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Mix beverage concentrations by mass

Find how much of two beverage mixtures to combine for a target mass concentration. All concentrations must describe the same dissolved substance.

Start with your own numbers

Editable example

An example is filled in. Replace it with your own data to calculate.

Use the same solute and mass-percentage definition for both drinks, then enter the target total grams.

First drink concentration by weight (%)20 g sugar in 100 g sugar water is 20% by weight. This is not volume percent or a refractometer reading.

Second drink concentration by weight (%)Use the same solute and mass-based definition. Pure water can be 0.

Target concentration (% by mass)Enter target concentration (% by mass), for example 10. Use the displayed unit; replace the example with your own value.

Final total mass (g)Enter final total mass (g), for example 500. Use the displayed unit; replace the example with your own value.

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Example result

Amount of the first drink

250g

20% by weight means 20 g of solute in 100 g. Do not directly substitute refractometer readings, volume percentages or medicine concentrations.

Amount of the second drink250 g

Total solute mass50 g

First drink mass = total mass × (target concentration − second concentration) ÷ (first concentration − second concentration). Conserves mass fraction for the same solute, such as mixing 20% sugar water with water to make 10%. Do not mix volume percentages, refractometer readings or different solutes. Not for alcohol volume contraction, medicines, disinfectants or infant formula. Equal starting concentrations cannot give a unique reverse calculation.

Method and scope

First-mixture grams equals total grams times (target minus second concentration) divided by (first minus second concentration). The remaining mass comes from the second mixture, preserving the dissolved substance by mass.

The target must lie between the two source concentrations. Equal source concentrations cannot identify a unique mixing ratio.

Do not mix mass percentages with volume percentages or refractometer readings. This tool is not for medicines, disinfectants, infant formula, different solutes or alcohol volume contraction.

References:OpenStax: algebra and applications

What this helps you do

Find how much of two beverage mixtures to combine for a target mass concentration. All concentrations must describe the same dissolved substance.

What to enter

Start with first concentration (% by mass), then fill the other relevant fields in the units shown. The field hints explain the required format and examples.

How the calculation works

Worked example

To make 300 g of 10% sugar water from 20% sugar water and water at 0%, combine 150 g of each. A 20% mass concentration means 20 g sugar in 100 g total mixture.

Understanding the answer

The target must lie between the two source concentrations. Equal source concentrations cannot identify a unique mixing ratio.

Scope and limitations