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Based on the glass-forming ability (GFA) during cooling process and the glass stability (GS) of heating process, a triangle to evaluate GFA and GS, namely Tri-FAS, with the combination of pseudo-four characteristic parameters as vertices was established. Accordingly, a GFA&GA criterion (G-FAS) was deduced as G-FAS=T_g/T_l+T_x/T_l+T_x/T_g (T_x is onset crystallization temperature; T_l is liquid temperature; T_g is glass transition temperature). Additionally, the criterion was modified based on the competitive relationship between amorphous phase and crystal phase during cooling process and the contribution of each component to the criterion: G-FAS_m=T_g/(1.5T_x)+T_x/T_l+T_x/T_g and G-FAS_m′=T_g/T_l+T_x/T_l+(T_x/T_g)^a (a≈1.5±0.2). The correlation between G-FAS and critical cooling rate R_c and that between G-FAS and T_xg (T_xg reflects the supercooled liquid region of glass, T_xg=T_x/T_g) were discussed, which could reflect GFA and GS, respectively. Through the determination results of GFA and GS of abundant metallic glasses and other glass formers, the validity of the proposed G-FAS criterion was evaluated. Results show that with respect to both GFA and GS, the G-FAS criterion is reliable in various glass former systems, showing wide applications. The proposed Tri-FAS and G-FAS criterion can provide guidance during the fabrication and application of metallic glasses.