The block Gram-Schmidt method computes the qr factorisation rapidly, but this is dependent on block size m. We endeavor to determine the optimal m automatically during one execution. Our algorithm determines m through observing the relationship between computation time and complexity. Numerical experiments show that our proposed algorithms compute approximately twice as fast as the block Gram-Schmidt method for some block sizes, and is a viable option for computing the qr factorisation in a more stable and rapid manner.