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IOL power calculation

TL;DR — The endpoint is prediction error: the difference between the refraction achieved and the refraction predicted for the lens actually implanted, reported as mean and median absolute error and as the percentage of eyes within ±0.25, ±0.50 and ±1.00 D. In normal eyes, modern formulas are close enough that meta-analyses rarely find statistically significant separation — in 15 studies of 2,395 short eyes, Barrett Universal II had the lowest MAE and MedAE (0.260 D) but no comparison reached significance (Shrivastava 2022, PMID 35225507). Differences emerge at the extremes and in atypical corneas. In long eyes (≥26 mm) Olsen, Kane and EVO ranked highest across 1,016 eyes (SUCRA 96.4%, 77.5%, 75.9% within ±0.25 D) though again without significance (Ma 2024, PMID 37726043); in short eyes (<22 mm) Kane, Haigis and Olsen Standalone led across 1,178 eyes (Zhang 2026, PMID 40971912). In keratoconus, Barrett True-K with measured posterior cornea ranked first on every metric (SUCRA 95–97%) and traditional formulas underperformed (Reitblat 2025, PMID 39626768). Two structural problems remain: the field's rankings are dominated by non-significant SUCRA orderings on small retrospective datasets, and a benchmark such as "71% within ±0.5 D" from a randomised trial is far below what formula papers imply (Day 2020, PMID 32386810).

The endpoint and how it is misreported

Prediction error (PE) = achieved postoperative spherical equivalent − predicted refraction for the implanted IOL. Standard reporting is mean PE (bias), mean and median absolute error (MAE, MedAE — accuracy) and the proportion within dioptric bands. Three reporting practices distort the literature:

  • Constant optimisation. Without optimisation, formulas differ mostly by systematic bias, not accuracy. In 139 post-myopic-LASIK eyes, PEARL-DGS gave mean PE +0.05 ± 0.65 D while all other formulas produced myopic shifts, with MedAEs of 0.39, 0.53, 0.65, 0.85 and 1.11 D for PEARL-DGS, Hoffer QST, Barrett True K, Shammas-PL and Haigis-L (Oh 2024, PMID 37914063). Zeroing the mean error changes rankings.
  • Ranking without significance. Network meta-analyses report SUCRA rankings even when all pairwise odds ratios exceed 1 with P > .05 (PMID 37726043; PMID 40971912). A ranking is not a difference.
  • Eye-level dependence. Both eyes of one person are correlated; paired-eye methods are required and often absent.

Real-world benchmarks anchor these numbers. In the 785-patient FACT randomised trial, 71% of eyes in both arms were within ±0.5 D of target and 92–93% within ±1.0 D (PMID 32386810). In 2,143 consecutive Japanese eyes across 12 centres, absolute error with SRK/T was significantly larger than with Barrett Universal II (P = 0.016) and SRK/T was significantly more hyperopic (Kamiya 2022, PMID 34108223). Refractive outcomes are the sum of many small error sources — the "error budget" framing (Khoramnia 2022, PMID 35204334).

Inputs and error propagation

Input Measurement Failure mode
Axial length Optical (partial coherence, swept-source OCT) or ultrasound Ultrasound compression; staphyloma; silicone oil; long-eye retinal-thickness offset
Keratometry / total keratometry Reflection-based K, Scheimpflug or OCT-derived posterior cornea Invalid after corneal refractive surgery; ocular surface disease distorts it
Anterior chamber depth, lens thickness, white-to-white SS-OCT biometry Feeds effective-lens-position prediction
Lens constants Manufacturer or user-optimised Un-optimised constants create systematic bias

Swept-source OCT biometers show excellent repeatability and reproducibility for keratometry, central corneal thickness, white-to-white, ACD, lens thickness, axial length and pupil diameter, but between-device agreement for some parameters is not sufficient to treat devices as interchangeable (Montés-Micó 2021, PMID 33315731). Between-centre variation in the inputs themselves is measurable: axial length (P = 0.003), ACD, lens thickness and central corneal thickness all differed significantly across 12 Japanese sites, while mean keratometry and corneal astigmatism did not (PMID 34108223). Optimising the ocular surface before measurement is part of the biometry, not a preliminary to it (Venkateswaran 2022, PMID 36211316; Narang 2024, PMID 37962881; Israni 2022, PMID 36018143).

