Transcriptional stochasticity can be measured by counting the number of mRNA molecules per cell. Cell-to-cell variability is best captured in terms of concentration rather than molecule counts, because reaction rates depend on concentrations. We combined single-molecule mRNA counting with single-cell volume measurements to quantify the statistics of both transcript numbers and concentrations in human cells. We compared three cell clones that differ only in the genomic integration site of an identical constitutively expressed reporter gene. The transcript number per cell varied proportionally with cell volume in all three clones, indicating concentration homeostasis. We found that the cell-to-cell variability in the mRNA concentration is almost exclusively due to cell-to-cell variation in gene expression activity, whereas the cell-to-cell variation in mRNA number is larger, due to a significant contribution of cell volume variability. We concluded that the precise relationship between transcript number and cell volume sets the biological stochasticity of living cells. This study highlights the importance of the quantitative measurement of transcript concentrations in studies of cell-to-cell variability in biology.