Giacomo Savini - Toric Calculators

Updated: Apr 19

Several calculators for toric IOLs are currently available. The most accurate ones do not only calculate the cylinder of the toric IOL based on the K1 and K2 readings (as well as the axial length and ACD measurements), but also modify the cylinder measured by keratometry (so-called keratometric astigmatism) in order to take the astigmatism of the posterior corneal curvature into account. It has shown that toric calculators predicting posterior and total corneal astigmatism are more accurate than toric calculators using direct total corneal astigmatism measurements.1 This apparently non-sense finding is likely to depend on the fact that estimating algorithms, in addition to posterior corneal astigmatism, take other sources of error into account (e.g. IOL tilting).

Abulafia-Koch toric calculator

This calculator uses a regression formula aiming to compensate for the effect of posterior corneal astigmatism.2 It has been incorporated into the toric calculator of Physiol ( and Hoya ( The formula takes anterior curvature-based corneal measurements and calculates a new net corneal astigmatism with a new magnitude and a new meridian. Its results are similar to those obtained with Barrett’s calculator.2

Barrett toric calculator

Barrett’s has been the first toric calculator to change the cylinder obtained as the keratometric astigmatism into a new value defined “net astigmatism”. With respect to keratometric astigmatism, net astigmatism is lower in eyes with with-the-rule astigmatism and higher in eyes with against-the-rule astigmatism. The mathematics behind Barrett’s calculator have never been published. However, it can be easily observed that net astigmatism also depends on the ACD and axial length values. Moreover, the version available on the APACRS website does not only calculate the cylinder, but also the spherical equivalent power of the IOL.

Barrett toric calculator offer the opportunity to predict the posterior corneal astigmatism (PCA) or to enter the PCA measured by instruments like the IOLMaster 700 or the Pentacam. A recent study did not find differences between the two approaches.3

In addition, a version for post-LASIK eyes is available (Barrett True-K toric calculator).

Several papers have demonstrated that Barrett toric calculator is one of the most accurate options to calculate the power of toric IOLs.3-5

EVO toric calculator

This calculator has been developed by Tun Kuan Yeo, MD, in Singapore. The EVO toric formula is based on the EVO formula. It combines theoretical posterior cornea astigmatism prediction, thick lens modelling for different types of toric IOLs, and a dynamically interconnected prediction of IOL power and toricity.

Holladay toric calculator

This calculator has been released in 2019 following a publication by the author.6 It is based on the difference between the preoperative keratometric astigmatism and the postoperative refractive astigmatism, as originally assessed in patients with non-toric IOLs.

Kane toric calculator

The Kane toric formula uses an algorithm incorporating regression, theoretical optics and artificial intelligence techniques to calculate the total corneal astigmatism. It then applies an effective lens position (ELP) based approach to calculate the residual astigmatism for a particular eye and IOL power combination. It is recommended to use an SIA of zero with the Kane toric formula when performing surgery with a temporal incision size of ≤2.75 mm.

In a large study published by the author, the Kane toric formula has been shown to be the most accurate toric formula.7 Another recent study found no difference with respect to Barrett’s toric calculator.

Næser-Savini toric calculator

The calculator developed by Drs. Kristian Næser and Giacomo Savini is based on the concept of optimized keratometry, a modification of the keratometric astigmatism that zeroes out the mean prediction, i.e. the difference between the predicted and the achieved refractive astigmatism.8 Like for Barrett’s calculator, also Næser-Savini toric calculator reduces the magnitude of the corneal astigmatism in eyes with a with-the-rule astigmatism and increases it in eyes with agains-the-rule astigmatism. The new cylinder is calculated according to the following equation:

Optimal keratometric astigmatism = 0.103 + 0.836 x Measured keratometric astigmatism + 0.457 x cos (2 x α)

This calculator takes the effective lens position and axial length into consideration, according to meridional analysis as described by Fam.9 It is available on the website of the Italian Society of Ophthalmology and on the website of the Hoffer QST formula: in the first case, meridional analysis is based on traditional vergence formulas, in the second case it is based on the new Hoffer QST.


1 - Ferreira TB, Ribeiro P, Ribeiro FJ, O’Neill J. Comparison of methodologies using estimated or measured values of total corneal astigmatism for toric intraocular lens power calculation. J Refract Surg 2017;33:794-800.

2 - Abulafia A, Koch DD, Wang L, Hill WE, Assia EI, Franchina M, Barrett GD. New regression formula for toric intraocular lens calculations. J Cataract Refract Surg 2016; 42:663–671

3 - Yang S, Byun YS, Kim HS, Chung SH. Comparative accuracy of Barrett toric calculator with and without posterior corneal astigmatism measurements and Kane toric formula. Am J Ophthalmol (in press)

4 - Reitblat O, Levy A, Kleinmann G, Abulafia A, Assia EI. Effect of posterior corneal astigmatism on power calculation and alignment of toric intraocular lenses: comparison of methodologies. J Cataract Refract Surg 2016; 42:217–225.

5 - Abulafia A, Hill WE, Franchina M, Barrett GD. Comparison of methods to predict residual astigmatism after intraocular lens implantation. J Refract Surg 2015; 31:699–707.

6 - Holladay JT, Pettit G. Improving toric intraocular lens calculations using total surgically induced astigmatism for a 2.5 mm temporal incision. J Cataract Refract Surg 2019;45:272-283.

7 - Kane JX, Connell B. A comparison of the accuracy of 6 modern toric intraocular lens formulas. Ophthalmology 2020;127:1472-1486.

8 - Savini G, Næser K, Schiano-Lomoriello D, Ducoli P. Optimized keratometry and total corneal astigmatism for toric intraocular lens calculation. J Cataract Refract Surg 2017;43:1140-1148

9 - Fam HB, Lim KL. Meridional analysis for calculating the expected sphero- cylindrical refraction in eyes with toric intraocular lenses. J Cataract Refract Surg 2007; 33:2072–2076

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