Determination of model order is an important task in many problems such as sinusoidal parameter estimation. In this paper we consider the data matrix corresponding to the given sequence and introduce the Ratio of Cumulative Sums (RCS) of eigenvalues. We then exploit the structure of RCS to obtain a performance that is comparable to the Cumulative Sums based method of Shah and Tufts (ST). However the advantage is that we do not require knowledge of the noise level; moreover, our method is computationally cheaper. RCS can also be used in conjunction with existing methods to improve performance: we showcase improved results for Cheng and Hua's least-squares (LS) method when RCS information is used. When there are three closely spaced sinusoids, our method outperforms both the ST and LS methods. © 2018 IEEE.