This value is calculated according to the system which matches the weight of a full shekel to the weight of 384 barley grains.
What’s the weight of a single grain of barley? According to an accepted halachic opinion, the weight of one barley grain is 0.05 grams. The weight of the full shekel is then about 19.2 grams and the weight of half a shekel is about 9.6 grams.
This issue has a practical importance on the eve of Purim. It’s customary to give three “half of a shekel” donations for every family member on the Eve of Purim prior to Mincha. The value of this “half of the shekel” donation thus fluctuates every year and can be calculated in accordance with the market price of silver.
For information only. For practical instructions on how to perform the custom of “Machatzit HaShekel” in your area, we advise you to consult your rabbi.