What is the central question of this study? Can the change in haemoglobin's affinity for oxygen in the human cerebral circulation be modelled in vivo? What is the main finding and its importance? We provide a novel method for modelling the oxyhaemoglobin dissociation curve at the cerebral capillary level in humans, so that the cerebral capillary and mitochondrial oxygen tensions can reliably be estimated. This may be useful in future human-experimental studies on cerebral oxygen transport. We provide a method for modelling the oxyhaemoglobin dissociation curve (ODC) in the cerebral capillary in humans. In contrast to most previous approaches, our method involves the construction of an averaged ODC based on paired arterial-jugular venous blood gas values, which enables the estimation of oxygen parameters in cerebral capillary blood. The method was used to determine the mean cerebral capillary oxygen saturation and tension from data previously collected from 30 healthy volunteers. The averaged ODC provided systematically higher capillary oxygen tensions than when assuming a 'fixed' standard arterial ODC. When the averaged and measured arterial ODC were used for constructing the capillary ODC, similar values were obtained during resting breathing, but not when the arterial ODC was modulated by hypocapnia. The findings suggest that our method for modelling the cerebral capillary ODC provides robust and physiologically reliable estimates of the cerebral capillary oxygen tension, which may be of use in future studies of cerebral oxygen transport in humans.