How the solar electromagnetic energy entering the Earth's atmosphere varied since preindustrial times is an important consideration in the climate change debate. Detrimental to this debate, estimates of the change in total solar irradiance (TSI) since the Maunder minimum, an extended period of weak solar activity preceding the industrial revolution, differ markedly, ranging from a drop of 0.75 W/m2 to a rise of 6.3 W/m2. Consequently, the exact contribution by solar forcing to the rise in global temperatures over the past centuries remains inconclusive. Adopting a novel approach based on state-of-the-art solar imagery and numerical simulations, we establish the TSI level of the Sun when it is in its least-active state to be 2.0 ± 0.7 W/m2 below the 2019 level. This means TSI could not have risen since the Maunder minimum by more than this amount, thus restricting the possible role of solar forcing in global warming.