The Accuracy of Different Generation Intraocular Lens Power Formulas in Eyes with Axial Length Lower than 22 millimeter




To investigate the accurate formulas for eyes with axial length (AL) lower than 22 millimeters among usually used six intraocular lens (IOL) calculation formulas.


A total of 122 eyes with short ALs that is lower than 22 mm of 122 patients who underwent phacoemulsification surgery with the same type of IOL implantation were included in this retrospective study. The biometric values of the patients were obtained by using optical low coherence reflectometry (OLCR) for six formulas involving Hoffer Q, SRK-T, Haigis, Barett Universal II, Holladay 2 and Hill-RBF. All patients had a postoperative best corrected visual acuity level that is equal or higher than 20/40. While comparing the accuracy of these six IOL calculation formulas, the mean absolute error (MAE), and the median absolute error (MedAE) values were taken into account.


The MAE values for Hoffer Q, SRK-T, Haigis, Holladay 2, Hill-RBF and Barrett Universal II formulas were 0.390, 0.390, 0.324, 0.327, 0.331 and 0.208 respectively. Also the rank of MedAE values for the mentioned formulas was 0.245, 0.310, 0.310, 0.250, 0.255 and 0.190. The lowest MAE and MedAE value was found in Barrett Universal II formula, whereas the highest one was in the SRK/T formula with a statistical significance (p<0.001). After Bonferroni correction, there were no statistically significant difference between Barret Universal II formula and the other formulas except SRK/T (p>0.01). Three patients (2.5%) were in the ±0.75 D range, 15 patients (12.3%) were in the ±0.50 D, and the remaining 104 (85.2%) patients were in the ±0.25 D at the first month follow-up.


Although Barrett Universal II appears to be the most accurate IOL calculation formula, third, fourth and other newer generation formulas have also a good predictive value for accurate estimation of IOL power in short eyes.


The lens extraction and IOL implantation surgery is performed either for removing the lens opasification, or for the purpose of refractive correction in subjects who are not suitable for keratorefractive approach. The combined advances in the surgical technique, and IOL desing such as small insicion cataract surgery with an implantation of aspheric monofocal, toric or multifocal IOL have increased the refractive outcomes for quality of vision. In uncomplicated lenticular surgery, there may be two main factors effecting the postoperatif good visual acuity. The first one is the surgical factor that may involve for example the site, and the width of the corneal insicion, and the second factor is the detection of the postoperatif accurate IOL power. Although first factor partially depends on the experience of the surgeon, the second one seems to be more predictable, if the proper IOL power is selected for the surgery.

The major determinants for the accurate calculation of IOL power are the precise measurement of axial length (AL), corneal power, namely, keratometry (K), and the estimation of postoperative effective lens position (ELP). Among these determinants the error in AL measurement is the most common cause of incorrect IOL power calculation [1, 2]. No major problem is pointed out for the IOL power calculation for normal eyes whose ALs are between 22–26 mm. However for those that is outside of this range, known as short (AL ≤ 22 mm) and long eyes (AL ≥ 26 mm), accurate lens determination may occasionally be problematic while using first (Binkhorst), second (SRK-II), third (Holladay 1,SRK-T and Hoffer Q) generation IOL calculation formulas incorporating mainly AL and K.

An important reason for miscalculating IOL power in short and long eyes has been noted to be due to the incorrect prediction of the postoperative ELP [3]. Therefore, apart from only the use of AL and K, additional parameters such as measurement of anterior chamber depth (ACD), lens thickness (LT), lens factor (LF), and white-to-white (WTW) distance were included in the fourth (Haigis, Holladay 2 and Olsen) and new (Barret Universal II, Hill-RBF) generation formulas for estimating the postoperative ELP [4, 5]. Although several studies have demonstrated insignificant difference between Haigis, Holladay 2, Hoffer Q, Holladay 1, SRK/T and SRK II for the calculation of accurate IOL power in short eyes [68], in the study of Macleran et al., Haigis was determined to be more accurate than Hoffer Q [9], while Gavin et al. have suggested that Hoffer Q yielded better results than SRK-T [10].

Aristodemou et al. have suggested in their comperehensive study that Hoffer Q has a good performance in IOL calculation for ALs from 20 to 20.99 mm, and also along with Holladay 1, from 21 to 21.49 mm [11]. However, in the literature, there is less investigation about the efficacy of new generation IOL calculation formulas, especially Barret Universal II, for the short eyes [3, 12].

In the present study, it was aimed to compare the effectiveness of IOL calculation formulas between third and fourth generation formulas like SRK-T, Hoffer Q, Holladay 2, Haigis and new generation formulas such as Barret Universal II, and Hill-RBF in short eyes.


