Crystalline nanowires exhibiting a wide range of size-dependent fracture and failure modes have been extensively studied, yet the fracture behaviors of amorphous materials and their size dependence remain elusive. Here extensive atomistic simulations are performed to reveal the deformation and fracture behaviors in a broad class of amorphous nanowires with varying sizes, including CuZr, CuZrAl, FeP, Si, and a ductile Lennard-Jones system. It is found that the fracture strain "f increases with nanowire length L but decreases with diameter D, which exhibits a linear relationship with the diameter-to-length ratio as "f cc D/L, -a scaling law valid in these five distinct glassy systems understudied. We develop a theoretical model, capturing the size of plastic zone at plastic yielding and its vital role in governing the final fracture strain, which shows an agreement with the simulation data. By taking into account the intrinsic atomic -level ideal strain, remarkably, all the size-dependent fracture strain data collapse, signifying the universality of fracture nature in a broad range of glassy materials.