Polyclonal or complex malarial infections can provide insight into the genetic diversity and population structure of parasites as well as their transmission and within-host dynamics. The proportion of complex infections and the complexity of infection (COI—the number of strains infecting an individual) have been shown to be the most informative for inferring transmission intensity. Current state-of-the-art methods to estimate the COI such as THE REAL McCOIL are computationally intensive when working with a large number of samples or numerous genetic loci. In this study, we determined two relationships that tie the population-level minor allele frequency and the within-sample frequency of the minor allele to estimate the COI. We derived easily calculable measures to directly estimate the COI from these parameters that are easily obtained from sequencing read depth data. Our methods are computationally efficient, estimating the COI of samples in less than a second, and perform well on simulated data. Furthermore, we demonstrate that our methods are comparably accurate to current methods in the literature. We apply both THE REAL McCOIL and our new methods to estimate the COI for 5,970 P. falciparum samples from 28 malaria-endemic countries collected as part of Pf3k (release 6). We explore the global heterogeneity of the COI and characterize the relationship between malaria prevalence at the time of sample collection and the COI. Lastly, we detail how our methods can be used to explore further within-sample parasite information, including the relatedness of parasites within mixed infections.