Most mammalian cells possess molecular circadian clocks generating widespread rhythms, e.g. in transcript and protein abundance. While circadian clocks are robust to fluctuations in the cellular environment, little is known about how circadian period is compensated for fluctuating metabolic states. Here, we exploit the heterogeneity of single cells both in circadian period and metabolic state, governing protein stability, to study their interdependence without the need for genetic manipulation. We generated cells expressing key circadian proteins (CRY1/2 and PER1/2) as endogenous fusions with fluorescent proteins and simultaneously monitored circadian rhythms and degradation in thousands of single cells. We found that the circadian period is compensated for fluctuations in the turnover rates of circadian repressor proteins and uncovered possible mechanisms using a mathematical model. In addition, the stabilities of the repressor proteins are circadian phase-dependent and correlate with the circadian period in a phase-dependent manner, in contrast to the prevailing model.