Both circadian rhythmicity and sleep play significant roles in the regulation of plasma cortisol concentration by the hypothalamo-pituitary-adrenal (HPA) axis. Numerous studies have found links between sleep and changes in cortisol concentration, but the implications of these results have remained largely qualitative. In this article, we present a quantitative phenomenological model to describe the effects of different sleep durations on cortisol concentration. We constructed the proposed model by incorporating the circadian and sleep allostatic effects on cortisol concentration, the pulsatile nature of cortisol secretion, and cortisol's negative autoregulation of its own production and validated its performance on three study groups that experienced four distinct sleep durations. The model captured many disparate effects of sleep on cortisol dynamics, such as the inhibition of cortisol secretion after the wake-to-sleep transition and the rapid rise of cortisol concentration before morning awakening. Notably, the model reconciled the seemingly contradictory findings between studies that report an increase in cortisol concentration following total sleep deprivation and studies that report no change in concentration. This work provides a biomathematical approach to combine the results on the effects of sleep on cortisol concentration into a unified framework and predict the impact of varying sleep durations on the cortisol profile.