Laser beam machining of Polymethyl methacrylate (PMMA) has gained traction because of its high absorptivity, dimensional stability, good abrasive resistance, easy operation and low cost. The main aim of this work is to develop an algorithm to solve the problem of determining the depth of thermoplastic materials for the known number of laser passes along with the determination of the number of passes for the known depth of cut. Two algorithms have been proposed, namely, algorithms I and II, based on the laser parameters. The algorithm-I predicts the depth for the predetermined laser passes, and algorithm-II predicts the laser passes for the known depth of cut. The developed algorithms have been validated with the experimental results and compared with the algorithm available in the literature and the machine learning algorithm. The performance analysis highlights the good convergence with the experimental results. The MSE, RMSE, MAPE, and MAD obtained for the developed algorithm are 0.014542603, 0.120592717, 8.60 %, and 0.114727889, respectively, which is comparatively converges closer than the algorithm available in the literature and the machine learning algorithm.