Lovibond) = 5 SRM

(19 + 5) / 5 gallons = 4.8 SRM
```

### Strike water

```Tw = (.2/R)(T2 - T1) + T2
R = Ratio of water to grain in quarts per pound
T1 = the temperature of the grains in Fahrenheit (or Celsius)
T2 = the target temperature of the mash in Fahrenheit (or Celsius)
```

For the mash ratio you can use between 1-2 quarts per pound of grain. Keep in mind that changing the ratio can have a direct impact on what kind of beer you will end up with. For example:

<1.25 qts per lb of grain:

• Less fermentables
• Sweeter
• Malty / More body

>1.25 qtsper lb of grain:

• More fermentables
• Drier
• Less body

### Infusion water

```Wa = (T2 - T1)(0.2G + Wm)/(Tw - T2)
Wa = The amount of infusion water to add
Wm = The total amount of water in the mash
T1 = The initial mash temperature
T2 = The target mash temperature
Tw = the actual temperature of the infusion water
G = The amount of grain in the mash
```

### Absorption Loss

```Absorption loss in gallons = (lbs of grain) x 0.20)
```

Note: each system can be a little different and therefore may use a different constant than 0.20 gallons per lb of grain.

Total kettle Wort:

(Mash Water - Absorption Loss) + Sparge Water

## Boiling

### Evaporation Rate

```Evaporation rate = Pre-Boil Wort * 0.10
```

The constant of 10% per hour can be different in every system. This can be a range from 6-15% depending on your equipment. To figure out exactly you can do a test boil and measure the amount of water left after the boil. So if you start with 10 litres of water and finish with 9 after one hour your evaporation rate would be (10-9) / 10 = .10 or 10%

### Evaporation Loss

```Evaporation loss = (Evaporation Rate / 60) x Total Boil Time
```

### Cooling Loss

```(Total Kettle Wort - Evaporation Loss) x 0.04
```

You will lose 4% volume do to cooling/shrinkage loss based on the fact that the liquid will lose density when cooling.

## Fermentation

### Alcohol By Volume

```ABV = ((1.05 * (Starting SG – Final SG)) / Final SG) / 0.79 * 100
```

or if you care to just get a close number:

```ABV = (Original Gravity - Final Gravity) x 131
```

### Alcohol By Weight

```ABW = (0.79 x ABV) / Final Gravity
```

### Degrees Plato

```Plato = (-463.37) + (668.72 x Original Gravity) - (205.35 x (Original Gravity ^ 2)
```

Here is an example using 1.040 for Original Gravity:

```(-463.37) + (668.72 x 1.040) - (205.35 x (1.040 ^ 2) = 9.99224 or 10 Plato
```

### Calories

```12oz bottle = ((6.9 x ABW) + 4.0 x (Real Extract - 0.10)) x Final Gravity x 3.55
```

I prefer ml's instead of oz's myself, and I use larger bottles than the 12 oz. So for my 500 ml and 1000 ml I change the above formula. If you remove the 3.55 at the end of the formula it will give you calories per 100ml of beer. Then just multiply that by the size of your bottles. Here is an example using a 500 ml beer:

```Calories per 500ml of beer = ((6.9 x ABW) + 4.0 x (Real Extract - 0.1)) x Final Gravity x 5
```

If you're using oz but your bottle is larger than 12oz use the below formula. Here is an example using an OG of 1.040 and FG of 1.010:

```Calories per bottle = ((6.9 x ABW) + 4.0 x (Real Extract - 0.1)) x Final Gravity   x 29.573 / 100 * (Bottle size in oz)
```

Example:

```((6.9 x 3.074) + 4.0 x (3.090347456 - 0.1)) x 1.010 x 29.573 / 100 * 16 = 174 Calories per 16 oz beer
```

### Real Extract

```Real Extract = (0.1808 x Plato Original Gravity) + (0.8192 x Plato Final Gravity)
```

Here is an example using an Original Gravity of 1.040 and Final Gravity of 1.010. Determine Plato for each gravity with above degree Plato formula and then punch then into the formula:

```(0.1808 x 9.99224) + (0.8192 x 2.559665) = 3.90347456
```

### Hydrometer Temp Correction

```Correction = 1.313454 - 0.132674 x T + 2.057793 x 2.71828 -3 x T^2-2.627634 x 2.71828-6 x T^3
T = Temperature Deg F
```

Example:

```1.313454-0.132674 x 64.4 + 2.057793 x 2.71828 -3 x 64.4 ^2-2.627634 x 2.71828-6 x 64.4 ^3 = .0006
```

If you use Degrees Celsius then multiply temperature by 1.8 and add 32. Here is an example below of the changed formula:

```1.313454-0.132674 x ((64.4x1.8)+32)+ 2.057793 x 2.71828 -3 x ((64.4x1.8)+32) ^2-2.627634 x 2.71828-6 x ((64.4x1.8)+32) ^3 = .0006
```

### Apparent / Real Attenuation

```Apparent = (Degrees Plato Final / Degrees Plato Start) - 1
Real/Actual = (Real Extract / Degrees Plato Start) -1
```

This measures how much of the sugars has been fermented in to alcohol... I show this number as a percent in my excel sheet.

## Bottling

### Priming Sugar

```Sugar in grams = 15.195 x Volume in Gallons ( Desired CO2 Volume - 3.0378 + .050062 * T - .00026555 * T * T )
T = Temperature at bottling in degrees F
```

For desired CO2 volume I usually check what the range is on that style of beer. For example an American Ale CO2 volume is between 2.2-2.8. I usually take a number between that range and plug it into my formula.

Example:

```15.195 x 5 ( 2.4 - 3.0378 + .050062 * 64.4 - .00026555 * 64.4 * 64.4 ) = 113 grams
```