Large-scale GWAS results are typically obtained by meta-analyzing GWAS results from multiple studies spanning different regions and/or time periods. This approach averages the estimated effects of individual genetic variants across studies. In case genetic effects are heterogeneous across studies, the statistical power of a GWAS and the predictive accuracy of polygenic scores are attenuated, contributing to the so-called 'missing' heritability. However, a theoretical multi-study framework, relating statistical power and predictive accuracy to cross-study heterogeneity, is not available. We address this gap by developing an online Meta-GWAS Accuracy and Power calculator that accounts for the cross-study genetic correlation. This calculator enables to explore to what extent an imperfect cross-study genetic correlation (i.e., less than one) contributes to the missing heritability. By means of simulation studies, we show that under a wide range of genetic architectures, the statistical power and predictive accuracy inferred by this calculator are accurate. We use the calculator to assess recent GWAS efforts and show that the effect of cross-study genetic correlation on statistical power and predictive accuracy is substantial. Hence, cross-study genetic correlation explains a considerable part of the missing heritability. Therefore, a priori calculations of statistical power and predictive accuracy, accounting for heterogeneity in genetic effects across studies, are an important tool for adequately inferring whether an intended meta-analysis of GWAS results is likely to yield meaningful outcomes.