A family of anti-perovskite nitrides of the formula Ca3MN, where M is a Group IV or a Group V element is reported. Ca3BiN, synthesized by mixing and pressing powders of Ca3N2 and Bi into a pellet and subsequently heating the pellet at 1000°C in flowing, dry N2 gas, is prototypical of this family of compounds. The bismuth in Ca3BiN has an uncommon oxidation state of 3− as suggested by the properties (semiconducting and diamagnetic) of the compound. The anionic bismuth can be substituted by other trivalent anions Sb3−, As3−, and P3− as expected. The structures of Ca3AsN and Ca3PN are distorted from the simple cubic anti-perovskite cell at room temperature because of the small size of As3− and P3−. More interestingly, Ca3N2 also reacts with Ge, Sn, and Pb at 1300°C to form similar anti-perovskites, resulting in metallic phases and the unusual open shell oxidation state of 3− for the Group IV elements.