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HomemiequipmentIOL Formulae Assessing Accuracy for Short Eyes

IOL Formulae Assessing Accuracy for Short Eyes

Cataract surgery is one of the most commonly performed medical procedures. No longer a visual rehabilitation procedure, good refractive outcome is one of the most important goals of the operation. Patients’ expectations for spectacle independence are quite high, particularly in high hyperopes, or short-eyed patients, who undergo refractive lens exchange as a purely refractive procedure.

This article presents findings from an Australian study that analysed refractive prediction accuracy of different IOL formulae for short eyes.

Cataract surgery has evolved immensely in the last few decades with the introduction of advanced surgical equipment, intraocular lens (IOL) designs, a needle-free procedure, and of course good refractive outcomes.

Surgeons should consider Kane and EVO 2.0 formulae for their cataract surgery and refractive lens extraction patients

Figure 1. Box plot comparison of APE after exclusion of the outliers.

Central to the refractive outcome are the IOL power calculation methods. Since the introduction of new lens power calculation formulae, refractive outcomes have improved to a great extent. In the last few years, we have seen the use of artificial intelligence (AI) in various forms in new formulae. Modern IOL formulae can be classified into theoretical, ray tracing, AI or a combination approach, or conventionally classified as generations of formulae.1

All IOL formulae use different parameters from the lens biometer for power calculations. These include keratometry (K), axial length (AL), anterior chamber depth (ACD), white-to-white (WTW) corneal diameter, central corneal thickness (CCT), and preoperative refractive error, age and sex. The newest formulae, whether with or without AI, do not necessarily use all of these parameters.

Short eyes have their own surgical challenges, but lens power selection is equally challenging. Since they are short in axial length, any movement in effective lens position (ELP) can cause a significant refractive shift from target. Short length of eyeball, combined with high power IOL, can cause large refractive surprise with a minimal shift in ELP. If we consider an example of an eye with 21.00mm AL, 7.7mm mean K, post-operative ELP of 4.27mm and IOL power of 35.00D, a 1mm shift in ELP can cause a myopic surprise of 2.73D and hyperopic surprise of 2.54D at the spectacle plane.2

This makes it important to properly discuss the target refractive error with the patient, and to counsel them about ways to manage should there be refractive surprises. Some patients might be keen on monovision, in which the non-dominant eye can be targeted as myopic to varying degrees to offer good uncorrected near vision, although stereopsis might be compromised to some extent.3

In the last decade, new IOL power calculation formulae have become available, which have provided better outcomes than conventional formulae. This article will predominantly focus on established formulae, along with new formulae that have been compared to established formulae in studies published in peer reviewed indexed journals.


First and Second Generation 

First and second generation IOL formulae – including Binkhorst, SRK, SRK-I, and SRK-are now obsolete. These were historical and regression-based formulae.

Third Generation 

Third generation formulae started using biometry parameters for lens power calculations. SRK-T, Holladay 1 and Hoffer Q aimed to predict the ELP by incorporating corneal power or K values. All three formulae used K and AL for ELP and lens power calculations. Personalising SRK-T formula requires optimisation of A-constant which is specific to IOL type. Data from 150 to 250 eyes is required to optimise the A-constant for a surgeon, which improves the refractive outcome.

Table 1. Refractive outcomes in absolute PE with different formulae.

Holladay 1 introduced the ‘surgeon factor’ (SF), a constant which could be optimised as well to improve refractive outcomes. Similarly, Hoffer Q introduced personalised ACD as a constant. All three formulae were a significant improvement over previous generation formulae. They performed quite well in average sized eyes but were prone to significant prediction error in short and long eyes as they relied on K and AL only for ELP.

Fourth Generation 

Fourth generation formulae used AL, K, AC, LT and WTW for prediction of ELP and IOL power. These formulae performed better in short and long eyes than the previous generation formulae. Haigis, T2 (a modification of SRK-T), Barrett Universal II (BU-II), and Holladay 2 are classified in this generation. BU-II has been one of the most commonly used formula around the world, and has earned the reputation of being one of the most accurate.

Ray Tracing Based Formulae 

As opposed to vergence based equations, the Olsen formula uses exact and para-axial ray tracing through the ocular refractive medial, along with the specific optical properties of an IOL to derive the ELP or postoperative ACD. The Olsen formula is based on ray tracing and has delivered good postoperative refractive outcomes in eyes of all AL.

