Many practical algorithms for sequence alignment, genome assembly and other tasks represent a sequence as a set of k-mers. CovEst uses this technique to estimate genome size and sequencing coverage from sequencing reads, without the need for sequence assembly. Our estimates are based on a histogram of k-mer abundance in the input set of sequencing reads and on probabilistic modeling of distribution of $k$-mer abundance based on parameters related to the coverage, error rate and repeat structure of the genome. Our method provides reliable estimates even at coverage as low as 0.5 or at error rates as high as 10%.