Kulp was born on July 16, 1970, in the United States and grew up in Margate, New Jersey.
He lives in Modi'in.
He earned a PhD at Bar-Ilan University.
Kulp's commentary on the Haggadah has been widely admired.Kulp was one of the founders of the Conservative Yeshiva, where he is a member of the faculty.
He also teaches at the Schechter Institute of Jewish Studies.
He also coordinates the Mishnah Yomit project through the United Synagogue of Conservative Judaism.