Numerous reasons have been offered as to why we specifically give half a shekel, and not a full shekel:

1. A MIDDAY SIN: The Jewish people assumed that Moshe would come down in the morning, and when the last hour of the morning arrived, they sinned and made an idol to take his place. Since they sinned halfway through the day, they were commanded to give half a shekel, and because they contravened the Ten Commandments [whose primary element is the monotheistic belief in Hashem], they would have to give a coin that weighs ten gerah (Yerushalmi Shekalim 2:3). On deeper level of understanding, we may explain that had the Jewish people waited until the beginning of the next day, they would have been fully Divine, and since they sinned halfway through the day, they retained only part of that Divinity. The contribution of a part shekel makes up for the deficient part.

2. REUNITING WITH HASHEM: At Sinai, we became united with Hashem in a Divine marriage, and that unity was compromised through the idolatrous sin of the Golden Calf. By means of the atonement achieved through the giving of the half-shekel, we restore our union with Hashem. Thus, we specifically give half, to symbolize the rededication of our half of the relationship.

3. BODY AND SOUL: A person is comprised of ten physical components given by his parents and ten spiritual components given by Hashem (Niddah 31a). Only the spiritual half of a person becomes sullied by sin and requires atonement. We therefore give half a shekel that weights ten gerah, corresponding to the spiritual half that is comprised of ten components (Kli Yakar). Shekel has the same numerical value as nefesh, soul (Chidah).

4. HALF OF THE NATION: The women of the Jewish people refused to participate in the sin of Golden Calf, nor was it in their power to prevent their husbands from participating. Since only the men required atonement, half of a shekel sufficed (Alshich).

5. PART OF A WHOLE: This mitzvah gives expression to the unity of the Jewish people. The Jewish people are counted as a whole by each individual giving half of a shekel, to symbolize that each Jew is incomplete and needs his fellow Jew to attain completion (Rav Shlomo Alkabetz, cited in Alshich). In order to give full expression to the idea that all Jews are essentially equal, the Torah specifies that the wealthy man may not give more and the poor man may not give less. This explanation is better understood in light of another view amongst the Sages that half-shekel atones for the sale of Yosef, and that for this reason, the half- shekel is precisely the same as the amount of profit that each brother received from the sale (Yerushalmi ibid.). Since the disunity amongst the forerunners of our nation resulted in the sale of Yosef, we merit atonement for this sin by uniting through the giving of a half-shekel.