Alloy Metal Weight Fraction Calculation

Iasad writes,
“Dear Dr. Ron,

I see that you have developed software to calculate the density of an alloy if given the weight fractions of the constituent metals. Is it possible to find the weight fractions of the metals in an alloy given the alloy’s density? Thank you!”
Unfortunately, finding the weight fractions of the metals in an alloy from the alloy’s density can only be accomplished with a two metal alloy. First we must use the equation:

Equation 1

Where x is the weight fraction of metal A and the rhos are the associated densities.  All that has to be done is to solve for x.  The solution is worked out below in Figure 2, the final result is:

Equation 2

As an example, let’s say you have a gold-copper alloy with a density of 18.42 g/cc.  The density of gold (metal A) is 19.32 g/cc and that of copper (metal B) is 8.92 g/cc.   Substituting these values into equation 2 gives the weight fraction of gold as 0.958.  Hence the weight fraction of copper is 1-0.958 = 0.042.

I have developed an Excel-based software tool to perform these calculations. An image of it is shown in Figure 1.  If you would like a copy of this tool send me a note.


Figure 1.  A screen shot of the alloy metal weight fraction calculator.


Figure 2. The derivation of the weight fraction formula.


Dr. Ron

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About Mike

Mike Buetow is president of the Printed Circuit Engineering Association ( He previously was editor-in-chief of Circuits Assembly magazine, the leading publication for electronics manufacturing, and PCD&F, the leading publication for printed circuit design and fabrication. He spent 21 years as vice president and editorial director of UP Media Group, for which he oversaw all editorial and production aspects. He has more than 30 years' experience in the electronics industry, including six years at IPC, an electronics trade association, at which he was a technical projects manager and communications director. He has also held editorial positions at SMT Magazine, community newspapers and in book publishing. He is a graduate of the University of Illinois. Follow Mike on Twitter: @mikebuetow