Natural ventilation is a low-energy design strategy that has the potential both to significantly reduce energy usage in buildings and to provide a healthy and comfortable indoor environment. It has particular potential for use in tall, multi-storey buildings. However, the integration of natural ventilation into these large building designs has seen mixed success. Furthermore, there is a gap between simple 'rule-of-thumb' design guidance and detailed, computational design tools. This research attempts to bridge the gap between the simple and detailed with the broad aim of providing rapid and intuitive guidance for use in preliminary design. We use a simple mathematical approach to develop a coherent and easy-to-use framework for modelling ventilating flows, which quantifies the interactions between a core set of design variables. We focus in particular on buoyancy-driven ventilation in buildings with atria, ventilation stacks and/or similar vertical spaces that span multiple floors. Simple methods centred around hand calculations and design charts are developed to inform the sizing of vents in an 'ideal design' scenario, in which the desired ventilation flow rates and air temperatures are delivered to all occupants within a building. We define a measure of the ventilation performance of an atrium and use this to provide an indication of when an atrium is beneficial to a ventilation system design and when it is detrimental. We also use a transient flow analysis to consider 'off-design' scenarios, in which undesirable flow regimes may occur, and to place design tolerances on the building envelope. It is hoped that this work will form a point of reference for further research and for future revisions of design guidance literature.