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Updated: May 6, 2026
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Published on: September 16, 2025
Accuracy of six contemporary toric formulas: analysis of 6753 eyes
Janusz Skrzypecki1, Douglas D Koch, Li Wang
1From the Department of Experimental Physiology and Pathophysiology, Medical University of Warsaw, Warsaw, Poland (Skrzypecki); Cullen Eye Institute, Department of Ophthalmology, Baylor College of Medicine, Houston, Texas (Koch, Wang).
Purpose:
To compare the predictive accuracy of 4 toric intraocular lens (IOL) formulas (Barrett, EVO, Hoffer QST, and Kane) integrated in the ESCRS calculator. Barrett and EVO were tested with measured (Barrett M and EVO M) and predicted (Barrett P and EVO P) posterior corneal curvature.
Setting:
Multiple surgical centers in the United States.
Design:
Retrospective database study.
Methods:
6753 eyes implanted with nontoric IOLs were analyzed. Preoperative biometry, including posterior corneal curvature, was obtained using the IOLMaster 700. Predicted residual astigmatism was calculated through the proprietary websites of the 4 toric formulas integrated into the ESCRS IOL power calculator. Primary endpoints were the mean vector magnitude error and proportions of eyes with vector magnitude prediction errors ≤0.50 diopters (D).
Results:
Kane demonstrated the lowest mean vector magnitude prediction error (0.537 D), significantly lower than EVO P (0.561 D), EVO M (0.57 D), Barrett M (0.579 D), Barrett P (0.583 D), and Hoffer QST (0.622 D) (all P < .001). This result was consistent in with-the-rule, against-the-rule, and oblique subgroups. Kane also achieved the highest proportion of eyes with prediction error ≤0.50 D ( P < .001). For all formulas, centroid values were significantly different from zero. The Kane formula showed the lowest total variances, significantly lower than all other formulas ( P < .001).
Conclusions:
The Kane formula showed statistically superior predictive accuracy with the lowest errors and variances and the highest proportion of eyes within 0.50 D. However, differences among formulas were small, and their clinical relevance for toric IOL outcomes remains uncertain.
