Help! with gravity calculation. math is hard

[HB_ATL73]

I just brewed a Belgian strong ale with BIAB (which is my 3rd time doing so I am still dialing in my efficiency). Goal was to reach 5.5 gallons into the fermenter and reach a 1.075 OG. Well, the volume that reached the fermenter was 4.75 gallons. When cooling my wort I took a sample for hydrometer reading- I cooled this to 70 deg and it read 1.090!

Needless to say, I then topped up the fermenter to 5 gal with water and pitched the entire yeast starter (1L starter with 100grams DME which should put it at 1.030-1.040) which ended up in my final volume of 5.25 gal.

Im struggling to get the math right for my new calculated OG with the added water and yeast starter. Could anyone help me with this math? With just a quarter gallon water and the starter added in I am sure my OG is still sitting in the high 1.080's- which is great efficiency thanks to the advice of many of you to make a finer crush for my grain for BIAB

Any help would be greatly appreciated

 

[Dgallo]

I just brewed a Belgian strong ale with BIAB (which is my 3rd time doing so I am still dialing in my efficiency). Goal was to reach 5.5 gallons into the fermenter and reach a 1.075 OG. Well, the volume that reached the fermenter was 4.75 gallons. When cooling my wort I took a sample for hydrometer reading- I cooled this to 70 deg and it read 1.090!

Needless to say, I then topped up the fermenter to 5 gal with water and pitched the entire yeast starter (1L starter with 100grams DME which should put it at 1.030-1.040) which ended up in my final volume of 5.25 gal.

Im struggling to get the math right for my new calculated OG with the added water and yeast starter. Could anyone help me with this math? With just a quarter gallon water and the starter added in I am sure my OG is still sitting in the high 1.080's- which is great efficiency thanks to the advice of many of you to make a finer crush for my grain for BIAB

Any help would be greatly appreciated

Why don’t you just recheck your gravity? If you topped up and pitched the starter you can just check it with a hydrometer. No one will be able to calculate it correctly for you since you don’t know the gravity of the starter when it actually went in. You may have started it at 1.030-1.040 but ithe yeast attenuated it and you didn’t check the gravity of that starter before pitching it.

 

[RPh_Guy]

Gravity points:
( 90 * 4.75 + 38 * 0.25 ) / 5.25 =

 

[HB_ATL73]

Why don’t you just recheck your gravity? If you topped up and pitched the starter you can just check it with a hydrometer. No one will be able to calculate it correctly for you since you don’t know the gravity of the starter when it actually went in. You may have started it at 1.030-1.040 but ithe yeast attenuated it and you didn’t check the gravity of that starter before pitching it.

Yeah I guess I could I just didn't wanna open it up again and have to sanitize. Maybe it would be the smart thing to do

 

[HB_ATL73]

Gravity points:
( 90 * 4.75 + 38 * 0.25 ) / 5.25 =

Thank you sir!

Just took another sample and measured...

Spot on calculation!

 

[Dovage]

I've had similar issues and for me it was underestimating my boil off. So I kept concentrating my wort. Once I figured that out my starting water volume had to increase.

 

[ScrewyBrewer]

Gravity points:
( 90 * 4.75 + 38 * 0.25 ) / 5.25 =

@RPh_Guy a nice formula and thanks for sharing. Question though, how did you arrive at the number 38?

 

[riceral]

@RPh_Guy a nice formula and thanks for sharing. Question though, how did you arrive at the number 38?

View attachment 652762

I *think* this is to account for the DME starter (0.25 gallons at 1.038).
Just a thought.

 

[kh54s10]

I *think* this is to account for the DME starter (0.25 gallons at 1.038).
Just a thought.

I wonder? Why would a starter gravity be at 1.038? I make starters starting between 1.040 and 1.038, fermentation would take that lower. And depending on how long the starter is run, there would be no constant number. It could be anywhere from almost 1.040 to totally fermented out = 1.00x? How low did the yeast take it?

