This is a review of the origins, derivations, and 'fidelity' of available equations for correcting PO2, PCO2, and pH for temperature, and for estimating blood-gas and acid-base variables from measured values: 1. Oxygen saturation (SO2) from PO2, PCO2, pH, and body temperature (T). 2. Oxygen concentration (CO2) from SO2, PO2, and hemoglobin concentration (Hb). 3. Base excess (BE) from pH, PCO2, and Hb. 4. 'In vivo BE' (BE3) from pH and PCO2. 5. 'Compensated BE3' (BEC) from PCO2. 6. Bicarbonate ([HCO3-]) and carbon dioxide concentrations (CCO2) from pH and PCO2. PHysiologic considerations are emphasized, with mathematical background when it contributes to understanding. Algorithms are variously compared with their graphic counterparts, with the data from which they were derived, and with each other.