Modern genomics techniques generate overwhelming quantities of data. Extracting population genetic variation demands computationally efficient methods to determine genetic relatedness between individuals (or "samples") in an unbiased manner, preferably de novo. Rapid estimation of genetic relatedness directly from sequencing data has the potential to overcome reference genome bias, and to verify that individuals belong to the correct genetic lineage before conclusions are drawn using mislabelled, or misidentified samples. We present the k-mer Weighted Inner Product (kWIP), an assembly-, and alignment-free estimator of genetic similarity. kWIP combines a probabilistic data structure with a novel metric, the weighted inner product (WIP), to efficiently calculate pairwise similarity between sequencing runs from their k-mer counts. It produces a distance matrix, which can then be further analysed and visualised. Our method does not require prior knowledge of the underlying genomes and applications include establishing sample identity and detecting mix-up, non-obvious genomic variation, and population structure. We show that kWIP can reconstruct the true relatedness between samples from simulated populations. By re-analysing several published datasets we show that our results are consistent with marker-based analyses. kWIP is written in C++, licensed under the GNU GPL, and is available from https://github.com/kdmurray91/kwip.