Tumour cellularity, the relative proportion of tumour and normal cells in a sample, affects the sensitivity of mutation detection, copy number analysis, cancer gene expression and methylation profiling. Tumour cellularity is traditionally estimated by pathological review of sectioned specimens; however this method is both subjective and prone to error due to heterogeneity within lesions and cellularity differences between the sample viewed during pathological review and tissue used for research purposes. In this paper we describe a statistical model to estimate tumour cellularity from SNP array profiles of paired tumour and normal samples using shifts in SNP allele frequency at regions of loss of heterozygosity (LOH) in the tumour. We also provide qpure, a software implementation of the method. Our experiments showed that there is a medium correlation 0.42 (Formula: see text-value=0.0001) between tumor cellularity estimated by qpure and pathology review. Interestingly there is a high correlation 0.87 (Formula: see text-value Formula: see text 2.2e-16) between cellularity estimates by qpure and deep Ion Torrent sequencing of known somatic KRAS mutations; and a weaker correlation 0.32 (Formula: see text-value=0.004) between IonTorrent sequencing and pathology review. This suggests that qpure may be a more accurate predictor of tumour cellularity than pathology review. qpure can be downloaded from https://sourceforge.net/projects/qpure/.