Increasing habitat connectivity is important for mitigating the effects of climate change, landscape fragmentation and habitat loss for biodiversity conservation. However, modelling connectivity at the relevant scales over which these threats occur has been limited by computational requirements. Here, we introduce the open-source software gflow, which massively parallelizes the computation of circuit theory-based connectivity. The software is developed for high-performance computing, but scales to consumer-grade desktop computers running modern Linux or Mac OS X operating systems. We report high computational efficiency representing a 173x speedup over existing software using high-performance computing and a 84x speedup using a desktop computer while drastically reducing memory requirements. gflow allows large-extent and high-resolution connectivity problems to be calculated over many iterations and at multiple scales. We envision gflow being immediately useful for large-landscape efforts, including climate-driven animal range shifts, multitaxa connectivity, and for the many developing use-cases of circuit theory-based connectivity.