How to calculate a liquid dilution ratio

What does a one-to-ten liquid dilution really mean? The answer depends on which ingredient comes first. For this example, the label says one part concentrate to ten parts water, by volume. Keep those labels attached to the numbers as we build the mix.

Picture one amber cup of concentrate beside ten equal teal cups of water. The recipe has eleven parts altogether, because the concentrate is a part of the finished mixture too. One-to-ten is the concentrate-to-water ratio. Turn the order around and the very same mixture reads ten-to-one, water to concentrate. Nothing about the liquid changed; only the order of the words and numbers did.

Now suppose we want twenty-two fluid ounces of this mix. Each of the eleven equal parts must be twenty-two divided by eleven, or two fluid ounces. The one concentrate part is two ounces. Ten water parts are ten times two, or twenty ounces. Pouring two ounces of concentrate and twenty ounces of water gives twenty-two ounces in total, assuming these volumes add closely enough for this recipe.

Check the ratio backward. Twenty ounces of water divided by two ounces of concentrate is ten. So water to concentrate is ten-to-one, and concentrate to water is one-to-ten. We can scale both ingredients together: four ounces of concentrate and forty ounces of water make forty-four ounces at exactly the same ratio. Doubling only the water would change the mixture.

How much of the twenty-two-ounce batch is concentrate? Divide the two concentrate ounces by all twenty-two ounces. That is one eleventh, about nine point zero nine percent of the nominal mixture by volume. It is not ten percent. A common error is to treat one-to-ten concentrate-to-water as one part out of ten total parts. That is a different instruction: one-to-ten concentrate-to-total would use one part concentrate and nine parts water. In a twenty-two-ounce batch, it would take two point two ounces of concentrate, not two.

This ratio tells us how much concentrate product is in the mix. It does not, by itself, tell us the concentration of an active ingredient already dissolved in that product. For precise solution work, use the stock concentration and final solution volume, and add solvent to the final-volume mark rather than assuming every pair of liquids adds perfectly.

So, first name the ratio order. Add its parts, divide the desired batch by that total, then multiply by each ingredient’s part count. Finally, check the amounts by dividing one ingredient by the other. For one part concentrate to ten parts water in twenty-two fluid ounces, the reusable answer is two ounces of concentrate and twenty ounces of water.