Intraoperative aberrometry offers an alternative route that bypasses axial length and keratometry altogether: aphakic autorefraction was correlated with emmetropic IOL power to derive an empiric predictive model, validated in 10 standard and 6 post-LASIK cases (Ianchulev 2005, PMID 16129287). Ray-tracing methods use physical measurements and IOL manufacturing data without approximations, with prediction error close to zero and wider applicability, though heterogeneity of reported data limits comparison (Steiner 2013, PMID 23629771).

Formula generations

Vergence formulas (SRK/T, Hoffer Q, Holladay 1/2, Haigis) predict effective lens position from a small number of measurements. Newer approaches — Barrett Universal II, Olsen, Kane, EVO, PEARL-DGS, Hoffer QST, Castrop, VRF, Naeser 2, Ladas Super Formula — add more inputs, thick-lens optics, regression on large datasets, or machine learning. A structured review of 15 new or updated formulas concluded that Kane and Barrett Universal II performed better than others across the whole axial-length spectrum; Kane was most accurate in long eyes (>26.0 mm), and Kane and EVO 2.0 in short eyes (<22.0 mm) (Kothari 2023, PMID 35776680).

Artificial-intelligence formulas are now a distinct class. Hill-RBF 3.0 showed significantly lower MAE than Haigis (SMD −0.12, 95% CI −0.21 to −0.02; p = 0.01), Holladay 1 (−0.08, −0.15 to −0.01; p = 0.04) and SRK/T (−0.07, −0.14 to 0.00; p = 0.04), and higher odds of ±0.50 D versus Haigis (OR 1.09, 1.01–1.19), Hoffer Q (1.11, 1.04–1.19), Holladay 1 (1.10, 1.02–1.18) and SRK/T (1.08, 1.01–1.16), across 28 quantitatively analysed studies (Li 2026, PMID 41651446). In 2,430 highly myopic eyes, the top AI formulas by SUCRA were XGBoost, Hill-RBF and Kane, more accurate than SRK/T, Holladay 1, Holladay 2, Haigis and Hoffer Q, and ranking above Wang-Koch-modified and Barrett/Olsen formulas (Zhou 2023, PMID 38026369).

Axial-length extremes

Setting Evidence base Leading formulas Caveat Source
Short eyes (AL <22 mm) 15 studies, 1,178 eyes, 12 formulas, NMA Kane (SUCRA 95.74% within ±0.25 D), Haigis (94.79%), Olsen Standalone (84.04%); Kane and Olsen lowest MedAE All ORs vs Haigis >1 but P > .05; authors call for large multicentre registry verification Zhang 2026, PMID 40971912
Short eyes 15 studies, 2,395 eyes, 11 formulas Barrett Universal II lowest MAE and MedAE (0.260 D); Holladay 1 and Hill-RBF highest % within ±0.50 D and ±1.00 D No comparison statistically significant Shrivastava 2022, PMID 35225507
Short eyes 14 studies, 1,476 eyes, 13 formulas PEARL-DGS highest within ±0.25 D and ±0.50 D (significantly higher than Barrett II, Haigis, Hoffer Q, Holladay 1 and 2, Olsen); Okulix best within ±1.0 D Retrospective and prospective series pooled Luo 2022, PMID 35080690
Long eyes (AL ≥26 mm) 10 studies, 1,016 eyes, 11 formulas, NMA Olsen (SUCRA 96.4%), Kane (77.5%), EVO (75.9%) within ±0.25 D; H1-WK, H1-MWK and EVO best within ±1.00 D All ORs vs Barrett Universal II >1 but P > .05 Ma 2024, PMID 37726043
Long eyes (AL >24.5 mm) 11 studies, 4,047 eyes, 6 formulas Barrett Universal II MAE significantly lower than Holladay 2 Older formula set Wang 2018, PMID 29498180
Extremely long eyes (AL >28 mm) 11 studies, 1,376 eyes, 10 formulas Barrett II, EVO, Kane and Hill-RBF had significantly lower MAE than SRK/T — Li 2024, PMID 38252627
High myopia (AL >26 mm) 10 studies, NMA Kane and Holladay 1 with original Wang-Koch adjustment ranked top three at all thresholds; Hill-RBF 3.0, EVO, Barrett II also top three at some — Vilaltella 2026, PMID 42589896
Nanophthalmos (AL ≤20.5 mm) 14 eyes (0.06% of 22,847 operations), mean AL 20.13 ± 0.44 mm 79% within target refraction; 21% had ≥1 D myopic shift Tiny sample; illustrates the limits of formula evidence Lai 2024, PMID 39407912

