Time representation is important in many applications, such as temporal databases, planning, and multi-agents. Since Allen’s work on binary interval relations (called interval algebra), many researchers have further investigated temporal information processing based on interval calculus. However, there are still some limitations, e.g. constraint satisfaction is a NP-hard problem in interval calculus. For this reason, we propose a new interpretation for interval relationships and their calculus in this paper, which establishes a new method to transform interval calculus into matrix calculus. Our experiments show that this method propagates temporal relations faster than interval algebra.