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Peer Review | Mar/Apr '18

Battle of the Calculators

Transitioning to modern-day IOL formulas.

Accurate IOL power calculation can be a source of frustration for ophthalmic surgeons. The formulas used are complex, and there is an ongoing debate about which formulas provide the best refractive predictions, especially when the patient’s axial length and keratometry measurements fall on the outer limits of the Gaussian curve. There is general consensus among practicing surgeons that the newer-generation formulas out-perform their older counterparts. At least two recent studies agree that the Barrett Universal II has the lowest predictive error of the traditional formulas.1,2

Historically, one of the greatest sources of frustration for surgeons has been predicting refractive outcomes in short eyes. In 2011, Aristodemou et al3 found that the Hoffer Q was the most accurate formula for axial lengths less than 21 mm. Many surgeons have used this finding to help guide their lens choice in hyperopic patients for the past several years.

However, a new study by Melles et al1 published early this year found that the Barrett Universal II formula provided far more accurate predictions than Haigis, Holladay 1, Holladay 2, Olsen, SRK/T, and even Hoffer Q in eyes with short axial lengths. In fact, in eyes with an axial length less than 22.5 mm, the Barrett had the lowest mean absolute prediction error, and the Hoffer Q had the greatest. Notably, all seven formulas included in this study provided results within 0.10 D of predicted spherical equivalent when applied to eyes with “normal” (23 to 25 mm) axial lengths.

When applied outside this range, each formula had its own downfalls tied to varying biometrics. The ray-tracing Olsen formula had the lowest mean absolute predictive error, and the Holladay 1 and Hoffer Q had the greatest when applied to long eyes. The SRK/T was especially affected by both flat and steep keratometry. The Hoffer Q and Olsen formulas showed significant bias with varying anterior chamber depth, whereas the Haigis showed little deviation. Last, the Haigis was uniquely affected by variation in lens thickness. Overall, the Barrett Universal II had the least bias and error across a range of axial lengths and biometrics.

Traditionally, formulas used to calculate IOL power are based on complex mathematics and optics that fall into two categories: (1) vergence and (2) ray tracing. All of the formulas discussed above, including the Barrett Universal II, are vergence formulas that use up to seven different variables to enhance their accuracy. The Olsen and lesser-known Okulix (Tedics Peric & Jöher) are ray-tracing formulas.


The newest calculator in use, the Hill-RBF, employs a completely different approach to IOL power calculation: artificial intelligence. Developed by Warren E. Hill, MD, the Hill-RBF algorithm (not a true formula) is based off data gathered from more than 12,000 eyes (as of March 2018). The algorithm will continue to gain accuracy as more data are added. Artificial intelligence is unique in that it “learns” through an internal validation process, creating a self-validating algorithm.4 Therefore, further data will lead to improved IOL prediction accuracy.

This foundation allows for a unique feature in that the algorithm provides an indication of the accuracy for any given calculation, notifying the surgeon when the answer provided is “out of bounds” for the knowledge base of the formula. This provides a unique paradigm for IOL power calculation and is the first model to inform the user of its accuracy. Importantly, like the Barrett Universal II formula, early data suggest that the Hill-RBF works equally well for short, average, and long eyes.5


Armed with modern IOL calculation methods such as the Barrett Universal II and Hill-RBF, ophthalmic surgeons are uniquely posed to achieve better refractive outcomes for their patients than ever before.

1. Melles RB, Holladay JT, Chang WJ. Accuracy of intraocular lens calculation formula. Ophthalmology. 2018;125(2):169-178.

2. Kane JX, Van Heerden A, Atik A, Petsoglou C. Intraocular lens power formula accuracy: comparison of 7 formulas. J Cataract Refract Surg. 2016;42(10)1490-1500.

3. Aristodemou P, Knox Cartwright NE, Sparrow JM, Johnston RL. Formula choice: Hoffer Q, Holladay 1 or SRK/T and refractive outcomes in 8108 eyes after cataract surgery with biometry by partial coherence interferometry. J Cataract Refractive Surg. 2011;37:63-71.

4. Kent C. IOL formulas: 10 questions answered. Rev Ophthalmol. 2018;XXV(1):16-28.

5. Hill WE. IOL power selection by pattern recognition. Cataract & Refractive Surgery Today Europe. November/December 2016.

Susannah L. Brown, MD
  • Resident, Storm Eye Institute, Medical University of South Carolina, Charleston
  • slbrown@musc.edu
  • Financial disclosure: None
Karolinne M. Rocha, MD, PhD | Section Editor
  • Director of Cornea and Refractive Surgery and Assistant Professor of Ophthalmology, Storm Eye Institute, Medical University of South Carolina, Charleston
  • karolinnemaia@gmail.com; Twitter @karolinnemr
  • Financial disclosure: None