The radial distribution function is usually determined by calculating the distance between all particle pairs and binning them into a histogram. The histogram is then normalized with respect to an ideal gas, where particle histograms are completely uncorrelated. For three dimensions, this normalization is the number density of the system ( ρ ρ ) multiplied by the volume of the spherical shell, which symbolically can be expressed as ρ ρ 4 π π r 2 d r .