So far this year I've brewed:

Secondary - ESB
Secondary - Ordinary Bitter
Secondary - Wild Grape Wine
Secondary - Wild Grape Wine
Bottled- APA
Bottled- APA

Latest Updates:

- Hydrometer Temp Correction (Incorrect formula was found but fixed thanks to Fredrik Nivert) - Update 5 Mar 2008

- Glenn Tinseth's IBU Equation- Update 13 Feb 2008

- Required Cell Count Formula - Update 7 Feb 2008

- Pictures All Grain Added - Update 7 Feb 2008

- Brewing Worksheet (Excel) - Update 7 Feb 2008 (Ver 3.0)  

Beer Math

I basically got into this because I wanted to create my own excel spreadsheet. Little did I know how complicated it can be to figure some of these values out. Here are some of the calculations I ran into.

If anyone else is making an excel sheet I would love to see it from time to time. Or if you have questions on what I did with mine feel free to drop me an email. Best of luck... (Grimmy - 7 feb 08)

Glenn Tinseth's IBU Equiation:

Here is another IBU formula created by Glenn Tinseth. This is a good calculation when doing full boils If you would like more information on what exactly these values are below visit Glenn Tinseths site and you can read all the technical. information until your head hurts.

Here is the formula:

          IBUs = (Boil Time Fact * Bigness Factor) * (mg/l of added alpha acids)

Here are the calculations required for this above formula:

          mg/l of added alpha acids =            decimal AA rating * ozs hops * 7490
                                                                           -------------------------------------------------
                                                                           volume of finished beer in gallons 

                             Boil Time factor =              1 - e^(-0.04 * time in mins)
                                                                             ----------------------------------
                                                                                               4.15

                                Bigness factor =              1.65 * 0.000125^(wort gravity - 1)
 

Here is an example I used for my excel sheet:

    NOTE:  Utilization = Boil Time Fact * Bigness Factor 

    NOTE: e = Base for natural logarithms (use 2.72)

Utilization = ((1.65 * 0.000125^(Original Gravity -1 )) * ((1 - 2.72^(-0.04 * Hop Boil Time))/4.14)

IBU = Utilization * ((oz * (AA% /100) * 7490 / Total batch in US Gallons)

Yeast Required Cell Count:

Required Cell Count = (0.75 million) * (Millilitres of wort) * (Degrees Plato of wort)

Here is an example I used for my excel sheet:

Cell Count = (750000) * (Liters of wort * 1000) * ((-463.37) + (668.72 * OG)-(205.35*(OG^2)))) * 0.000000001)

 Note: (I used the 0.000000001 to move the decimal point)

Now to determine how many packs you will need for Wyeast Smack Packs, White labs vials, and Dry Yeast Grams you can use the calculations below:

Wyeast = Required Cell Count /100

White Labs = Required Cell Count /100

Dry Yeast Grams = Required Cell Count /20

Alcohol By Volume:

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

Calculating 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

Calculating Calories per 12oz bottle of beer:

This will calculate calories on a 12oz bottle of beer.

((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:

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

If your using oz but your bottle is larger than 12oz use the below formula . Here is an example using an Origin Gravity of 1.040 and Final Gravity of 1.010.

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

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

International Bitterness Units (IBU): (Standard Easy way!)

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

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:

 Example: ((8.8 AA% x 0.75 oz ) x 30) /  7.25 = 27.31 IBU's

Standard Reference Method (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 Grain x 1.9 Lovibond) = 19.0 SRM's

                                  (0.50 Lbs Grain x 10.0 Lovibond) = 5 SRM's

                                  (19 + 5) / 5 gallons = 4.8 SRM's

Hydrometer Temp Correction:

T1 = Temperature Deg F

T2 = Temperature Deg F

T3 = Temperature Deg F

NOTE: ^ means "to the power of"

Temp Correction = 1(1.313454-0.132674 x T1 + 0.002057793 x  T1 ^2-0.000002627634 x T1^3) / (1000)

For below result a .0006 is the correction to be added to your OG. So for example if you had an OG of 1.030 you would have 1.0306. I would then round up to 1.031 for my final OG temp corrected.

Example: (1.313454-0.132674 x 64.4 + 0.002057793 x 64.4 ^2-0.000002627634 x 64.4 ^3) / (1000)= .0006

Predicting Original Gravity:

(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:

(10 lbs of grain x 30 points) / 5 us gallons = 60

To convert this 60 back divide by 1000 and add 1 so 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

Determine Priming Sugar Required For Carbonation in grams:

T = Temperature at bottling in degrees F

15.195 x Volume in Gallons ( Desired CO2 Volume - 3.0378 + .050062 * T - .00026555 * T * T )

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. For a list of CO2 volumes for each style of beers try this site.

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

Determine Forced Carbonation required for desired volume in PSI:

T = Temperature at bottling in degrees F

Vol = Desired CO2 Volume level

NOTE: ^ means "to the power of"

 -16.6999 - 0.0101059 * T+0.00116512 * T ^2+0.173354 * T * Vol +4.24267 * Vol - 0.0684226 * Vol ^2

This will give you the required PSI to set your system at in order to hit your target desired CO2 volume level. You could also use a chart as many exist on the internet but then you would miss out on all the fun on getting this to work automatically in your spreadsheets ;) Refer to the link  in the above "Determine Priming Sugar Required For Carbonation in Grams" section for typical volume levels for your style of beer.

Example:

 -16.6999 - 0.0101059 * 64 +0.00116512 * 64  ^2+0.173354 * 64 * 2.3 +4.24267 * 2.3 - 0.0684226 * 2.3 ^2

= 22.3 PSI

Apparent Attenuation:

Apparent = (Degrees Plato Final / 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.

Real Attenuation:

Real = (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.

Mash Water:

Mash Water = Mash Ratio x Lbs Grain

For the mash ratio you can use between 1-2 quartz 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:

Less than1.25 Quartz per lb of grain:
- Less fermentables
- Sweeter
- Malty / More body

greater than 1.25 Quartz per lb of grain:
- More fermentables
- Drier
- Less body

So here we will use 1.3 quartz of water per pound of grain...

1.3 x 10 lbs of grain = 1.3 Quartz of mash water

Absorption Loss:

(lbs of Grain) x 0.20) = Absorption loss in gallons

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

Evaporation Rate (10% / hr):

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 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.

Brewhouse Efficiency:

((Original Gravity x 1000) -1000) / (Total Gravity points / Mash Volume in Gallons) = BH Efficiency

Here is an example with an Original Gravity of 1.040 and the following grain bill.

10 lbs 2 Row x 36  Gravity Points = 360

1 lb Crystal 40 x 34 Gravity Points = 34

Total Gravity points  = 360 + 34 = 394.00

After we have our Total Gravity Points we can now finish our brewhouse efficiency calculation...

((1.060 x 1000) -1000) / (394.00 / 5) = 0.76 or 76%

Created -- 2007-2008, Marc Tremblay, All Rights Reserved
This page was last updated Wednesday, March 05, 2008