The Kaplan–Meier (product-limit) estimator of the survival function of randomly censored time-to-event data is a central quantity in survival analysis. It is usually introduced as a non-parametric maximum likelihood estimator, or else as the output of an imputation scheme for censored observations such as redistribute-to-the-right or self-consistency.Following recent work by Robins and Rotnitzky, we show that the Kaplan–Meier estimator can also be represented as a weighted average of identically distributed terms, where the weights are related to the survival function of censoring times. We give two demonstrations of this representation; the first assumes a Kaplan–Meier form for the censoring time survival function, the second estimates the survival functions of failure and censoring times simultaneously and can be developed without prior introduction to the Kaplan–Meier estimator.