The aerodynamic center of an airfoil is commonly estimated to lie at the quarter-chord. This traditional estimate is based on thin airfoil theory, which neglects aerodynamic and geometric nonlinearities. Even below stall, these nonlinearities can have a significant effect on the location of the aerodynamic center. Here, a method is presented for accurately predicting the aerodynamic center of any airfoil from known lift, drag, and pitching-moment data as a function of angle of attack. The method accounts for aerodynamic and geometric nonlinearities, and it does not include small-angle, small-camber, and thin-airfoil approximations. It is shown that the aerodynamic center of an airfoil with arbitrary amounts of thickness and camber in an inviscid flow is a single, deterministic point, independent of angle of attack, and lies at the quarter-chord only in the limit as the airfoil thickness and camber approach zero. Furthermore, it is shown that, once viscous effects are included, the aerodynamic center is not a single point but is a function of angle of attack. Differences between this general solution and that predicted by the thin airfoil theory can be on the order of 3%, which is significant when predicting flutter speeds. Additionally, the results have implications for predicting the neutral point of a complete aircraft.