# Calculate weights of the mixtures to get desired final mixture concentration

This online calculator calculates the weights of the input mixtures of given concentrations needed to get the given weight and the given concentration of the final mixture

In other words, this calculator can answer the question of what weights of each input product is required in order to achieve a certain % at a fixed final weight. For example, you need to achieve a total weight of 5000kg with 75% concentration. You will use 65% and 85% to create the final concentration. What weight of each product would be required to achieve the total weight at the correct %? Formulas, as usual, can be found below the calculator.

#### Calculate weights of the mixtures to get desired final mixture concentration

Digits after the decimal point: 2
Weight of the first mixture

Weight of the second mixture

### Mixing products of different concentrations

We can get the result only under the assumption that the volume of the final mixture equals to the sum of the volumes of two inputs, i.e. the rule of additivity of volumes is satisfied. Obviously, the total amount of mass is conserved during mixing. Thus we can write using mass concentration:
$C_x=\frac{m_x}{V_x}=\frac{m_1+m_2}{V_1+V_2}=\frac{C_1V_1+C_2V_2}{V_1+V2}$, where
Cₓ is the target mass concentration
mₓ is the final mass of the mixture
Vₓ - final volume of the mixture
m₁ - mass of the first input
C₁ - mass concentration of the first input
V₁ - volume of the first input
m₂ - mass of the second input
C₂ - mass concentration of the second input
V₂ - volume of the second input

From the obtained formula we express the ratio of volumes of input mixtures
$C_x=\frac{C_1V_1+C_2V_2}{V_1+V2}\\C_xV_1+C_xV_2=C_1V_1+C_2V_2\\C_x\frac{V_1}{V_2}+C_x=C_1\frac{V_1}{V_2}+C_2\\C_x\frac{V_1}{V_2}- C_1\frac{V_1}{V_2}=C_2-C_x\\\frac{V_1}{V_2}(C_x-C_1)=C_2-C_x\\\frac{V_1}{V_2}=\frac{C_2-C_x}{C_x-C_1}$
This formula is what is used in the calculator to get the ratio. Then this ratio is applied to the final mass to get the mass of each input.

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PLANETCALC, Calculate weights of the mixtures to get desired final mixture concentration