Strong to violent tornadoes cause a disproportionate amount of damage, in part because the width and length of a tornado damage track are correlated to tornado intensity (as now estimated through enhanced Fujita scale ratings). The tendency expressed in the observational record is that the most intense tornadoes are often the widest. Herein the authors explore the simple hypothesis that wide intense tornadoes should form more readily out of wide rotating updrafts. This hypothesis is based on an application of Kelvin’s circulation theorem, which is used to argue that the large circulation associated with a wide intense tornado is more plausibly associated with a wide mesocyclone. Because a mesocyclone is, strictly speaking, a rotating updraft, the mesocyclone width should increase with increasing updraft width. A simple mathematical model that is quantified using observations of mesocyclones supports this hypothesis, as do idealized numerical simulations of supercellular thunderstorms.