The curve is usually best described by a sigmoid plot, using a formula of the kind:
A hemoglobin molecule can bind up to four oxygen molecules in a reversible method.
The shape of the curve results from the interaction of bound oxygen molecules with incoming molecules. The binding of the first molecule is difficult. However, this facilitates the binding of the second, third and fourth, this is due to the induced conformational change in the structure of the hemoglobin molecule induced by the binding of an oxygen molecule.
In its simplest form, the oxyhemoglobin dissociation curve describes the relation between the partial pressure of oxygen (x axis) and the oxygen saturation (y axis). Hemoglobin's affinity for oxygen increases as successive molecules of oxygen bind. More molecules bind as the oxygen partial pressure increases until the maximum amount that can be bound is reached. As this limit is approached, very little additional binding occurs and the curve levels out as the hemoglobin becomes saturated with oxygen. Hence the curve has a sigmoidal or S-shape. At pressures above about 60 mmHg, the standard dissociation curve is relatively flat, which means that the oxygen content of the blood does not change significantly even with large increases in the oxygen partial pressure. To get more oxygen to the tissue would require blood transfusions to increase the hemoglobin count (and hence the oxygen-carrying capacity), or supplemental oxygen that would increase the oxygen dissolved in plasma.
Although binding of oxygen to hemoglobin continues to some extent for pressures about 50 mmHg, as oxygen partial pressures decrease in this steep area of the curve, the oxygen is unloaded to peripheral tissue readily as the hemoglobin's affinity diminishes.
The partial pressure of oxygen in the blood at which the hemoglobin is 50% saturated, typically about 26.6 mmHg (3.5 kPa) for a healthy person, is known as the P. The P is a conventional measure of hemoglobin affinity for oxygen. In the presence of disease or other conditions that change the hemoglobin oxygen affinity and, consequently, shift the curve to the right or left, the P changes accordingly. An increased P indicates a rightward shift of the standard curve, which means that a larger partial pressure is necessary to maintain a 50% oxygen saturation. This indicates a decreased affinity. Conversely, a lower P indicates a leftward shift and a higher affinity.
The plateau portion of the oxyhemoglobin dissociation curve is the range that exists at the pulmonary capillaries (minimal reduction of oxygen transported until the p(O) falls 50 mmHg).
The steep portion of the oxyhemoglobin dissociation curve is the range that exists at the systemic capillaries (a small drop in systemic capillary p(O) can result in the release of large amounts of oxygen for the metabolically active cells).
To see the relative affinities of each successive oxygen as you remove/add oxygen from/to the hemoglobin from the curve compare the relative increase/decrease in p(O) needed for the corresponding increase/decrease in s(O).