Abstract- A gradually varied flow computation is important for the design of water structures. To design dimensions of channels, examining the depth of water in a gradually varied flow is required. In this study, experiments study were performed to evaluate different methods for calculating the lengths of gradually varied flow curves in mild slope circular open channel. The study was performed in a circular flume with an inner diameter equal to 24.40 cm with a mild slope equal to 0.00083 for different discharges from 2.38 l/sec to 14.08 l/sec. The objective of this study is to compare water surface profiles resulting from experimental measurements with the water surface profiles computed from graphical integration method), direct step method, and Runge-Kutta method for two gradually varied flow curves M3 and M2. The graphical integration method has a minimum percentage error of -0.18% and a maximum of -8.68% for M3 curves, while it has a minimum percentage error of 0.78% and a maximum of 8.37% for M2 curves. The direct step method has a minimum percentage error of 0.04% and a maximum of 9.34% for M3 curves while having a minimum percentage error of 0.91% and a maximum of 8.25 for curves M2 curves. For the Runge-Kutta method, the maximum error in water surface for all runs is -5.00% for M3 curves and 1.95% for M2 curves. The Runge-Kutta method perfectly fits in the circular channels.