Note the disagreement: three high-quality reviews of short eyes name three different leading formulas (Kane, Barrett Universal II, PEARL-DGS) (PMID 40971912; PMID 35225507; PMID 35080690). This is not a contradiction to be resolved by preferring one review; it is the signature of an effect too small relative to sample size and dataset heterogeneity.

Post-refractive and irregular corneas

Prior corneal refractive surgery invalidates the keratometric index assumption. Approaches divide into history-dependent (Barrett True-K History, Double-K) and no-history methods (Barrett True-K No History, Haigis-L, Shammas, EVO post-LASIK/PRK, PEARL-DGS), plus total keratometry, ray tracing and intraoperative aberrometry (Ting 2024, PMID 37962882).

Setting Result Source
Post-myopic LASIK/PRK, 302 eyes MAE ranking: Haigis-L 0.61 D, ASCRS average 0.63, Barrett True-K No History 0.67, EVO 2.0 0.68, Shammas 0.69; Haigis-L significantly lower than all others Lanza 2022, PMID 35858195
Post-myopic laser surgery, 139 eyes (mean AL 27.4 ± 2.1 mm) PEARL-DGS MedAE 0.39 D and mean PE +0.05 ± 0.65 D, others myopic-shifted Oh 2024, PMID 37914063
Post-hyperopic laser surgery, 107 eyes Shammas significantly less accurate than Barrett True-K No History and EVO 2.0 (p < 0.05) Boccia 2025, PMID 40142798
Radial keratotomy, 52 eyes Comparison of True K (History/Partial History/No History), Double-K Holladay 1, Potvin-Hill, Haigis, Haigis −0.50 D offset Turnbull 2020, PMID 31561878
Radial keratotomy, 674 eyes, 24 formulas, Bayesian NMA Within ±0.5 D: Barrett True-K History and Partial History better than Double-K Holladay 1; Shammas No History and Holladay 1 performed poorly; within ±1.0 D, Shammas No History and Barrett Universal II poor Guo 2026, PMID 40960597
Radial keratotomy, comparative series Barrett True-K and Hoffer QST had minimal bias (PE −0.06 D and −0.07 D, p > 0.05); PEARL-DGS most stable (SD 0.97) and best within ±0.25 D (20.8%) Li 2026, PMID 41704059
Keratoconus, 7 studies, 530 eyes, Bayesian NMA Barrett True-K Measured and Kane Keratoconus highest accuracy; Barrett True-K Predicted best in mild disease, SRK/T comparatively good in moderate disease; Hoffer Q and Holladay worst, especially in advanced disease Aljahdali 2026, PMID 42199326
Keratoconus, 9 studies, 623 eyes, 25 methods, NMA Barrett True-K with measured posterior cornea ranked first for % within ±0.50 D, ±1.00 D, mean PE and MAE (SUCRA 95%, 95%, 97%, 95%); by severity — EVO and BTK MPC in mild, BTK PPC and MPC in moderate, Kane KCN in severe Reitblat 2025, PMID 39626768
Keratoconus, toric and non-toric IOLs, 14 studies, 456 eyes Prediction errors reported by keratoconus stage I–III Yahalomi 2022, PMID 35566583
After deep anterior lamellar keratoplasty, 82 eyes Mean PE negative with all formulas; MedAE ranking SRK/T 0.805 D, Kane 0.810, EVO 0.845, Hoffer QST 0.847, Barrett 0.895 (Friedman P = 0.005) Pellegrini 2022, PMID 34845828
After vitrectomy with silicone oil tamponade, 7 studies, 1,060 eyes, 12 formulas Kane optimal within ±0.50 D; EVO best within ±1.00 D with Kane and RBF also high Zhao 2026, PMID 41785196
Primary angle-closure conditions, 6 studies, 419 eyes, 8 formulas Formula accuracy compared against SRK/T reference Lu 2022, PMID 36240196

Keratoconus deserves a specific caution: even with keratoconus-specific formulas, prediction errors remain higher than in normal eyes, and toric IOLs are effective only in carefully selected mild-to-moderate cases (Sarnicola 2026, PMID 41175387). The Bayesian rankings in this literature are explicitly labelled exploratory because of limited and heterogeneous data (PMID 42199326).

