Gaussian rough surfaces can be characterized by two roughness parameters, the root-mean-square height and correlation length. For accurate estimation of these parameters from measured surface height-profile, data samples with sufficiently long record length are necessary. In this letter, an expression of correlation length in terms of a surface slope function is introduced in order to estimate correlation length and analytical expression of the data record length required for accurate estimation is derived. The result shows that the method using the slope function can reduce the data record length approximately 60% as compared to the commonly employed method using the correlation function. In order to check the result, a Monte Carlo simulation is also carried out and the validity of the result is confirmed.