The set of all possible positions r and momenta p is called the phase space of the system; in other words a set of three coordinates for each position coordinate x, y, z, and three more for each momentum component , , . The entire space is 6-dimensional: a point in this space is , and each coordinate is parameterized by time t. The small volume ("differential volume element") is written 
Since the probability of  molecules, which all have  and  within , is in question, at the heart of the equation is a quantity  which gives this probability per unit phase-space volume, or probability per unit length cubed per unit momentum cubed, at an instant of time . This is a probability density function: , defined so that,
is the number of molecules which all have positions lying within a volume element  about  and momenta lying within a momentum space element  about , at time . Integrating over a region of position space and momentum space gives the total number of particles which have positions and momenta in that region:
which is a 6-fold integral. While  is associated with a number of particles, the phase space is for one-particle (not all of them, which is usually the case with deterministic many-body systems), since only one  and  is in question. It is not part of the analysis to use ,  for particle 1, ,  for particle 2, etc. up to ,  for particle N.
It is assumed the particles in the system are identical (so each has an identical mass ). For a mixture of more than one chemical species, one distribution is needed for each, see below.