 

[RPh_Guy]

OG is before any fermentation. 38 points represents the OG of the starter wort.

 

[kh54s10]

OG is before any fermentation. 38 points represents the OG of the starter wort.

If you are adding starter wort to the beer where does the .38 come from. As I said I start many of my starters at 1.038. By the time the starter is added to the beer it is no longer at .38 What am I missing?

 

[RPh_Guy]

When calculating OG we used pre-fermentation gravity.

 

[kh54s10]

When calculating OG we used pre-fermentation gravity.

Yes, but isn't the starter already at least partially fermented when added to the wort thus not adding .38 to the OG calculation? It seems to me that it would be closer to adding volume to the top up water in the equation.

 

[ScrewyBrewer]

Yes, but isn't the starter already at least partially fermented when added to the wort thus not adding .38 to the OG calculation? It seems to me that it would be closer to adding volume to the top up water in the equation.

I would have thought the same thing, it would be 38 (1.038) if adding the starter wort. But the fermented starter wort would be more like 12 (1.012) which is closer to water. Thank you all for helping to clear this up for me and others.

 

[RPh_Guy]

Yes, but isn't the starter already at least partially fermented when added to the wort thus not adding .38 to the OG calculation? It seems to me that it would be closer to adding volume to the top up water in the equation.

The calculation I gave is NOT to calculate the gravity at the time of "blending", but rather it is to calculate the actual Original Gravity which will be used to estimate attenuation and ABV.

If you use 12 points for the starter gravity to calculate "OG", then your final ABV and attenuation will be incorrect.

 

[ScrewyBrewer]

Since .25 gallons of top off water has zero gravity, shouldn’t the 1.090 OG calculation include it in the volume as
(90 * (4.74 + .25))?

The OP gave a starter gravity range of 1.030 to 1.040, was the 38 value then an assumed value within that range?

The .25 gallon (32 ounces) of top off water is included in the initial formula but the liter (33.8 ounces) of starter volume is not included in the formula. Both volumes including, the low gravity liter of starter and the zero gravity quart of top off water should be included, to equal the total 5.25 gallon volume stated.

 

[kh54s10]

The calculation I gave is NOT to calculate the gravity at the time of "blending", but rather it is to calculate the actual Original Gravity which will be used to estimate attenuation and ABV.

If you use 12 points for the starter gravity to calculate "OG", then your final ABV and attenuation will be incorrect.

I am still missing something or you are wrong. The OP had high gravity so he added water and pitched the starter before fermentation. So the starter did not add .38. It really only added something like .10. So your calculation of OG will read too high. IMO

 

[RPh_Guy]

Since .25 gallons of top off water has zero gravity, shouldn’t the 1.090 OG calculation include it in the volume as
(90 * (4.74 + .25))?

No.

Here's the calculation including the top up water:
( 90 * 4.75 + 38 * 0.25 + 0 * 0.25 ) / 5.25

The .25 gallon (32 ounces) of top off water is included in the initial formula but the liter (33.8 ounces) of starter volume is not included in the formula. Both volumes including, the low gravity liter of starter and the zero gravity quart of top off water should be included, to equal the total 5.25 gallon volume stated.

I hope it's now obvious why I didn't include it. The 0.25 gal water is multiplied by zero. It contributes no gravity points.

The OP gave a starter gravity range of 1.030 to 1.040, was the 38 value then an assumed value within that range?

Yes, based on the amount of DME used.

I am still missing something or you are wrong. The OP had high gravity so he added water and pitched the starter before fermentation. So the starter did not add .38. It really only added something like .10. So your calculation of OG will read too high. IMO

OK.....
Consider you have 5 gallons of fermented beer at FG 1.010. You add 0.25 gal of 1.040 wort.

How do you calculate the OG?

