Semantic ambiguity is typically measured by summing the number of senses or dictionary definitions that a word has. Such measures are somewhat subjective and may not adequately capture the full extent of variation in word meaning, particularly for polysemous words that can be used in many different ways, with subtle shifts in meaning. Here, we describe an alternative, computationally derived measure of ambiguity based on the proposal that the meanings of words vary continuously as a function of their contexts. On this view, words that appear in a wide range of contexts on diverse topics are more variable in meaning than those that appear in a restricted set of similar contexts. To quantify this variation, we performed latent semantic analysis on a large text corpus to estimate the semantic similarities of different linguistic contexts. From these estimates, we calculated the degree to which the different contexts associated with a given word vary in their meanings. We term this quantity a word's semantic diversity (SemD). We suggest that this approach provides an objective way of quantifying the subtle, context-dependent variations in word meaning that are often present in language. We demonstrate that SemD is correlated with other measures of ambiguity and contextual variability, as well as with frequency and imageability. We also show that SemD is a strong predictor of performance in semantic judgments in healthy individuals and in patients with semantic deficits, accounting for unique variance beyond that of other predictors. SemD values for over 30,000 English words are provided as supplementary materials.