In what ratio would you combine skim milk and higher-fat dairy to reach an equivalent of e.g. whole milk? I ran out of whole the other day making bread, tried to add a splash of half-and-half to 2%, but it didn't come out that well - but it must be possible in the right ratio, yes?
If you want a fat fraction of f, starting from cream with a fat fraction c and milk with a fat fraction of m, then the fraction of cream to use is (f-m)/(c-m).
All you have to do is multiply that by the total volume to get how much cream to use, and then fill in the rest of the total with milk.
For example, if you want to approximate 1 cup of 3.25% whole milk using 36% heavy cream and 0% skim milk, you need (3.25-0)/(36-0) * 1 cup = 0.09 cups of cream, or 1.5 tablespoons. So take 1.5 tablespoons of cream, and add skim milk to reach 1 cup.
Or if you want two cups of 10.5% half and half using 33% whipping cream and 2% milk, you need (10.5-2)/(33-2) * 2 cup = 0.55 cups, or about 1/2 cup + 1 tablespoon of cream. So take 1/2 cup plus 1 tablespoon of cream, and add 2% milk to reach 2 cups.
Unfortunately it's hard to provide a really useful table of examples, because fat content of dairy products varies around from country to country, and even within countries. Probably the most useful single thing to know is that you can use Google, e.g. search for (10.5-2)/(33-2)*2 cups in tablespoons to do the calculation from the previous paragraph.
For example, in the US, I believe:
- whole milk - usually 3.25%
- half-and-half - usually 10.5% or maybe 12% (can be up to 18%)
- light cream - usually 18% (can be up to 30%)
- whipping cream - usually 33% (can be 30-36%)
- heavy whipping cream - usually 36% (can be higher)
Resources for finding fat contents if not given:
Derivation is pretty simple. If x is the fraction of cream, then the resulting fat fraction is:
f = x * c + (1-x) * m.
This is simply a weighted average of the component fat ratios: x is the fraction of cream, so 1-x is the fraction of milk. (If you really wanted to convince yourself of this, you could write out the amount of milk in each component and the total, and the volumes of everything, and divide to get this.)
Solving for x yields the formula given at the beginning of the answer.
And if there's no fat percentage on the package (half-and-half, light or heavy cream)? Dec 21, 2016 at 17:21
@DavidHeyman Added some. Unfortunately it's not entirely straightforward, since these terms are specific to the country you're in, and regulation generally only provides acceptable ranges for each term. Dec 21, 2016 at 17:28
You seem to be assuming a volume percentage of fat (at least I see no density conversion) - but I am pretty sure it is a weight percentage, not volume percentage. Dec 21, 2016 at 21:48
@rumtscho It looks like density doesn't actually vary that much (found this saying just a few percent difference between cream and skim milk). So I don't think it's really an issue - within a reasonable tolerance, the volumes add and the density remains constant. That makes it not actually matter whether the percentages are by volume or by weight; it just changes what the units are in that equation. Dec 21, 2016 at 21:55
Credit to Karl S on Chowhound:
Add the following to 1 cup of skim milk to approximate 1 cup of:
- 1.5t heavy cream= 1% milk
- 1T heavy cream= 2% milk
- 2T heavy cream= whole milk
- 5T 1t heavy cream= half-&-half
- 9T heavy cream= light cream
- 1T light cream= 1% milk
- 1T 2t light cream= 2% milk
- 3T light cream= whole milk
- 5 oz light cream= half-&-half
- 2T half & half= 1% milk
- 3T half & half= 2% milk
- 4T half & half= whole milk
This chart is unfortunately vague - is that "1 cup skim plus X makes >1 cup Y, take 1 cup of result" or "X, add skim to total 1 cup"? I'm not sure how to check, but an earlier comment on the page that shows math seems to indicate the former.
Clarify - you say add to one cup to approximate one cup, which is clearly not the case (or not a very good approximation) when you add 9T to one cup and have more than 1-1/2 cups. Perhaps you mean start with X amount high-fat milk product and then add skim until it's 1 cup total of the mixture?– EcnerwalDec 21, 2016 at 1:31
@Ecnerwal I have directly quoted the cited source, and it is that vague. I see two possibilities: yours, or "add one cup of skim to X of something else, take 1 cup of result". I have not found a second source to cross-reference with this one to determine which reading is correct. Dec 21, 2016 at 3:11
Oh, found a possibility. Editing. Dec 21, 2016 at 3:19
vA is volume of A
fA is fraction of milkfat in A
vB is volume of B
fB is fraction of milkfat in B
fD is the desired fraction
fD must be between fA and fB
fD = (fA*vA + fB*vB) / (vA + vB) fD*vA + fD*vB = fA*vA + fB*vB vA*(fD - fA) = vB*(fB - fD) vA/vB = (fB - fD) / (fD - fA)
vA/vB is the ratio
So to make .5 from .25 and .75 you should mix 1:1
2It looks like you're aiming for 2% fat, not whole milk? It might also be nice to solve this in terms of x/(x+y), since you'll usually be aiming for a given volume of whole milk, and even to give example values. Dec 21, 2016 at 15:50
I am not sure I understand what you mean here. "To make .5 from .25 and .57 you should mix 1:1" - do you mean making a dairy product which has 0.5 milkfat fraction (so 50% fat) or a product which has a 0.5% milkfat fraction? Which product is this? I have never seen a product which has either 57% or 0.57% fat either. And, you seem to be assuming volume-based percentages, but fat percentage in dairy is measured by weight. The difference is not extremely large, but especially if you meant 50% fat, it would make a significant difference if you don't convert the density. Dec 21, 2016 at 21:52
@rumtscho I meant 75. Not realistic numbers but just and example. Oh happy dv. Dec 21, 2016 at 21:53
I did not downvote you, but the unrealistic numbers might be a part of why others did. Dec 21, 2016 at 21:55
@rumtscho Cool I am not going to sweat it. If you want to base on mass then just use mass for V. But I doubt the density of milkfat is much different from the density of non-milkfat. Cream does rise to the top. Dec 21, 2016 at 22:06