 

[Gnomebrewer]

I am still missing something or you are wrong. The OP had high gravity so he added water and pitched the starter before fermentation. So the starter did not add .38. It really only added something like .10. So your calculation of OG will read too high. IMO

OG stands for ORIGINAL Gravity. It's concerned with the gravity points of the original worts. The fact that the starter has partially (or completely) fermented is irrelevant. Consider that the main reason we want to know the OG is to calculate how much alcohol is present. If we use a lower gravity for the starter wort, simply because it has partially (or completely) fermented, we can't account for the alcohol that is already present.

 

[ScrewyBrewer]

The original post asked about wort gravity not alcohol content. Logic dictates it you add nearly half a gallon of water and very low gravity starter wort (in the form of one quart water and one liter of low gravity wort) to a 1.090 gravity wort the resulting wort volume will increase by half a gallon and be diluted, or watered down, to a gravity lower than 1.090. Which is the question posed by the original poster.

 

[ScrewyBrewer]

No.

Here's the calculation including the top up water:
( 90 * 4.75 + 38 * 0.25 + 0 * 0.25 ) / 5.25

I hope it's now obvious why I didn't include it. The 0.25 gal water is multiplied by zero. It contributes no gravity points.

Of course, but the point is the water will increase the total wort volume which will dilute the original 1.090 wort gravity.

 

[balrog]

I feel there are two ways people are looking at this. "What would OG have been adding all sugar and all volume" and "What would I have measured my OG after adding my finished starter", which are two slightly different things. There's all the water and sugars of the wort, would give an OG, then add <some> starter that now has a SG of <something> which will blend with OG to give some slightly lower OG'. Then there's the all water and sugars of the wort plus all water and sugars of the starter for total water and sugars if they were all together at the start to know a grand SG representing all sugars and all water.

If I make 5.0gal 1.050 wort, and add 0.25gal 1.010 starter, I should see measured SG of ... ?
(1.05 * 5 + 1.01 * .25) / (5.0 + 0.25) = 1.048

If I had put in the starter DME (to make 1.040 SG) with the sugars in the wort, it might have been
(1.05*5 + 1.04*.25)/5.25 = 1.0495

Frankly I rarely think about what a 1L starter adds/subtracts from a 5gal batch. And maybe I'm too simplistic but I would have just said to the OP that if you measured 1.090 * 4.75 = 427.5 sugar points divide by final vol of 5.0 = OG of 1.0855, and use that for any calculation.

 

[kh54s10]

I think balrog hit it. I am of the thinking of OG of the wort in the fermenter. Adding a starter will add to alcohol content. I still believe that the starter should not be considered as full strength by the time it is added. In any case the amount of change made by the starter would be well within the margin of error of just reading a hydrometer. - negligible.

 

[bracconiere]

Is there a similar way to do this for ABV? if add a starter that already has 6% ABV to a beer that has a potential 9% ABV? (not a serious question, just sayin', i count calories and it'd be important to me)

edit: so it depends if you want to know attenuation and ABV, or BH efficiency

 

[balrog]

I would do the multiple abv thinking of it like this:
Get OG/FG of wort, taking OG/Vol before add starter, then FG after racking off the sediment. Gives you final vol and OG/FG, for Vol1 at ABV1. Then do exactly the same for the starter, taking OG, FG, so you have starter SVol at ABV2. Then it's just adding two liquids of different abv for a final combined vol.

(Vol1 * ABV1 + SVol * ABV2) / (Vol1 + SVol) should be ABV total (and I greatly suspect it will be not that much different than ABV1

Example: 5 g OG 1.050, after sediment, yielding 4.6gal 1.010, 5.25%abv
1 liter starter, 1.040, no sediment, yielding 1 liter 1.010, 3.94%

Total (4.6 * .0525 + 0.264 * .0394) / (4.6 + 0.264) = 5.17% abv

 

[bracconiere]

I would do the multiple abv thinking of it like this:
Get OG/FG of wort, taking OG/Vol before add starter, then FG after racking off the sediment. Gives you final vol and OG/FG, for Vol1 at ABV1. Then do exactly the same for the starter, taking OG, FG, so you have starter SVol at ABV2. Then it's just adding two liquids of different abv for a final combined vol.