After the institutional review board of Canakkale University approved the study protocol, this retrospective clinical study was carried out by examining the medical records of the patients who experienced a cataract surgery between 2014 and 2018 years. The patients with AL lower than 22 millimeters who underwent an uneventful cataract surgery with same type of monofocal IOL implantation (Acriva UD 613®, VSY Biotechnology, Turkey) were included in this study. Another inclusion criteria for this study were the availability of the measurement of IOL power obtained by only using OLCR (Lenstar LS-900, Haag-Streit AG, Koeniz, Switzerland), and the determination of postoperative best corrected visual acuity level ≥ 20/40 in the first month visit. The patients with a history of traumatic cataract, previous refractive surgery, and retinal detachment, as well as the ones with keratoconus, corneal scarring, corneal dystrophy, macular oedema, complicated cataract surgery, and also the patients who had not come to first month visit were excluded from the present study.

All patients were subjected to detailed ophthalmic examination with a slit-lamp biomicroscopy during the pre- and postoperative period. The AL and K values, and ACD measurements were obtained by OLCR. The phacoemulsification surgery was performed with 2.8 mm clear-corneal insicion, 5.0-5.5 mm capsulorrhexis diameter, and in the bag implanted IOL. None of the corneal insicion was needed suture. The characteristics of the implanted IOL are as follows; a monofocal lens with a plate haptic design, the optical diameter is 6.0 mm, total diameter is 13.0 mm, the haptic-optic angle is 0 degree, refractive index is 1.46. In previous studies, since all formulas were not registered in one device, calculation of new generation formulas were made from the websites. The optimization values of the Acriva UD 613 can be also found in ULIB website [(A constant = 118.0), (Haigis a0 = 0.95, a1 = 0.40, a2 = 0.10), (Hoffer Q pACD = 5.19), Holladay 1 (sf = 1.43), and (A constant for SRK/T = 118.4)]. Lenstar LS-900 contains software of the IOL calculation formulas that were included in this study and all formulas were preinstalled on this biometer. Therefore, no additional calculation from the websites was used in the current study.

A total of six formulas, Holladay 2, Hoffer Q, SRK/T, Haigis and the Hill-RBF- an artificial intelligence based radial base function method were compared with Barett Universal II. In terms of number of containing the IOL calculation variable, formulas are as follows; Hoffer Q and SRK/T formulas have 2 variables [K and AL values], Haigis formula has 3 variables [ACD in addition to K and AL]. Barrett Universal II formula has 5 variables [AL, K, ACD, WTW, and LT]. Holladay 2 formula has 7 parameters [K, AL, ACD, LT, WTW, preoperative refraction and patient age].

In order to reduce the problems owing to IOL constant optimisation, as the study of Carifi et al. [13], only the subjects with same type of monofocal IOL (Acriva UD 613®, VSY Biotechnology, Turkey) were included in this study.

The refractive prediction error, namely, the MAE and also the MedAE values were calculated by substracting the postoperative spherical equivalent (SE) value from the estimated error value for each formula. The MAE values were used as the main data for the comparison of the accuracy of formulas. For each formula, the benchmarks as ± 0.25 D, ± 0.50 D, and ± 0.75 D were calculated. The subjective refraction was performed at the first month visit. The SE value was calculated by adding the half of the cylindirical power to the spherical power.

Statistical Analysis

For statistical analysis, Statistical Package for the Social Sciences and Social (Version 21.0, SPSS, Inc.) program was used. Friedman test was applied for the comparison among the groups. Bonferroni correction was implemented for multiple comparisons, and the statistically significance was accepted as a p value of less than 0.01 after Bonferroni correction.


In total, 137 eyes of 122 patients were included in this study. Fifteen patients were operated on two eyes and a randomly selected eye was included in the study. The mean age of the patients was 66.5 ± 5.7 (min: 55, max: 81) years. Forty-three patients were female (35%) and 79 were male (65%). The mean AL was 21.38 ± 0.53 (min: 20.03, max: 21.98, median: 21.59) mm. The mean IOL power was 26.4 ± 2.2 (min: 23.5, max: 32.5) D. The data ​​related to the refractive values ​​are given in Table-1.

