Temporal and spatial reasoning is a central task for numerous applications in many areas of Artificial Intelligence. For this task, numerous formalisms using the qualitative approach have been proposed. Clearly, these formalisms share a common algebraic structure. In this paper we propose and study a general definition of such formalisms by considering calculi based on basic relations of an arbitrary arity. We also describe the QAT (the Qualitative Algebra Toolkit), a JAVA constraint programming library allowing to handle constraint networks based on those qualitative calculi.