First of all don’t call it a “hat”! In technical academic regalia lingo, graduates wear “caps” as part of their ceremonial costume, but they do come in different shapes and sizes according to the degree you are receiving.
There are two types of academic caps worn at WashU Commencement ceremonies:
WHEN TO WEAR
Those wearing academic costumes always wear their caps in academic processions and during the ceremony of conferring degrees.
Men may remove caps during prayer, the playing of the national anthem and the alma mater, and at other specified times, e.g., during the baccalaureate sermon or the commencement address.
THE TASSLE
There is no hard and fast rule about tassels, but WashU, like many universities, has follows the custom of wearing the tassels on the right front side before degrees are conferred and to shift them to the left at the moment when degrees are awarded.