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Starter Calculations

Based on the collective experience of the Homebrew Digest a recommeded pitching rate of 1:10 was recommended for rapid starts and a reduced risk of external contamination.

Conversion Factors
1.0 gal = 3.78 liters = 128 fl ounces

Practical Starter Size suggestions for Batch sizes

Step-up Ratio	Batch Size	Volumes
1:10.6	1 gal	12 fl oz (beer bottle)
1:7.3	5 gal	12 fl oz (beer bottle) -> 2.5 liter (3 liter soda bottle)
1:10.3	10 gal	12 fl oz (beer bottle) -> 1 gal (milk jug)
1:4.7	10 gal	12 fl oz (beer bottle) -> 1.6l (8/10 of 2 liter bottle) -> 2.1gal (2 - 1gallon milk jugs)
1:5.4	15 gal	12 fl oz (beer bottle) -> 1.9 (2 liter bottle) -> 2.7gal (2 - 1 gallon milk jugs + 1 - 1/2 gallon milk jug)

How to calculate your own starter sizes
Take the volume you will be pitching into (batch size) and divide that by the initial starting volume. Next take the square root, cubed root, ... of that number untill you achive a pitching ratio close to what you are looking for. You will then multiply your starting volume by the ratio to find the next volume. An Example follows:

12 fl.oz * Ratio * Ratio = 1280 fl.oz (10 gallons)
1280 / 12 = Ratio * Ratio
107 = Ratio²
Sqrt(107) = Ratio
Ratio=10.3

For a ratio of 10.3 starter volumes will be 12 and 124 fl.oz finally pitching into 1280 fl.oz. Working with a cubed root yields a Ratio of 4.8, yielding starter sizes of 12, 58, 279 fl.oz pitching finally into your 10 gallon batch.

How to calculate the amount of DME to add to make your starter
Many will agree that starters should be cultured in the same S.G. as the wort you will be pitching into. Below is a formula to help calculate how much liquid/dry malt extract to add to a volume of water to get the appropriate S.G. in your starter.

V = Volume
D = Density

The applicable equations

( V_Starter * D_Starter ) = ( V_Water * D_Water ) + ( V_Fermentable * D_Fermentable )

V_Starter = V_Water + V_Fermentable

D_Water = 1.0

Joining and Simplifying the equations:

( V_Starter * D_Starter ) = ( V_Water * 1.0 ) + ( V_Fermentable * D_Fermentable )

( V_Starter * D_Starter ) = V_Water + ( V_Fermentable * D_Fermentable )

( V_Starter * D_Starter ) = V_Starter - V_Fermentable + ( V_Fermentable * D_Fermentable )

( V_Starter * D_Starter ) - V_Starter = ( V_Fermentable * D_Fermentable ) - V_Fermentable

V_Starter * ( D_Starter - 1 ) = V_Fermentable * ( D_Fermentable - 1 )

What does it mean?

Based on your desired Specific Gravity of your starter, the desired volume of the starter, and the Specific Gravity of your fermentable sugars, calculate the Volume of sugars to add to your starter container. Remember to keep your volume measurements in the same scale and system i.e. all in ounces, liters, or gallons. Next fill your starter container to the starter volume and mix. Voila. The specific gravity should be what you desired.

Standard Reference

Dry Malt Extract (DME)

The following is based on experimental data and are only as accurate as my dietary scale and my measuring spoons. The deduced equations should be very good at getting your starter close to your desired specific gravity. Here are the two equations I used to develop the equations:

1.6oz DME + 24fl.oz. HOH = SG of 1.030 (experimental)
0.0oz DME + 24fl.oz. HOH = SG of 1.000 (fact)

Based on the above 2 equations 1.6 oz DME + 24 fl.oz. HOH increases the SG by 0.030. Further simplification and reduction produces the following equation for guessing the amount of DME(in ounces) to add to Volume(in fluid oz) to achieve a desired SG.

(SG-1) * Volume * 2.22 = ounces DME to add to Volume of HOH (water) to achieve your desired specific gravity.

On a related note:
Ounces DME / 4.8 = cups DME, based on 1/3 cup = 1.6 oz. DME

Liquid Malt Extract (LME)

Coming soon.