We present synthetic experiments of lactic acid (LA) polycondensation to produce poly(lactic acid) (PLA), as well as kinetic modeling calculations that capture the polymer molecular weight increase with time, given the initial concentrations. Tin-octoate-catalyzed polycondensation of (D,L)- or L-lactic acid, was carried out in pre-dried toluene after azeotropic dehydration for 48-120 hours at 130-137 °C. The polymerization was optimized by varying lactic acid and catalyst concentrations as well as the temperature. Gel Permeation Chromatography was used to experimentally follow the evolution of molecular weights and the products were characterized by NMR, TGA, DSC and IR. Under optimal conditions, PLLA with weight-average molecular weight (Mw) of 161 kDa could be obtained. The rate equations that describe polycondensation kinetics were recast in a condensed form that allowed very fast numerical solution and calculation of the number-average molecular weight with time. Deviations with respect to the experiment were minimized in a least-squares fashion, to determine rate constants. The optimized kinetics parameters are shown to reproduce the experimental data accurately