Paediatric eyes

Paediatric IOL calculation is a different problem: the eye grows, the target is deliberately hyperopic, and the achieved refraction must be judged against a moving endpoint. In IATS, targeting +8.0 D for infants 28–48 days and +6.0 D for those 49 days to <7 months using Holladay 1, mean absolute prediction error was 1.8 ± 1.3 D with mean PE +1.0 ± 2.0 D; 41% of eyes were within 1 D but 41% exceeded 2 D (VanderVeen 2012, PMID 22411658). A comparison of Hoffer Q, Holladay 1, Holladay 2, SRK II and SRK/T in 43 infantile eyes (mean AL 18.1 ± 1.1 mm) found no formula solving the problem (VanderVeen 2013, PMID 24011524). Pooled paediatric data are more favourable but still worse than adult performance: across 12 studies and 1,647 eyes, Holladay 1 had the smallest absolute prediction error (0.97, 95% CI 0.92–1.03); for AL <22 mm SRK/T beat SRK II (MD −0.37, −0.63 to −0.12) and for children <24 months SRK/T beat Hoffer Q (Zhong 2021, PMID 34901049). A 2024 review of 14 recent paediatric studies found Barrett Universal II most often best within ±1.0 D (Stopyra 2024, PMID 39124667). In 47 eyes of children with congenital cataract, mean PE was 0.67 ± 1.77 D and absolute PE 1.55 ± 1.06 D, with PE correlated to axial length (r = −0.29, P = 0.04) (AlObaisi 2024, PMID 39230787). See congenital and paediatric cataract.

Astigmatism

Residual astigmatism has its own prediction problem. With-the-rule and against-the-rule components can now be predicted reasonably well while oblique astigmatism remains problematic; total corneal astigmatism predicts residual astigmatism better than anterior corneal astigmatism alone, and vector decomposition is required to evaluate it properly (Kawahara 2022, PMID 36548932). Toric IOL selection is treated in intraocular lenses.

When calculation fails

Residual refractive error after otherwise successful surgery is managed by enhancement. LASIK is the most accurate procedure for correcting residual refractive error after cataract surgery; lens-based options (toric IOL rotation for excess residual cylinder, IOL exchange for dissatisfaction with multifocal optics or dislocation) are less predictable (Alio 2015, PMID 25321444).

Open questions

  • Do formula differences translate into patient-noticed differences? The literature ranks formulas on dioptric bands (PMID 37726043; PMID 40971912), but no study in this evidence set links a given improvement in % within ±0.5 D to a measurable change in spectacle dependence or a PROM score.
  • Can the extreme-eye question be settled? Three systematic reviews of short eyes name three different leading formulas with no significant pairwise differences (PMID 35225507; PMID 35080690; PMID 40971912), and the authors of the largest network meta-analyses explicitly call for large multicentre registry studies (PMID 40971912; PMID 37726043) — which as of 2026-08-31 had not been reported in the searches behind this page.
  • What minimum dataset makes formula studies comparable? Constant optimisation, device model, axial-length range and paired-eye handling all change rankings (PMID 37914063; PMID 33315731), yet no agreed reporting standard is in use across these reviews.
  • Are AI formulas generalisable? Hill-RBF 3.0 and XGBoost outperform vergence formulas in pooled analyses (PMID 41651446; PMID 38026369), but external validation in populations differing from the training data has not been reported here.
  • Is intraoperative aberrometry worth its cost? The principle is twenty years old (PMID 16129287) and it appears in post-refractive rankings (PMID 40960597), but no randomised comparison against best-available preoperative formulas with refractive endpoints was identified in this session's searches.

References

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