degrees of freedom
1. When a substance is heated its kinetic energy increases. Kinetic energy is made up from the translation and rotation of particles, and the vibration of atoms which constitute the molecules of a substance. A substance may, therefore, absorb heat energy supplied to it in several ways, and is said to possess a number of degrees of freedom. In general, a molecule consisting of N atoms will have 3N degrees of freedom; thus for a diatomic molecule there will be six degrees of freedom: three will be translational, two rotational, and one vibrational. In a phase diagram, describing, for example, a three-phase system (such as ice-water-vapour), pressure and/or temperature can be altered independently, in an area where only one phase exists, without altering the one-phase condition. Along the line separating two areas, if temperature is altered then pressure must alter accordingly, or vice versa, to maintain the two-phase equilibrium. At a point where three phases are in equilibrium, alteration of either temperature or pressure will cause one phase to disappear. The system thus possesses (a) two degrees of freedom in the area; (b) one degree of freedom along the line; and (c) no degrees of freedom at the point.

2. In statistics, the number of independent variables involved in calculating a statistic. This value is equal to the difference between the total number of data points under consideration, and the number of restrictions. The number of restrictions is equal to the number of parameters which are the same in both observed data set and theoretical data set, e.g. total cumulative values, means.