Extensive research has been conducted on the approximation equations that describe the relationship between load and central deflection in clamped circular thin plates, due to their wide application in engineering. In this study, Galerkin’s method is utilized to derive a load-deflection formula represented as a polynomial fraction by introducing a new displacement field involving two unknown parameters. The results from this research are compared with Timoshenko’s model and numerical solution obtained through finite difference methods, demonstrating very high precision in representing load as a function of central deflection. Additionally, it shows that the proposed vertical displacement field closely reproduces the shape of the plate when compared with Timoshenko’s model, also suggesting that the acquired radial displacement is almost precise since it does not violate the in-plane equilibrium equation unlike Timoshenko’s model. The formulas developed could provide a reliable alternative to existing formulas for analyzing large deflections of thin plates found in literature.