The authors propose an accurate method for detecting the numerical rank of a sparse matrix, using orthogonal factorization along with a one-norm incremental condition estimator. The method uses only static data structures and is implemented with an overhead of \(O(n_ U\log n)\) operations where \(n_ U\) is the number of nonzeros in the upper triangular factor. Also it can be implemented with an overhead of \(O(\max\{n_ U, n\log n\})\) operations, but this implementation is very complicated. This method can be efficiently implemented on message- passing architectures. A prototype implementation is done and tests show that the method is accurate and efficient. Ways in which the condition estimator and the rank detection method can be used are also discussed, along with the rank-revealing orthogonal factorizations of \textit{L. V. Foster} [Linear Algebra Appl. 74, 47-71 (1986; Zbl 0589.65031)].