Web services, as an aspect of cloud computing, are becoming an important part of the general IT infrastructure, and scientific computing is no exception to this trend. We propose a simple approach to develop chemical Web services, through which servers could expose the essential data manipulation functionality that students and researchers need for chemical calculations. These services return their results as JSON (JavaScript Object Notation) objects, which facilitates their use for Web applications. The ChemCalc project http://www.chemcalc.org demonstrates this approach: we present three Web services related with mass spectrometry, namely isotopic distribution simulation, peptide fragmentation simulation, and molecular formula determination. We also developed a complete Web application based on these three Web services, taking advantage of modern HTML5 and JavaScript libraries (ChemDoodle and jQuery).