Risk matrices are a common way to communicate the likelihood and potential impacts of a variety of risks. Until now, there has been little empirical work on their effectiveness in supporting understanding and decision making, and on how different design choices affect these. In this pair of online experiments (total n = 2699), we show that risk matrices are not always superior to text for the presentation of risk information, and that a nonlinear/geometric labeling scheme helps matrix comprehension (when the likelihood/impact scales are nonlinear). To a lesser degree, results suggested that changing the shape of the matrix so that cells increase in size nonlinearly facilitates comprehension as compared to text alone, and that comprehension might be enhanced by integrating further details about the likelihood and impact onto the axes of the matrix rather than putting them in a separate key. These changes did not affect participants' preference for reducing impact over reducing likelihood when making decisions about risk mitigation. We recommend that designers of risk matrices consider these changes to facilitate better understanding of relationships among risks.