Based on theoretical calculations using the fragility concept and the nucleation theory for a model glass-forming system, we propose a dimensionless criterion, phi, expressed by T-rg(Delta T-x/T-g)(a), with T-rg, the reduced glass-transition temperature, Delta T-x, the width of the supercooled liquid region when heating a glass, T-g, the glass transition temperature, and a, the exponent. The application of this simple criterion to various glasses, including network, metallic, and molecular glasses (except pure water), indicates an excellent correlation between the critical cooling rate R-c and phi in a Log R-c-phi single master plot with a = 0.143. (c) 2006 Elsevier B.V. All rights reserved.