For metallic glasses, it is of vital importance to understand the glass formation properties and to be able to predict the crystallization process in the supercooled liquid. In the present work, we model the process of nucleation and growth using a combination of classical nucleation and phase-field theory. A diffusion coupled phase-field model is used to evaluate the work of formation and the growth behavior of the critical nucleus. The results are combined with classical nucleation and JMAK theory in order to estimate the glass forming ability of the compositions Cu64Zr36, Cu10Zr7 and CuZr2 in terms of TTT-diagrams and critical cooling rates. It is found that the work of formation of the critical nucleus from the phase-field theory agrees with the classical theory when the critical size is larger than the width of the solid-liquid interface. At smaller critical sizes, the work of formation deviates approximately linearly between the two theories. Furthermore, it is shown that the growth behavior from the phase-field simulations agree with analytical expressions of the growth rate from the classical theory.