Numerical and analytical solutions to calculate the radius of an amyloid-β (Aβ) plaque over time were obtained. To my knowledge, this is the first model simulating the growth of Aβ plaques. It is shown that the plaque can reach the diameter of 50 μm after 20 years of growth only if degradation machinery responsible for degradation of Aβ monomers is malfunctioning. A mathematical model incorporates a nucleation and an autocatalytic growth using the Finke-Watzky model. The obtained system of ordinary differential equations was solved numerically, and for the simplified case of infinitely long Aβ monomer half-life, an analytical solution was found. Assuming that Aβ aggregates stick together, and using the distance between the plaques as an input parameter of the model, it was possible to calculate the plaque radius from the concentration of Aβ aggregates. This led to the formulation of the "cubic root hypothesis," which posits that Aβ plaque size increases as the cubic root of time. This hypothesis helps explain why larger plaques grow more slowly. Furthermore, the obtained results suggest that the plaque size is independent of the kinetic constants governing Aβ plaque agglomeration. This indicates that the kinetics of Aβ plaque agglomeration is not a limiting factor for the plaque growth. Instead, the plaque growth rate is limited by the rates of Aβ monomer production and degradation.