Shanti patha formulas of this kind close most substantial Vedic and Upanishadic recitations, and the threefold repetition here is one of several ways Sanskrit intensifies or completes an utterance by saying it three times rather than once, a pattern also seen in other closing and opening formulas across the literature. Because it functions as a closing rather than as a mantra recited for its own sake, it very rarely appears alone in the older sources, it is nearly always the last line of something longer, and its transmission has therefore been as an attached formula rather than an independent unit, at least until the twentieth century, when it was lifted free of any particular text and adopted as a generic closing chant in yoga classes and interfaith settings well beyond its Vedic home.
Commentators differ on why three repetitions specifically. The most widely cited explanation reads them against the three traditional categories of affliction, adhyatmika, suffering that originates within the person, adhibhautika, suffering caused by other beings, and adhidaivika, suffering attributed to cosmic or divine forces beyond human or animal agency, so that the triple peace addresses all three sources at once. An older and less common explanation treats the three repetitions as addressed outward, to the heavens, the atmosphere and the earth, asking for peace across the whole of the traditional threefold cosmos rather than across three categories of personal misfortune. Both readings are defensible from within the tradition and neither has displaced the other, so translators and teachers routinely give both without treating the question as settled.