As particles are extended three-dimensional objects, only a perfect spherical particle allows for a simple definition of the particle size x, as the diameter of the sphere. In practice, spherical particles are very rare. So usually equivalent diameters are measured, representing the diameter of a sphere which behaves as the real (non-spherical) particle in a specific sizing experiment. Unfortunately, the measured size is now depending on the method used for sizing. So one can only expect identical results for the particle size if the particles are either spherical or the same sizing method, i.e. the same equivalent diameter, is used.
In most applications more than one particle is observed. As each individual particle may have its own particle size, methods for data reduction have been introduced - the particle size distribution, a fit to a specific model distribution and moments or an average particle size are used.