Multi-omic studies combine measurements at different molecular levels to build comprehensive models of cellular systems. The success of a multi-omic data analysis strategy depends largely on the adoption of adequate experimental designs, and on the quality of the measurements provided by the different omic platforms. However, the field lacks a comparative description of performance parameters across omic technologies and a formulation for experimental design in multi-omic data scenarios. Here, we propose a set of harmonized Figures of Merit (FoM) as quality descriptors applicable to different omic data types. Employing this information, we formulate the MultiPower method to estimate and assess the optimal sample size in a multi-omics experiment. MultiPower supports different experimental settings, data types and sample sizes, and includes graphical for experimental design decision-making. MultiPower is complemented with MultiML, an algorithm to estimate sample size for machine learning classification problems based on multi-omic data. Multi-omics studies are popular but lack rigorous criteria for experimental design. We define Figures of Merit across omics to comparatively describe their performance, and present new algorithms for sample size calculation in multi-omics experiments aiming either at feature selection or sample classification.