AI Based Formulae 

Hill radial basis function (RBF), which currently has version 3.0 (Hill RBF 3.0) available,4 works on a mix of AI and regression analysis of postoperative outcome of thousands of eyes. This formula tries to recognise the pattern for an eye under question with the ones in its database to predict ELP. Its major limitation is lower accuracy in eyes which are different from the ones in its database, which are reported as ‘out of bound’ by the formula.

Table 2. Percentage of eyes and PE, including outliers.

Kane formula5 is based on a mix of theoretical optics and AI. The required parameters are K, AL, ACD, sex and A-constant. LT and CCT are optional parameters that would further improve the accuracy. Various studies have reported promising results.

Emmetropia verifying optical (EVO),which has version 2.0 available, is one of the new formulae. This formula uses K, ACD and AL for prediction of ELP. LT and CCT are optional parameters. Few studies have reported good outcomes with the EVO formula, which is a combination of thick lens optical principles, multiple regression and iterative components based on a theoretical ideology (personal communication with the author).


An audit using nine different formulae, used to assess refractive prediction accuracy in short eyes, analysed results for cataract surgery in short eyes from Broadmeadows Hospital, which is part of Northern Health in Victoria. The hospital caters to a multicultural demographic consisting of Caucasian, Middle Eastern and South Asian communities.

Material and Methods 

Only eyes with AL <22.00mm were included for data collection.

Exclusion criteria included eyes with best corrected visual acuity <6/12, any corneal pathology, any retinal conditions, glaucoma, unreliable biometry measurements, use of ultrasound A scan for AL measurements, intraoperative complications, sulcus fixation of IOL and the need for anterior vitrectomy.

Table 3. Pairwise comparisons using paired t -tests. Statistically significant values are highlighted.

A total of 299 eyes were selected based on the inclusion criteria of <22.00mm, out of which 133 eyes were excluded due to incomplete data. Out of 166 remaining eyes, 92 were unilateral and 74 were bilateral.

Multiple surgeons, including consultants and training registrars, performed surgery at the hospital. All included patients had their postoperative subjective refraction more than three weeks after their operation. Only one eye was randomly selected from the bilateral eye patients, hence 129 eyes were left for final analysis.

Prediction error (PE) was calculated for each formula by subtracting predicted spherical equivalent (SEQ) refractive error from actual postoperative subjective refraction SEQ in dioptres (D). Negative PE indicated myopic surprise and positive indicated hyperopic from the predicted refraction. Average, median, standard deviation (SD) of PE and of absolute prediction error (APE) were calculated. A pairwise comparison, using paired t-tests with a Bonferroni correction, was done among all nine formulae. The percentage of eyes within +/- 0.25D, +/- 0.5D, +/-0.75D, +/- 1.00D of PE was calculated for each formula.


After an outlier check (box plot comparison), 11 eyes were further excluded (Figure 1). Data was found to be normally distributed after excluding outliers, hence optimisation of IOL formulae wasn’t required. The average APE was lowest in Kane and EVO 2.0 for our data set (Table 1), the median APE was lowest with the Kane formula. Hoffer Q performed worst of all formulae.

EVO 2.0 had nearly 38% of eyes within +/-0.25D; both EVO 2.0 and Kane had 65% of eyes within +/- 0.50D. EVO 2.0 had nearly 80% of eyes within +/- 0.75D and Olsen had nearly 90% of eyes within +/- 1.00D (Table 2).

Overall, Kane and EVO 2.0 were the most accurate of all the nine formulae analysed. Pairwise comparison, using the paired t-test for average PE between different formulae, showed some formulae were statistically better than others. Statistically significant values are in bold in Table 3.


In today’s world of chasing perfect refractive outcomes, surgeons should use the most accurate formula for their patients. Hyperopes or short-eyed patients are a particularly difficult cohort of patients, where achieving good refractive outcomes can be challenging. Kane and EVO 2.0 are delivering much better outcomes than the previous generations of formulae.

