To estimate the potential reduction in HIV incidence, we constructed a risk equation based on a flow diagram of the HIV cascade, linking HIV diagnosis and treatment coverage with estimates of annual incidence and prevalence. This was applied to numerous settings. Some countries have already achieved high diagnosis and treatment levels, and if the Joint United Nations Programme on HIV/AIDS (UNAIDS) targets of 90% diagnosis and 90% antiretroviral therapy (ART) coverage were achieved, then population incidence could not reduce very substantially. Other countries have a high HIV diagnosis level but low treatment coverage; the United States, for example, could expect to achieve up to a 50% reduction in incidence by prioritizing treatment scale-up to achieve a 48% increase among those diagnosed, together with only a 4% increase in diagnosis to reach targets. Other countries have low diagnosis and treatment levels; if, for example in Indonesia, both are scaled up by approximately 60% to reach UNAIDS targets, it is possible to achieve a 50%-55% reduction in incidence (or around 65% reduction if they also achieve 90% viral suppression). Finally, some countries, including across sub-Saharan Africa, have high treatment coverage but low diagnosis levels, requiring testing to be scaled up to maximize ART benefits of up to 35%-40% reductions in incidence, requiring a greater than 40% increase in diagnosis and 10% increased coverage of ART on top of covering most of those newly diagnosed with ART. The HIV testing or treatment scale-up required to maximize reduction in the incidence of HIV is context specific; attainable relative reductions are inversely related to baseline levels.