We present a set of universal curves that predict the range and intensity of backscattered electrons which can be used in conjunction with electron beam lithography to create high fidelity nanoscale patterns. The experimental method combines direct write dose, backscattered dose, and a self-reinforcing pattern geometry to measure the dose provided by backscattered electrons to a nanoscale volume on the substrate surface at various distances from the electron source. Electron beam lithography is used to precisely control the number and position of incident electrons on the surface of the material. Atomic force microscopy is used to measure the height of the negative electron beam lithography resist. Our data shows that the range and the intensity of backscattered electrons can be predicted using the density and the atomic number of any solid material, respectively. The data agrees with two independent Monte Carlo simulations without any fitting parameters. These measurements are the most accurate electron range measurements to date.