It is relevant to consider uncertainty in individual predictions when quantitative structure-activity (or property) relationships (QSARs) are used to support decisions of high societal concern. Successful communication of uncertainty in the integration of QSARs in chemical safety assessment under the EU Registration, Evaluation, Authorisation and Restriction of Chemicals (REACH) system can be facilitated by a common understanding of how to define, characterise, assess and evaluate uncertainty in QSAR predictions. A QSAR prediction is, compared to experimental estimates, subject to added uncertainty that comes from the use of a model instead of empirically-based estimates. A framework is provided to aid the distinction between different types of uncertainty in a QSAR prediction: quantitative, i.e. for regressions related to the error in a prediction and characterised by a predictive distribution; and qualitative, by expressing our confidence in the model for predicting a particular compound based on a quantitative measure of predictive reliability. It is possible to assess a quantitative (i.e. probabilistic) predictive distribution, given the supervised learning algorithm, the underlying QSAR data, a probability model for uncertainty and a statistical principle for inference. The integration of QSARs into risk assessment may be facilitated by the inclusion of the assessment of predictive error and predictive reliability into the "unambiguous algorithm", as outlined in the second OECD principle.