The real test for an IOL formula lies in its accuracy for small eyes. Goecke et al7 compared seven formulae in short eyes; BU-II, Hoffer Q, Haigis, Hill RBF, Holladay 1 and Holladay 2, Olsen. After optimising formulae by reducing the mean to zero, there was no statistically significant difference between the formulae. Kane and Melles8 published their results of refractive outcomes in eyes needing IOL power higher than 30 dioptres (short eyes). The study optimised the constants for each formula. They found Kane and EVO 2.0 to be the most accurate of all. The authors admitted there might be some advantage to the Kane formula in this study since the formula relied on Alcon SA60AT IOL data similar to their study.

Darcy et al9 published results of 10,930 eyes for the United Kingdom’s National Health Service and found the Kane formula to be the most accurate in small, medium and long eyes. EVO 2.0 wasn’t included in this study. For comparison’s sake, almost 80% of eyes can be within +/- 0.5D if refractive outcomes are averaged over short, intermediate and long eyes, and just 65% for the short eyes cohort.10


Surgeons should consider Kane and EVO 2.0 formulae for their cataract surgery and refractive lens extraction patients, particularly for short eyes. They should have an open discussion with their patients and set realistic expectations. Laser enhancement for residual refractive error is a suitable option to consider if expectations are not met.

Dr Nishant Gupta is a cataract, cornea and refractive surgeon. He is the Director of Frankston Eye and Laser Centre in Frankston, Victoria. Dr Gupta combines his private work with public appointments at The Royal Victorian Eye & Ear Hospital (RVEEH) in East Melbourne, Broadmeadows Hospital and Monash Health.

Dr Gupta completed his ophthalmology training in India where he had extensive experience managing complex corneal cases and cataract surgeries. He completed two fellowships in corneal transplantation and other anterior segment surgeries at the RVEEH and the Royal Perth Hospital. Dr Gupta has a Post Graduate Diploma in Cataract and Refractive Surgery from Ulster University, United Kingdom. He has presented in international and national conferences, and published in peer reviewed journals.

Dr Sheetal Shirke is an ophthalmologist with more than 12 years’ experience in ophthalmology. After completing her postgraduate training in India, she completed a fellowship in paediatric ophthalmology and strabismus with prestigious institutes including BC Children’s Hospital in Canada and the RVEEH in Melbourne. She currently works as a senior registrar at RVEEH. She is a clinician with keen interest in teaching and research. Dr Shirke has presented many posters and papers in various national and international conferences and journals.


  1. Kane X. Jack, Chang David F. Intraocular lens power formulas, biometry and intraoperative aberrometry. Ophthalmology , 2020 Aug 13;S0161-6420(20)30789-2. doi: 10.1016/j.ophtha.2020.08.010.Online ahead of print.
  2. Wendelstein, J, Hoffmann, P, Hirnschall, N et al. Project hyperopic power prediction: accuracy of 13 different concepts for intraocular lens calculation in short eyes. Br J Ophthalmol, 2021 Jan 27;bjophthalmol-2020-318272. doi: 10.1136/bjophthalmol-2020-318272. Online ahead of print.
  1. Wilkins, R. Mark, Allan, D. Bruce, Rubin, S. Gary et al. Randomised trial of multifocal intraocular lenses versus monovision after bilateral cataract surgery. Ophthalmology, 2013, 120: 2449-55.
  2. rbfcalculator.com.
  3. www.iolformula.com.
  4. www.evoiolcalculator.com.
  5. Gokce, Sabite E., Zeiter, John H, Weikert, P. Mitchell et al. Intraocular lens power calculations in short eyes using 7 formulas. J Cataract Refract Surg, 2017, 43: 892-97.
  6. Kane, Jack X., Melles, Ronald B. Intraocular lens formula comparison in axial hyperopia with a high-power intraocular lens of 30 or more diopters. J Cataract Refract Surg, 2020, 46: 1236-39.
  7. Darcy Kieren, Gunn David, Tavassoli Shokufeh et al. Assesment of the accuracy of new and updated intraocular lens power calculation formulas in 10,930 eyes from UK National Health Service. J Cataract Refract Surg, 2020, 46: 2-7.
  8. Melles B. Ronald, Hollady T. Jack, Chang J. William et al. Accuracy of Intraocular Lens Calculation Formulas. Ophthalmology, 2018, 125: 169-78.