# Percentage of metals in the alloy

This online calculator uses the characteristics of the alloy of two metals - mass and volume - to calculate the percentage of metals in the alloy based on their densities.

The formulas for calculating the percentage of metals in an alloy are listed below the calculator.

#### Percentage of metals in the alloy

Density, g/cm³

Density, g/cm³

Digits after the decimal point: 2
Percentage of the first metal in the alloy

Percentage of the second metal in the alloy

### Calculating the percentage of metals in an alloy of two metals

Let us know the physical characteristics of the alloy, mass and density, which can be simply measured, and the densities of the metals that make up the alloy (for example, these can be obtained from a reference book).
We have the following obvious relations:
$m_1=V_1\cdot \rho_1\\m_2=V_2\cdot \rho_2\\V=V_1+V_2\\m=m_1+m_2$,
where
m - mass of the alloy,
V is the volume of the alloy,
m₁ is the mass of the first metal,
V₁ is the volume of the first metal,
ρ₁ - density of the first metal,
m₂ is the mass of the second metal,
V₂ is the volume of the second metal,
ρ₂ is the density of the second metal.

m₁, V₁, m₂, m₂, V₂ - four unknowns for four equations - there is a single solution.

By performing substitutions, we can obtain rather cumbersome formulas for m₁ and m₂
$m_1 = \rhrac{\rho_1(V\rho_2-m)}{\rho_2 - \rho_1}\\m_2 = m - \rhrac{\rho_1(V\rho_2-m)}{\rho_2 - \rho_1}$

The percentages are obtained by dividing the masses of the metals by the mass of the alloy.

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PLANETCALC, Percentage of metals in the alloy