(Vol1 * ABV1 + SVol * ABV2) / (Vol1 + SVol) should be ABV total (and I greatly suspect it will be not that much different than ABV1

Example: 5 g OG 1.050, after sediment, yielding 4.6gal 1.010, 5.25%abv
1 liter starter, 1.040, no sediment, yielding 1 liter 1.010, 3.94%

Total (4.6 * .0525 + 0.264 * .0394) / (4.6 + 0.264) = 5.17% abv

LOL, now my brain hurts too! i'm not sure if this session is helping the OP... the title does say "math is hard"!

Is there a VB script that will do this? i think that's what he needs......lol

 

[Gnomebrewer]

The original post asked about wort gravity not alcohol content.

The OP asked about calculated Original Gravity of the entire wort, not wort gravity (or SG) at the time of combining.

Im struggling to get the math right for my new calculated OG with the added water and yeast starter.

Thus (4.75*90 + 0.25*38) / 5.25 is correct (for gravity points).

Of course, but the point is the water will increase the total wort volume which will dilute the original water gravity.

The increased total wort volume is accounted for by dividing by 5.25, which is the total wort volume including the water.

 

[ScrewyBrewer]

Yep, it's clear to me now knowing the number 38 used in the formula was an estimate of the starter wort OG, which wasn't included in the original post.

 

[RPh_Guy]

@ScrewyBrewer
Do you understand now?

@balrog @kh54s10
How about we use the OP's numbers?

OG:
1.083 (assuming 1.038 starter OG)

SG at blending:
1.082 (assuming 1.010 starter FG)

I simply answered the OP's question. He wanted the OG.

@bracconiere
You can use any blending calculator online or otherwise. The effect of the starter is small because it's a relatively small volume. Most of us ignore it for simplicity.

The math is also very easy to do yourself if you understand the basic equation.

 

[ScrewyBrewer]

@ScrewyBrewer
Do you understand now?

@RPh_Guy yes I do now, again thank you for sharing.

 

[balrog]

@RPh_Guy , fair enough, let's use his numbers.
He has 4.75Gal measured at 1.090 and adds 0.25 water. If he measured SG right now, he should see I think (4.75 * 90 / 5)/1000 + 1 = 1.0855 (please correct me if I'm wrong).

If he now adds a starter, let's say it's 0.25gal, I don't care what it started at, it is a 0.25gal liquid of 1.0?? SG. I have to assume 1.010 but it could be 1.005 or 1.015. The thing I'm stuck on is that adding 0.25gal of 1.010 to 5 gal at 1.0855 will calculate to about (5*1.0855 + .25*1.010)/5.25=1.0812 which is what I think the hydrometer would measure after adding the finished starter. This is not the same as "what are the total gravity points ever added to the batch" which is what you calculate, which would be 1.0832 ( 90 * 4.75 + 38 * 0.25 ) / 5.25. I was going more for "what would Mr. Hydrometer read" given the OP's boundary conditions. And I am only trying to make sure I understand.

 

[ScrewyBrewer]

Since the OP didn't post the OG and FG of the starter wort, or the final combined OG measurement, assuming the accuracy of the hydrometer and reading were good, we would have had more to go on. Although I do love the mental exercise and an opportunity to learn.

 

[lump42]

@RPh_Guy , fair enough, let's use his numbers.
He has 4.75Gal measured at 1.090 and adds 0.25 water. If he measured SG right now, he should see I think (4.75 * 90 / 5)/1000 + 1 = 1.0855 (please correct me if I'm wrong).

If he now adds a starter, let's say it's 0.25gal, I don't care what it started at, it is a 0.25gal liquid of 1.0?? SG. I have to assume 1.010 but it could be 1.005 or 1.015. The thing I'm stuck on is that adding 0.25gal of 1.010 to 5 gal at 1.0855 will calculate to about (5*1.0855 + .25*1.010)/5.25=1.0812 which is what I think the hydrometer would measure after adding the finished starter. This is not the same as "what are the total gravity points ever added to the batch" which is what you calculate, which would be 1.0832 ( 90 * 4.75 + 38 * 0.25 ) / 5.25. I was going more for "what would Mr. Hydrometer read" given the OP's boundary conditions. And I am only trying to make sure I understand.

