Advances in single-cell RNA sequencing provide an unprecedented window into cellular identity. The abundance of data requires new theoretical and computational frameworks to analyze the dynamics of differentiation and integrate knowledge from cell atlases. We present ‘single-cell Type Order Parameters’ (scTOP): a statistical, physics-inspired approach for quantifying cell identity given a reference basis of cell types. scTOP can accurately classify cells, visualize developmental trajectories and assess the fidelity of engineered cells. Importantly, scTOP does this without feature selection, statistical fitting or dimensional reduction (e.g. uniform manifold approximation and projection, principle components analysis, etc.). We illustrate the power of scTOP using human and mouse datasets. By reanalyzing mouse lung data, we characterize a transient hybrid alveolar type 1/alveolar type 2 cell population. Visualizations of lineage tracing hematopoiesis data using scTOP confirm that a single clone can give rise to multiple mature cell types. We assess the transcriptional similarity between endogenous and donor-derived cells in the context of murine pulmonary cell transplantation. Our results suggest that physics-inspired order parameters can be an important tool for understanding differentiation and characterizing engineered cells. scTOP is available as an easy-to-use Python package.