The MAE values were 0.390 for Hoffer Q, 0.390 for SRK-T, 0.324 for Haigis, 0.327 for Holladay 2, 0.331 for Hill-RBF, and 0.208 for Barrett Universal II. Also the rank of MedAE values for the mentioned formulas was repectively as 0.245, 0.310, 0.310, 0.250, 0.255 and 0.190. The lowest MAE and MedAE value was found in Barrett Universal II, while the highest value was in the SRK/T formula. All MAE and MedAE values ​​are given as minimum, maximum and standard deviations in Table-2. Although there were a statistically significant difference between Barret Universal II and SRK/T formula (p < 0.001), after Bonferroni correction, no statistically significant difference was determined between Barret Universal II and the other formulas in terms of MAE value (p > 0.01). Also statistically insignificant difference was found between the other formulas other than Barret Universal II formula (p > 0.01).

While the mean, and the median of preoperative SE values were respectively as + 4.47 D and + 4.38 D, their postoperative values were − 0.16 D and − 0.25 D, respectively. Three patients (2.5%) were in +/- 0.75 D range, 15 patients (12.3%) in +/- 0.50 D, and the remaining 104 patients (85.2%) were in +/- 0.25 D in the first month visit. All patients were in the benchmark of 1.00 D suggested by Gale et al. [14].


Unlike the ones with long and normal AL, the IOL power calculation can sometimes be difficult in patients with short eye. This condition is mostly attributed to incorrect estimation of postoperative effective lens position (ELP) that is defined as the distance between secondary principle plane of the cornea and the principle of the IOL [15]. The minimal deviation in the ELP is said to cause a considerable error in postoperative refraction particularly in patients with short eyes, likely due to the implantation of thicker IOLs [9]. A potential risk of myopia may occur if the IOL is even minimally more anteriorly located than the expected, while hyperopic shift can emerge in case of its posterior location. Olsen et al. have put in order the important sources of error for IOL power calculation as incorrect measurements of AL (%54), ACD(38%), and corneal power (8%) [4]. However, Olsen reported in his another study that the most of the faults in IOL power calculations might be related to the underestimation of ACD rather than AL [2]. One milimeter error in the measurement of ACD results in approximately 1 D, 1.5 D, and 2.5 D postoperative refractive error in myopic, emetropic, and hyperopic eyes respectively [16]. Also, each 0.1 mm error in the AL measurement results in nearly 0.27 D deviation in the optical plane [2]. Therefore, the correct estimation of postoperative ACD becomes as important as AL measurement especially in patients with short eyes.

The refractive surprises encountered owing to the incorrect measurement of AL have been substantially resolved with the use of non-contact biometry devices such as OLCR. When taking into consideration the fact that measurement error in short eyes causes 5 times more refractive error than myopia [2], the resolution of problems in AL measurement with the use of non-contact biometry has improved the refractive outcomes particularly in these subjects. Another important benefit of non-contact biometry is their providing correct measurement of ACD. The factors effecting the ELP are classified firstly as anatomic causes such as K value, AL, white-to-white distance, preoperative ACD and lens thickness (LT), and secondly as the IOL related causes such as shape, length, elasticity, angle, and haptic material of the IOL. As it is known that members of third generation formulas like SRK/T, Holladay I and Hoffer Q respectively use A constant (differs its value depending on the manifacturer and type of the IOL, and also its position inside the eye ), surgeon factor (SF), and postoperative ACD for the estimation of ELP. However, different from the third generation, fourth generation formulas involving Haigis formula (a0, a1, a2 constants), Holladay II formula (AL, K, ACD, LT, W-to-w, preoperative refractive error, and age) and Olsen formula (AL, K, white-to-white, LT and ACD) use additional variables besides the measurement of preoperative ACD for strengthen the estimation of ELP.

Several studies comparing the accuracy of IOL power calculation between third, fourth and newer generation formulas (Barrret Universal II, Hill-RBF) either in patients with various AL, or in patients with short eyes can be found in the literature. According to these studies, almost all of the IOL calculation formulas have been suggested to yield favoruable refractive outcomes in avarage ALs. However, some IOL power calculation formulas have become more preferable in patients with short AL because of their success in the reduction of refractive surprises. Narvaez et al. have reported equal refractive results when compared the effectiveness of Hoffer Q, Holladay 1, Holladay 2 and SRK/T formulas in short, medium and long eyes [17]. Karabela et al. have obtained good outcomes in both short and long eyes by using SRK/T formula [18]. In contrast to these studies, Aristodemou et al. have demonstrated the superiority of SRK/T and Hoffer Q in eyes with AL greater than 26 mm, and less than 21.5 mm respectively in their comprehensive study [11]. However, either the study of MacLaren et al. or the study of Wang et al. have revealed that Haigis formula can yield more accurate postoperative refractive results than Hoffer Q, SRK/T and Holladay 1 in short eyes [9, 19]. Although, Haigis formula was also found to obtain more accurate results than Hoffer Q, SRK/T and SRK II for shorter eyes in a meta analysis of Wang et al. [15], Roh et al. reported the insignificant difference between Haigis and Hoffer Q formulas [20]. Since both Hoffer Q and Haigis formulas involve the preoperative ACD measurement, their improved accuracy in shorter eyes may stem from increased true estimation of ELP. Olsen has defined an equation containing preoperative ACD, preoperative LT and “C constant” for the presice prediction of postoperative IOL position [21]. On the other hand, a new generation formula that is a mathematical approach, Hill-RBF does not use vergence formula and ELP separately for IOL power calculation. This formula makes calculation with using ACD, AL, K and a special software that is preinstilled in OLCR (Lenstar, Haag-Streit) device.

