Next generation of space-based coronagraphs such as HabEx and LUVOIR will employ deformable mirrors (DM) with tens of thousands of actuators and collect measurements from hundreds of millions of pixels. The task of high-order wavefront sensing and control (HOWFSC) is to shape the DM, based on image plane measurements, to correct optical aberrations caused by factors that are not possible to characterize and plan for before the instruments’ launch. The HOWFSC system works to reduce the residual starlight (speckles in the dark hole) so that dim companion objects like exoplanets can be observed within it . One challenge is that HOWFSC algorithm complexity scales superlinearly with the number of pixels and actuators. This challenge is further exacerbated by the limited computational power of available space-rated processors, resulting in potentially significant observation time loss for the missions. We split the HOWFSC algorithms into “calibration”, “dark hole creation” and “dark hole maintenance” phases and assess their computational complexity for some of the most capable existing algorithms in each category. We then compare estimates for the computation time required to run these algorithms onboard HabEx and LUVOIR with the RAD5545 processor. Our results suggest that given current processor architectures, the telescopes could spend weeks to months computing their DM influence function (calibration) and controls (when creating the dark hole). We consider alternative processors and their technology development needs as well as different mission configurations that could help mitigate the HOWFSC computation challenge.