How does a yeast starter affect original gravity reading?

I've prepared a 1qt (~1L) yeast starter according to instructions from Wyeast.com. I didn't measure its gravity, but in theory it should be about 1.040.

I am brewing a 5 gallon batch of high gravity stout @ 1.076 target original gravity.

So, after pitching the starter, the total volume in the fermenter will be 5.25 gallons.

How do I calculate a more accurate gravity reading from the blended starter and wort?

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If the starter fully fermented, most of the 1.040 should be gone; normal yeast attenuation is around 75%, so you should have 1L of 1.010 beer in the starter vessel.

1L of 1.010 beer into 19L of 1.076 OG wort would reduce the OG down to about 1.073. (76 points * 19L + 10 points * 1L) / 20L = 72.7 points = 1.073.

Though if possible, you should try to cold-crash the yeast, decant off most of the starter liquid, only retaining enough liquid to swirl the yeast back up into a slurry, and pitch that.

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I think you should use the original gravity of the starter, not the final gravity, when doing the weighted average. Otherwise your ABV calculation will be off for the completed beer. – Tobias Patton Jan 19 '14 at 16:56
Oh! Use an average formula. Makes sense now. But I think @Tobias-Patton is right that you should use the OG for both wort contributions. – gfullam Feb 7 '14 at 4:23

The easiest way to determine the effect of starter gravity is to decant the starter so the amount is negligible. In addition, I've found that it makes better beer.

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Average it!

Multiply your starter volume and wort volume by their original gravities respectively to produce numbers that can be combined to derive an average gravity reading from the blend.

Do this by dividing the sum of the gravity-volume products by the sum of all wort:

( ( OG1 * V1 ) + ( OG2 * V2 ) ) / ( V1 + V2 ) = SG

Where...

• OG1 is the original gravity of your starter wort
• V1 is the volume of your starter wort
• OG2 is the original gravity of your wort
• V2 is the volume of your wort
• SG is the specific gravity of the blend

If blending more than two parts:

( ( OG1 * V1 ) + ( OG2 * V2 ) [ + ( OGn * Vn ) ] ) / ( V1 + V2 [ + Vn ] ) = SG

In this case:

( ( 1.040 * 0.25 ) + ( 1.076 * 5 ) ) / ( 0.25 + 5 ) =

( 0.26 + 5.38 ) / 5.25 =

5.64 / 5.25 =

1.074 specific gravity of blended starter and wort

Kudos to @jsled and @tobias-patton for providing the clues to solve this problem

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Holy bold text Batman! – Scott Feb 7 '14 at 5:07