Despite Gokce et al. have suggested smilar results between Barrett Universal II, Haigis, Hill-RBF, Hoffer Q, Holladay 1, Holladay 2, and Olsen formulas in 86 patients with AL equal to or less than 22 mm, the highest MAE value was determined in Haigis formula followed by Olsen formula in their study [3]. In consistent with this study, besides the superiority of Barret Universal II formula on SRK/T, Hoffer Q and Hill-RBF formulas, it was also found insignificant difference in terms of MAE value between some third, fourth and new generation formulas in short eyes in the current study. Because in the present study, all formulas except SRK/T contains of ACD variable for IOL power calculation, the highest MAE value due to the SRK/T formula might have been arisen from decreased prediction of ELP. In the current study, the second highest MAE values followed by SRK/T formula were detected in Hoffer Q and Hill-RBF formulas. The reason for the higher MAE value in these formulas may be result of reduction in the prediction of ELP, because Hill-RBF uses ELP estimation separetly, and different from Hoffer Q formula, fourth and newer generation formulas involve more variables to strenghten the precise prediction of ELP apart from using ACD, such as Haigis formula contains a0, a1 and a2 constants.

Although in contrast to the present study, Kane et al. have revealed lower MAE value by using Hill-RBF formula in comparison to Barret Universal II formula in shorter eyes, in consistent with the result of the current study, none of the new generation formula was shown to yield more accurate postoperative refractive outcome than Barret Universal II formula, or the best third generation formulas in the same study [22].

In Olsen formula two different software, OlsenStandalone, and OlsenOLCR have been suggested to give distinct outcomes [23]. In the present study, Olsen formula could not be included into the comparison, because of the lack of information about its version instilled in biometry device, namely, it was not known whether OlsenStandalone, or OlsenOLCR software, and it is considered as the major limitation of the present study.


It is thought that depite the superiority of Barret Universal II formula on the estimation of accurate refractive outcome in shorter eyes, other generation IOL power calculation formulas can also yield satisfactory results for these patients in case of unavaibility of software of new generation formulas in biometry device.


ACD: anterior chamber depth,  AL: axial length, ELP: effective lens position, IOL: intraocular lens, K: keratometry, MAE: mean absolute error, MedAE: median absolute error, LF: lens factor, LT: lens thickness,  OLCR:  optical low coherence reflectometry, SE: spherical equivalent, ULIB: user group for laser interference biometry, WTW: white to white.





No funding was obtained for this study

Availability of data and materials

The data information for this study was reported in the article.

Authors’ contributions

The design, conception and conduct of the study (AY), literature screening and selection (SA), data collection (AY), management (AY), acquisition of data or performing statistical analysis and interpretation of the data (AY, SA), preparation and review (AY, SA). All authors read and approved the final manuscript.

Competing interests

The authors declare that they have no competing interests.

Consent for publication

Not applicable.

Ethics and consent to participate

The institutional review board of Canakkale University approved the study protocol (desicion date: 02.01.2019, desicion number: 2019-11). All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.


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   Refractive Outcome

















Mean  ±SD

-6.45  ± 2.7

-0.42  ± 0.78

-6.76 ± 2.75

-0.27 ± 0.31

-0.65 ± 0.66

-0.51 ± 0.21


-1.75 to-17.00

-2.00 to +2.50

-1.38 to-17.00 


-0.25 to-1.25  

-2.00 to 2.00 

0.12 to -1.00  


           Table-1: SD: Spherical diopter, SE: Spherical equivalent, CD: Cylindirical diopter, 

           Min: Minimum, Max: Maximum, SD: Standard Deviation           


                                                               Prediction values in all formula


Hoffer Q








0.331 ±0.2

0.39 ± 0.3


0.327 ±0.3

 0.331 ±0.3

0.208  ± 0.165








   MedAE                   0.245             0.310           0.310             0.250           0.255           0.190



Table-2: MAE: Mean absolute error,   MedAE: Median of Absolute Error.