axes. The most common convention is for the longitudinal axis to be labelled and the transverse axes to be labelled and . Emittance has units of length, but is usually referred to as "length × angle", for example, "millimeter × milliradians". It can be measured in all three spatial dimensions. Geometric transverse emittance When a particle moves through a circular accelerator or storage ring, the position and angle of the particle in the x direction will trace an ellipse in phase space. (All of this section applies equivalently to and ) This ellipse can be described by the following equation: where x and are the position and angle of the particle, and are the Courant–Snyder (Twiss) parameters, calculated from the shape of the ellipse. The emittance is given by , and has units of length × angle. However, many sources will move the factor of into the units of emittance rather than including the specific value, giving units of "length × angle × ." This formula is the single particle emittance, which describes the area enclosed by the trajectory of a single particle in phase space. However, emittance is more useful as a description of the collective properties of the particles in a beam, rather than of a single particle. Since beam particles are not necessarily distributed uniformly in phase space, definitions of emittance for an entire beam will be based on the area of the ellipse required to enclose a specific fraction of the beam particles. If the beam is distributed in phase space with a Gaussian distribution, the emittance of the beam may be specified in terms of the root mean square value of and the fraction of the beam to be included in the emittance. The equation for the emittance of a Gaussian beam is: where is the root mean square width of the beam, is the Courant-Snyder , and is the fraction of the beam to be enclosed in the ellipse, given as a number between 0 and 1. Here the factor of is shown on the right of the equation, and would often be included in the units of emittance, rather than being multiplied in to the computed value. The value chosen for will depend on the application and the author, and a number of different choices exist in the literature. Some common choices and their equivalent definition of emittance are: {| class="wikitable" |- !