Previous quantitative descriptions of cellular ultrastructure have focused on spatial content (volume, surface area and number of organelles and membrane domains). It is possible to complement such descriptions by also quantifying spatial arrangements. Hitherto, applications of stereological methods for achieving this (notably, estimation of covariance and pair correlation functions) have been confined to organ and tissue levels. This study explores 3-dimensional subcellular arrangements of key organelles within acinar cells of rabbit parotid salivary glands, highly polarised epithelial cells specialised for exocrine secretion of α-amylase. It focuses on spatial arrangements of secretion product stores (zymogen granules), rough endoplasmic reticulum (RER) and mitochondria. Systematic random samples of electron microscopical fields of view from 3 rabbits were analysed using test grids bearing linear dipole probes of different sizes. Unbiased estimates of organelle volume densities were obtained by point counting and estimates of covariance and pair correlation functions by dipole counting. Plots of pair correlation functions against dipole length identified spatial arrangement differences between organelle types. Volumes within RER and mitochondrial compartments were positively correlated with themselves at distances below 4 μm and 2 μm respectively but were essentially randomly arranged at longer distances. In sharp contrast, zymogen granules were not randomly arranged. They were clustered at distances below 6–7 μm and more widely scattered at greater distances. These findings provide quantitative confirmation of the polarised arrangement of zymogen granules within acinar cells and further support for the relative invariance of biological organisation between subjects.