Loss of circularity when creating metal ring-shaped products by ring rolling is a significant industrial issue. This paper explores the previously tacit knowledge that plastic changes in curvature - required to maintain circularity - principally occur as material passes through the roll gap. Through a series of experiments and numerical simulations on half-ring workpieces, the ‘free curvature change’ is explored for the first time, finding that the ring can ‘curl up’ - the radius reducing by as much as -39% in a single pass - unless the inner roll is much smaller than the outer roll. An analytical model of free curvature change is proposed based on force equilibrium and compatibility. Under a range of ‘normal’ operating conditions this predicted free curvature change to within 7%. In (full) ring rolling the radius of curvature must continually increase. This paper proposes that regulation of curvature is achieved through bending moments at the roll entry and exit; largest when the tool size ratio is furthest from the optimum. This hypothesis is supported by Finite Element simulations of full ring rolling, finding entry and exit moments up to a quarter of the moment for a fully plastic hinge. This work could be of direct use to process designers in choosing tool sizes and guide roll force limits and suggests new ways to use guide rolls to better maintain circularity in challenging situations.