extrapops simulates extra-galactic populations of gravitational waves sources and models their emission during the inspiral phase. The code approximately assesses the detectability of individual sources by LISA and computes the background due to unresolved sources in the LISA band using different methods. The simulated populations can be saved in a format compatible with LISA LDC. Simulations are well calibrated to produce accurate background calculations and fair random generation at the tails of the distributions, which is important for accurate probability of detectable events. extrapops uses a number of ad-hoc techniques for rapid simulation and allows room for further optimization up to almost 1 order of magnitude.