# Formulas for IOL Power Calculation

Which modern intraocular lens (IOL) calculation formula gives the best results for prediction of the effective lens position (ELP) is a widely debated topic. In this section you'll find an overview of the latest generation of formulas for rotationally symmetrical IOL designs (post-laser vision correction eyes are excluded) with their philosophy explained in a nutshell. Furthermore the parameters of each formula used for the ELP prediction are listed as well as recommendations of formulas for different eye types according to various sources.

### Barrett

The Barrett Universal 2 formula uses a theoretical model eye in which anterior chamber depth (ACD) is related to axial length (AL) and keratometry. A relationship between the A-constant and a "lens factor" is also used to determine ACD.^{1} The important difference between the Barrett formula and other formulas is that the location of the principle plane of refraction of the IOL is retained as a relevant variable in the formula.

AL, corneal power, ACD (optional), lens thickness (optional), white-to-white corneal diameter (optional).

The Barrett formula is recommended for short – long eyes.^{2}

### Haigis

The Haigis formula recommends an IOL power based on a three-variable (a_{0}, a_{1} and a_{2}) function. The a_{1} constant is tied to the measured ACD, while the a_{2} constant is tied to the measured AL. This allows all three constants to be optimized for a wide range of ALs and ACDs using double-regression analysis.

These are AL and ACD.

Haigis (a_{0} optimized only): normal eyes^{2}

_{0}, a

_{1}, a

_{2 }optimized): short – long eyes

^{2,}*

### Hoffer Q

The Hoffer Q formula relies on a personalized ACD, AL and corneal curvature. The personalized ACD (pACD) is developed from any given series of a particular IOL style. It includes (1) a factor that increases the ACD with increasing AL, (2) a factor that increases the ACD with increasing corneal curvature, (3) a factor that moderates the change in ACD for extremely long and short eyes, and (4) a constant added to the ACD.^{3}

These are AL and corneal power.

The Hoffer Q formula should be used for eyes measuring < 22 mm, according to the Royal Collage of Ophthalmology guidelines.^{4}

### Holladay 1

The Holladay 1 formula uses the postoperative stabilized refraction value, the dioptric power of the implanted IOL, and the preoperative corneal and AL measurements to calculate a personalized surgeon factor. Thus, the surgeon factor is defined as the distance from the post-operative anterior iris plane to the effective optical plane of the IOL. As with other constants the surgeon factor is not actually a measurement, but a number representing a particular surgeon's previous experience.^{5}

These are AL and corneal power.

The Holladay 1 is recommended for eyes measuring between 24.6 mm – 26.0 mm.^{4}

### Holladay 2

The Holladay 2 formula is conceptually based on the Holladay 1 formula; however it uses seven parameters for predicting the surgeon factor. These are the AL, corneal power, ACD, lens thickness, age, white-to-white corneal diameter and pre-operative refraction data. How the formula works in detail has not yet been revealed by Jack Holladay.

These are AL, corneal power, ACD, lens thickness (optional), age (optional), white to-white corneal diameter (optional), pre-operative refraction data (optional).

The Holladay 2 formula is recommended for short – long* eyes.^{2}

*W-K adjustment has been shown to extend the usage from "short – normal eyes" to "short – long eyes" for meniscus IOLs designs in the low plus to minus power range.^{6}

### SRK/T

The SRK/T formula is a theoretical (T) approach to IOL power calculation under the SRK umbrella of empirical formulas using existing A-constants and optimization methods. Empirical optimization methods of the SRK/T model primarily consist of (1) postoperative ACD prediction, (2), a retina thickness correction factor and (3) corneal refractive index.^{7}

These are AL and corneal power.

The SRK/T formula should be used for eyes > 26 mm. A combination of Hoffer Q, Holladay 1, and SRK/T should be used for eyes 22.0–24.5 mm.^{4}

### SRK I and SRK II

The SRK I and SRK II formulas are obsolete and should no longer be used.^{8}

- An improved universal theoretical formula for intraocular lens power prediction. Barrett GD. J Cataract Refract Surg. 1993 Nov;19(6):713-20.
- IOL Power Calculations Which Formula? http://www.doctor-hill.com/iol-main/formulas.htm.
- The Hoff er Q f ormula: A comparison of theoretic and regression f ormulas Kenneth J. Hoffer, M.D. J CATARACT REFRACT SURG-VOL 19, NOVEMBER 1993.
- The Royal College of Ophthalmologists Cataract Surgery Guidelines September 2010 Scientific Department The Royal College of Ophthalmologists. https://www.rcophth.ac.uk/wp-content/uploads/2014/12/2010-SCI-069-Cataract-Surgery-Guidelines-2010-SEPTEMBER-2010.pdf
- A three-part system for refining intraocular lens power calculations Jack T. Holladay, M. D. Thomas C. Prager, Ph.D. Thomas Y. Chandler, M. D. Kathryn H. Musgrove, M.D. John W. Lewis, M.D. Richard S. Ruiz, M.D. J CATARACT REFRACT SURG-VOL 14, JANUARY 1988.
- Optimizing intraocular lens power calculations in eyes with axial lengths above 25.0 mm Li Wang, MD, PhD, Mariko Shirayama, MD, Xingxuan Jack Ma, Thomas Kohnen, MD, PhD, FEBO, Douglas D. Koch, MD J Cataract Refract Surg 2011; 37:2018–2027
- Development of the SRK/T intraocular lens implant power calculation formula John A. Retzlaff, M.D., Donald R. Sanders, M.D., Ph.D., Manus C. Kraff, M.D. J CATARACT REFRACT SURG-VOL 16, MAY 1990.
- Nemeth J, Fekete O, Pesztenlehrer N. Optical and ultrasound measurement of axial length and anterior chamber depth for intraocular lens power calculation. J Cataract Refract Surg 2003; 29(1):85-8.

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