It's been over a week since the OP, I hope his gravity is lower if it was measured right now!

In all honesty if this is the OP's third batch, they're likely using a triple scale hydrometer with a mark every .002 points. Either way if they were to measure the gravity they'd just as likely read it at 1.082.

 

[lump42]

Since the OP didn't post the OG and FG of the starter wort, or the final combined OG measurement, assuming the accuracy of the hydrometer and reading were good, we would have had more to go on. Although I do love the mental exercise and an opportunity to learn.

The OP did respond in post #5 and said that RPh_Guy's calulations were spot on. Triple scale hydrometers only have a mark every .002 points, not exactly a precision equipment.

 

[RPh_Guy]

He has 4.75Gal measured at 1.090 and adds 0.25 water. If he measured SG right now, he should see I think (4.75 * 90 / 5)/1000 + 1 = 1.0855 (please correct me if I'm wrong).

Correct

The thing I'm stuck on is that adding 0.25gal of 1.010 to 5 gal at 1.0855 will calculate to about (5*1.0855 + .25*1.010)/5.25=1.0812 which is what I think the hydrometer would measure after adding the finished starter.

Try the calculation again.
I get 1.0819 (which is rounded to 1.082)

That's exactly what I said:

SG at blending:
1.082 (assuming 1.010 starter FG)

Yes, that's the s.g. at the time of blending, after some fermentation has already occurred.

The OG (pre-fermentation) is a more meaningful number because it allows you to accurately calculate ABV and attenuation.

Its fine to ignore the starter if you want, with the understanding that there will be a small error.

Since the OP didn't post the OG and FG of the starter wort, or the final combined OG measurement, assuming the accuracy of the hydrometer and reading were good, we would have had more to go on. Although I do love the mental exercise and an opportunity to learn.

He posted the volume of the starter and the amount of DME.
Malt extract adds a highly predictable amount of sugar. Therefore my assumed OG should be accurate within a couple points, close enough to give an accurate OG of the blend.

In all honesty if this is the OP's third batch, they're likely using a triple scale hydrometer with a mark every .002 points. Either way if they were to measure the gravity they'd just as likely read it at 1.082.

Can't argue with that

 

[balrog]

Thanks. Now I'm going to go relearn how to use a calculator correctly.

 

[bracconiere]

@RPh_Guy

sorry, had to use my memory....

Spot on calculation!

 

[kh54s10]

I'll have to read through all this again when I have time. But you have 4.75 gallons at 1.090 .25 gallons of water was added. A starter was added. That starter was fermented from somewhere between 1.030 and 1.040. It had fermented so it was no longer at 1.038 as the number keeps being said.

I guess I am thinking of what you would measure if you took a sample from the fermenter after the water and starter were added. I believe that would not equal the 1.082 the calculations come up with.

I can see if you are looking for the total from the start of each step = 1.082----- math.. not an actual number that you could measure with a hydrometer.

 

[RPh_Guy]

Yes, please read again.

 

[kh54s10]

Went back and re-read.

In the end the difference is so small that the whole exercise is just a math problem to solve.

IMO, the difference is well within the margin of error of just READING the hydrometer. Unless of course you have a very accurate narrow range hydrometer.

 

[HB_ATL73]

It's been over a week since the OP, I hope his gravity is lower if it was measured right now!

In all honesty if this is the OP's third batch, they're likely using a triple scale hydrometer with a mark every .002 points. Either way if they were to measure the gravity they'd just as likely read it at 1.082.

Third batch- not even close... 3rd BIAB yes. Also, yes triple scale cheap hydrometer- so given the calculations I'm sure it would be easy to miss .001-.002 points