Dilution and mixing solutions calculator

When you mix two solutions, the dissolved substance does not disappear: the mixture contains exactly the amount you poured in from both containers together. That is the whole mixing equation.

Diluting with water is the same, except that the second “solution” is pure water with a concentration of zero.

Mixing two solutions

Enter the amounts in grams, millilitres or any other unit, as long as you use the same unit for both solutions. The result comes out in the same units.

How much water to add

You want to dilute a solution to a lower concentration.

How it works

A solution of mass m₁ and concentration c₁ is mixed with a solution of mass m₂ and concentration c₂, giving m₁ + m₂ of solution with concentration c:

$$m_1\cdot c_1+m_2\cdot c_2=(m_1+m_2)\cdot c$$

When diluting with water, the amount of dissolved substance stays the same, m₁ · c₁, but it is spread over a larger amount, which must be such that the concentration comes out as c₂. So the amount of water to add is

$$m_{\text{water}}=m_1\cdot (\frac{c_1}{c_2}-1)$$

In the first calculator, we mix 300 g of 40% sugar syrup with 200 g of 10% syrup. Together they contain this much sugar:

$$300\cdot 0.40+200\cdot 0.10=120+20=140\text{g}$$

and the mixture weighs 300 + 200 = 500 g. The concentration of the mixture is

$$c=\frac{140}{500}=0.28=28\mathrm{\%}$$

In the second, we have 500 g of 8% vinegar and want 5% vinegar for a salad. It contains 500 · 0.08 = 40 g of acetic acid, and these 40 g must make up 5% of the solution, so the solution must weigh $40÷0.05=800$ g. We add the difference in water:

$$500\cdot (\frac{8}{5}-1)=500\cdot 0.6=300\text{g}$$

It is tempting to think that to halve the concentration, you add half as much water. In fact, you must add as much water as there already is in the container: from 500 g of 8% vinegar, you make 4% vinegar by adding 500 g of water.

The calculator works with mass percentages. It also works with volume percentages (alcohol, spirits), but only approximately: a litre of water and a litre of alcohol make a little less than two litres when mixed. The full explanation, including a problem about how much stronger solution to add, is in the article on dilution and mixing solutions.