There are formulas to calculate resulting purity of an alloy, but
they are of little use to beginner. Let me offer simpler
The formula is not difficult.
Suppose you have two gold alloys: one of carat C1 and the other of
You want to know what proportions of each alloy is needed to produce
a new alloy of carat C.
Assume you have W1 units (gms or oz) of C1, and W2 of C2, then, as
explained in an earlier post:
C = 24x(C1xW1/24 + C2xW2/24)/(W1+W2)
C = (C1xW1 + C2xW2)/(W1 + W2)
If the required proportion of W2 to W1 is R, then R=W2/W1 or W2=RxW1
and the equation above becomes:
C = (C1xW1 + C2xRxW1)/(W1 + RxW1) = (C1 + RxC2)/(1 + R)
which rearranges as C + CxR = C1 + C2xR or Rx(C - C2) = C1 - C
so R = (C - C1)/(C2 - C)
For example. You have 5gms of 9ct and want to know how much 18ct is
required to make a 14ct alloy.
C1 = 9
C2 = 18
C = 14,
therefore R = (14-9)/(18-14) = 5/4
so you need 5x5/4 gms = 6.25gms of 18ct
If you don’t like the maths, the final formula is easy enough: the
ratio of hi carat to lo carat is equal to the wanted carat minus the
lo carat divided by the hi carat minus the wanted carat.
Regards, Gary Wooding