Voice is increasingly being used as a biometric entity in many applications. These range from speaker identification and verification systems to human profiling technologies that attempt to estimate myriad aspects of the speaker's persona from their voice. However, for an entity to be a true biometric identifier, it must be unique. This paper establishes a first framework for calculating the uniqueness of human voice objectively. The approach in this paper is based on statistical considerations that take into account a set of measurable characteristics of the voice signal that bear a causal relationship to the vocal production process, but are not inter-dependent or derivable from each other. Depending on how we quantize these variables, we show that the chances of two people having the same voice in a world populated by 10 billion people range from one in a few thousand, to one in a septillion or less. The paper also discusses the implications of these calculations on the choices made in voice processing applications.