Fitness is not well estimated from growth curves of individual isolates in monoculture. Rather, competition experiments, which measure relative growth in mixed microbial cultures, must be performed to better infer relative fitness. However, competition experiments require unique genotypic or phenotypic markers, and thus are difficult to perform with isolates derived from a common ancestor or non-model organisms. Here we describe Curveball, a new computational approach for predicting relative growth of microbes in a mixed culture utilizing mono- and mixed culture growth curve data. We implemented Curveball in an open-source software package (http://curveball.yoavram.com) and validated the approach using growth curve and competition experiments with bacteria. Curveball provides a simpler and more cost-effective approach to predict relative growth and infer relative fitness. Furthermore, by integrating several growth phases into the fitness estimation, Curveball provides a holistic approach to fitness inference from growth curve data.