Fiber spinnability is the ability of a glass‐forming melt to be steadily stretched and spun into defect‐free fiber filaments. However, its quantification has not been well established owing to many controlling factors such as melt fragility, melt strength, surface tension, liquidus temperature, liquidus viscosity, and crystallization. To understand and quantify the fiber spinnability of a glass melt, we consider two key aspects: fiberizing viscosity window and melt stability. The fiberizing viscosity window is defined by the upper and lower viscosity limits. Fibers rupture above the upper viscosity limit, whereas a stable melt stream cannot form below the lower limit (ηlow). We introduce a simple parameter to quantify fiber spinnability, namely, Kfib=ηL/ηlow, where ηL is the viscosity at liquidus temperature (TL). A fiber can only form if Kfib>1. To quantify melt stability we propose the parameter of S=(TL‐TC)/(TL‐Tg), where TL and TC are the liquidus temperature, and the onset temperature of melt crystallization during cooling, respectively. Both parameters (Kfib and S) are important for a rational design of glass fiber compositions, and fiberizing process. We use two basalt melts as examples of this study to demonstrate the high sensitivity of fiber spinnability to a minor variation in chemical composition of melts.