Use the noun peacefulness when you talk about a state of calm or tranquility. Many people feel a sense of peacefulness when they're hiking in the woods.
One kind of peacefulness is quiet and restful, the sort you find at a yoga studio or on an empty stretch of beach. Peacefulness can also refer to an absence of conflict or violence — though it's more common to call this peace. The root of both words is the Latin pacem, which means "peace treaty, tranquility, agreement, or compact."