The kinetic energy of flying insect prey is a formidable challenge for orb-weaving spiders. These spiders construct two-dimensional, round webs from a combination of stiff, strong radial silk and highly elastic, glue-coated capture spirals. Orb webs must first stop the flight of insect prey and then retain those insects long enough to be subdued by the spiders. Consequently, spider silks rank among the toughest known biomaterials. The large number of silk threads composing a web suggests that aerodynamic dissipation may also play an important role in stopping prey. Here, we quantify energy dissipation in orb webs spun by diverse species of spiders using data derived from high-speed videos of web deformation under prey impact. By integrating video data with material testing of silks, we compare the relative contributions of radial silk, the capture spiral and aerodynamic dissipation. Radial silk dominated energy absorption in all webs, with the potential to account for approximately 100 per cent of the work of stopping prey in larger webs. The most generous estimates for the roles of capture spirals and aerodynamic dissipation show that they rarely contribute more than 30 per cent and 10 per cent of the total work of stopping prey, respectively, and then only for smaller orb webs. The reliance of spider orb webs upon internal energy absorption by radial threads for prey capture suggests that the material properties of the capture spirals are largely unconstrained by the selective pressures of stopping prey and can instead evolve freely in response to alternative functional constraints such as adhering to prey.