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The use of solar photovoltaic has strongly increased in the last decade. A significant part of this growth comes from home owners installing rooftop photovoltaic. Despite this key role, most long-term model-based scenarios do not consider decentralized supply of rooftop photovoltaic but concentrate on utility-scale photovoltaic instead. In this paper, we implement rooftop photovoltaic in the Integrated Assessment Model IMAGE to study its possible role in energy and climate scenarios. We first calculated the global technical and economic potential to derive regional cost-supply curves for rooftop photovoltaic. Next, we have added a new decision in the IMAGE model allowing household investment in rooftop photovoltaic based on the comparison of the whole-sale electricity price with the price of rooftop photovoltaic. The global suitable roof surface area was assessed at 36 billion m2, or 4.7 m2 capita−1, leading to a potential for rooftop photovoltaic of 8.3 PWh y−1, roughly 1.5 times the 2015 global residential electricity demand. In the baseline scenario, adding rooftop photovoltaic could lead to a 80–280% increased share of photovoltaic electricity production in 2050 (i.e. from 6% to 17% in total power production). This increase depends on regional characteristics that are essential to the deployment of rooftop photovoltaic: differences in social-economic and policy factors (capital costs, household income, and electricity prices) are considerably more important than physical factors, such as solar irradiance.