Quantitative in vivo measurements are essential for developing a predictive understanding of cellular behavior. Here we present a technique that converts observed fluorescence intensities into numbers of molecules. By transiently expressing a fluorescently tagged protein and then following its dilution during growth and division, we observe asymmetric partitioning of fluorescence between daughter cells at each division. Such partition asymmetries are set by the actual numbers of proteins present, and thus provide a means to quantify fluorescence levels. We present a Bayesian algorithm that infers from such data both the fluorescence conversion factor and an estimate of the measurement error. Our algorithm works for arbitrarily sized data sets and handles consistently any missing measurements. We verify the algorithm with extensive simulation and demonstrate its application to experimental data from Escherichia coli. Our technique should provide a quantitative internal calibration to systems biology studies of both synthetic and endogenous cellular networks.