Estimating the availability of phosphorus in soils and sediments is complicated by the diverse mineralogical properties of iron (hydr)oxides that control the environmental fate of phosphorus. Despite various surface complexation models have been developed, lack of generic phosphate affinity constants (logKPO4s) for iron (hydr)oxides hinders the prediction of phosphate adsorption to iron (hydr)oxides in nature. The aim of this work is to derive generic logKPO4s for the Charge Distribution-Multisite Complexation extended-Stern-Gouy-Chapman (CD-MUSIC-eSGC) model using a large phosphate adsorption database and previously derived generic protonation parameters. The optimized logKPO4s of goethite, hematite and ferrihydrite are located in a much narrower range than those in the RES3T database. Specifically, the logKPO4 ranges of FeOPO3, FeOPO2OH, FeOPO(OH)2, (FeO)2PO2, and (FeO)2POOH complexes were 17.40-18.00, 24.20-27.40, 27.90-29.80, 26.50-29.60, and 30.70-33.40, respectively. A simplified CD-MUSIC-eSGC model with species FeOPO2OH and (FeO)2PO2 and generic logKPO4 values 26.0±0.9 and 27.9±0.8, respectively, provides an accurate prediction of phosphate adsorption and dominant speciation to the iron (hydr)oxides at environmental pH and phosphate levels. For ferrihydrite at low pH and high phosphate levels the species FeOPO(OH)2 and (FeO)2POOH cannot be neglected. The simplified model expands the application boundaries of CD-MUSIC-eSGC model in predicting the phosphate adsorption on natural iron (hydr)oxides without laborious characterization.