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How much is one to give for the Half Shekel?
One is to give three coins to charity. Each coin is to be half of the currency amount used in his country. Hence in the Unites States that the currency is one dollar one is to give three half dollar coins. In Israel that the currency is one Shekel one is to give three half shekel coins and so on and so forth for the currency of each country. [Some Poskim however rule that if one has the ability, he is to give a half coin which contains real silver and is worth at least the monetary value of the half Shekel in the times of the Temple [as will be explained]. If such a coin is not available then he should give other coins which add up to the monetary equivalent of the half Shekel, as it was worth in the times of the Temple. The half shekel was originally worth in Temple times 9.6 grams of pure silver. The value of the half Shekel thus fluctuates in accordance to the price of silver. [As of January 2018 one gram of silver was worth $.54 for a total of $5.20 for the half silver Shekel. Each Purim one must verify the current market price for silver, according to this opinion.] Thus one who desires to fulfill the Mitzvah in its highest form is to give this amount of money to charity. If he cannot afford it, he may give the half of the country’s currency coin as stated above.]
Giving on behalf of ones family? The custom is for the father of the house to give three half coins on behalf of each member of his family, including his [wife and] small children [both male and female], including even on behalf of the fetus of a pregnant woman. [Furthermore, it is best to give the children the money for them to fulfill the Mitzvah themselves.]
One is to give three half coins to charity. Each coin is to be half of the currency amount used in his country. The custom is for the father of the house to give three half coins on behalf of each member of his family including his wife and small children [both male and female], including even for a fetus of a pregnancy. It is best to give the children the money for them to fulfill the Mitzvah themselves.
Must one specifically give half dollars as Machatzis Hashekel?
In the U.S.A one is to give half dollar coins, as that is half of the American currency. Other countries are to give half of their currency coin. Many however are accustomed that even outside of the U.S., the Gabaiy of the Shul prepares three half dollar coins, which are then exchanged. See the above Halacha and footnotes there for an elaboration on this topic.
What is one to do if he does not have any half coins available?
He is to donate three whole coins with intent that half of each coin is being given as Machatzis Hashekel and the other half as a present.
The meaning of the half Shekel and its connection to Purim:
The Gemara states that Haman gave Shekalim on behalf of destroying the Jewish people and in order to counteract his Shekalim, Hashem gave us a Mitzvah of giving Shekalim. The Mefarshim explain that Haman wanted the moneys to be distributed to charity in order to gain Divine consent for the successfulness of his plot. This is why the Gemara states that the Jews already preceded their Shekalim to the Shekalim of Haman, as they preceded their charity to Haman’s charity.
 Rama 694/1
 Rama ibid
The reason: This is in commemoration of the three times that it states the word Teruma in the Parsha. [Rama ibid] Alternatively it corresponds to the three days of fasting instituted by Esther. [Hisvadyos 1989 2/439]
Custom of four coins: The Rama writes that some opinions say one is to give 4 half coins to charity, meaning another half coin in addition to the three half coins. Practically he concludes that the custom is not like this opinion.
Other Opinions: Some Poskim question the custom to give three half coins to charity in correspondence to the three times is says Teruma, as in truth there is only one time that the word Teruma refers to the half Shekel donation, while the other two Terumas refer to the one time donation given to the Mishkan at the time of Moses. Hence why the need to commemorate these other two Terumas if they were never repeated even in the times of the Temple. They thus conclude that in truth one is only required to give a single half Shekel, and so is the custom in certain places. [Mateh Yehuda 694; Maaseh Rav of Gr”a 233 brought in Kaf Hachaim 694/23]
 So rules Rama ibid and so is the custom.
Other Opinions: Some rule there is no need to give a half coin to Tzedakah and rather any amount suffices in commemoration of the charity. [Minchas Elazar 1/30; Darkei Chaim Veshalom 843] It may even be given as a bill or check. [Piskeiy Teshuvos 694/4]
 Se however next part in this Halacha that even in Israel some have a custom to give three half dollars.
 Kaf Hachaim 694/20; Shiureiy Torah p. 294-295; See Rambam Shekalim 5 that the half coin used for the half Shekel Mitzvah was never worth less than the half shekel in the times of Moshe.
 Shiureiy Torah p. 294-295; A silver Shekel is 6 Darham of silver [19.23 grams]. Thus a half a shekel is 3 Darham [9.615 grams]; Piskeiy Teshuvos 694/4
 M”B 694/5
 Daas Torah 694; Orchos Chaim; Leket Yosher (student of Terumos Hadeshen); See Darkei Chaim Veshalom 843; Sheivet Halevy 7/183; Piskeiy Teshuvos 694/5 footnote 31; Sefer Haminhagim p. 172 [English Edition]
Background and Other Opinions: The M”B 694/5 omitted the custom of giving on behalf of one’s wife and female children [although he does write a pregnant woman gives on behalf of her fetus], as rules the M”A 694/3 that women are exempt from giving the half Shekel. [Piskeiy Teshuvos 694/5] So also rules Siddur Yaavetz that one only gives on behalf of his male family members. Nevertheless, despite these opinions, the custom is to give the half Shekel on behalf of all family members, including one’s wife and female children. [Daas Torah 694; Orchos Chaim; Leket Yosher (student of Terumos Hadeshen); See Darkei Chaim Veshalom 843; Sheivet Halevy 7/183; Piskeiy Teshuvos 694/5 footnote 31.]
The Chabad custom: In Sefer Haminhagim p. 172 [English Edition] it is recorded the custom of the Rebbe to give the half Shekel on behalf of his family, including his wife and children. Although there it is stated explicitly that this is not meant as a directive for the public, nevertheless in Sichas Taanis Esther 1989 the Rebbe explicitly stated that the custom is to give for one’s entire household.
 M”B 694/5; Poskim brought in previous footnote; Sefer Haminhagim p. 172 [English Edition]
 See previous footnote and Poskim there
 Darkei Moshe 694/1 “A pregnant woman gives on behalf of her fetus”; Elya Raba brought in M”B 694/5; Kaf Hachaim 694/24
The reason: The above custom to give three half coins even on behalf of a fetus is hinted to from the verse “Zeh Yitnu Kol Haubar” which through a play of words can be translated as fetus. [Darkei Moshe ibid]
 Sefer Hasichos 1992 p. 787
 Daas Torah 694; Tzitz Eliezer 13/72; Minchas Elazar 1/30 rules there is no need to give a half coin to Tzedakah and rather any amount suffices in commemoration of the charity.
 Megillah 13b
 Iyun Yaakov Megillah 13b