<p>This paper presents a systematic classification and experimentally validated comparative evaluation of single-frequency phase measurement algorithms utilized in phase shifting interferometry. The study begins by elucidating the fundamental principles of these algorithms, followed by an examination of their methodologies, benefits and limitations. This work categorizes the single-frequency phase shifting algorithms into the following categories: Traditional algorithms, Iterative algorithms, Non-iterative algorithms, and Hybrid algorithms. Experimental validation of all the algorithms is conducted by performing quantitative phase measurement on the test samples to evaluate their performance. The traditional five step algorithm is used as the standard reference. The root mean square (RMS) value of the difference between the surface profiles obtained using each algorithm and the five step algorithm is used to evaluate the accuracy, while repeatability across multiple measurements has been used to quantify the precision of each algorithm. This work concludes that non-iterative algorithms outperform iterative and hybrid algorithms in terms of execution time while maintaining the same accuracy in quantitative phase measurement. More precisely, the universal phase shifting algorithm is found to be the most suitable algorithm for surface profiling from just three interferograms in the lowest time of execution. However, principal component analysis with neighbouring pixels, which uses five interferograms, exhibited better accuracy with comparable repeatability to the universal phase shifting algorithm. Another observation is that the two frame algorithms are significantly influenced by the imperfect filtering of the background intensity of the interferograms. Therefore, this work contributes insights into the performance of single-frequency phase measurement algorithms, providing a valuable reference to select an appropriate algorithm for precision surface profiling applications.</p>