Abstract
PURPOSE: To evaluate the performance of seven modern intraocular lens (IOL) power calculation formulas in two different PARTIAL-Range of Field (RoF) extend IOL designs, and a novel IOL constant optimization method. METHODS: 200 eyes implanted with Acrysof IQ Vivity or Tecnis Symfony IOL were included. Postoperative refractive outcomes of the Barrett Universal II (BUII), Cooke K6, EVO 2.0, Hill-RBF 3.0, Hoffer QST, Kane, and Pearl DGS formulas were compared. IOL constant is optimized by using ‘three variable optimization’ (TVO) (https://ioloptimization.com/calculator). Formula Performance Index (FPI), root-mean-square absolute prediction error (RMSAE), and SD of prediction errors were selected as the primary endpoints. RESULTS: In the Vivity group, the FPI in descending order was Cooke K6 (0.613), Kane (0.496), Hill-RBF 3.0 (0.478), Pearl DGS (0.474), BUII (0.430), EVO 2.0 (0.405), and Hoffer QST (0.341). No significant inter-formula differences were found in RMSAE and SD. In the Symfony group, the FPI in descending order was Cooke K6 (0.495), Pearl DGS (0.473), Hill-RBF 3.0 (0.428), BUII (0.403), Kane (0.385), EVO 2.0 (0.352), and Hoffer QST (0.310). Cooke K6 outperformed Hoffer QST (P = 0.032) and Pearl DGS (P = 0.027) in SD. The optimized A-constants vary among formulas derived from the same IOL model (Vivity: range 118.97 to 119.14; Symfony: range 119.17 to 119.36). All formulas achieved a mean prediction error of less than 0.012 D after constant optimization. CONCLUSIONS: Modern IOL power calculation formulas exhibit high accuracy for PARTIAL-RoF extend IOLs, with performance varying by IOL model. The TVO proved to be an effective and convenient tool. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12886-026-04725-9.