When planning cataract surgery, one of the most crucial stages for treatment success is choosing the correct intraocular lens (IOL) power.¹  To reach the targeted refraction, the selection must be performed according to the anatomical and optical parameters of the eye.²  In most cases, the target refraction is emmetropia but in some cases, depending on the specific needs and demands of the individual patient, other targets might be required, such as leaving some level of residual myopia in one eye (monovision).³  One of the most important parameters in IOL calculation, particularly in non-syndromic myopia, is axial length (AL). AL is a combination of anterior chamber depth (ACD), lens thickness and vitreous chamber depth and can change the IOL power by up to 2.5 to 3 times. [Meng 2011, Eyewiki] Corneal power is another important component of IOL power determination and keratometry (K) is the measurement of the corneal radius of curvature. The cornea is the transparent part of the eye that covers the iris, pupil and anterior chamber and it accounts for around two thirds of the eye's total optical power. Changes in corneal power can alter the IOL power in a ratio of nearly 1:1. As well as AL and K, other parameters that may be also required, depending on the type of formula used, are the preoperative ACD5  and the corneal white-to-white distance (WTW; also called the horizontal corneal diameter).⁶  The anterior chamber is the fluid-filled space between the iris and the innermost surface of the cornea and the WTW distance is the horizontal distance between the borders of the corneal limbus.

The only parameter that cannot be measured preoperatively is the position where the IOL "settles down" after surgery, which is also known as the effective lens position (ELP). Prediction of this parameter is initially performed by the IOL manufacturer in form of the A-constant. The A-constant is an empirical value and is specific to the design of the IOL. This constant is later refined by statistical optimizations that reflect the variance of the patient's particular preoperative biometry, and the surgeon's personal surgical technique is also taken into account. ELP is defined as the effective distance between the anterior surface of the cornea and the lens plane if the lens was infinitely thin.^4,5  The ELP is considered to be the main limiting factor for refractive predictability after cataract surgery, as the accuracy of AL and corneal power measurements has been widely  demonstrated.⁷  Improvements in IOL power calculations over the past 30 years are the result of improved predictability of the ELP variable.

Mathematical formulas have been developed for best estimation of the ELP, most of which are based on paraxial optics (Figure 1).^2,4  In these formulas, some ocular parameters are required and the surgeon should know the intended target refraction.^2,4

Many published and unpublished IOL formulas are available. The most frequently used formulas are based on two measurements, AL and K, as well as a single IOL constant⁸  (Holladay 1,⁹  SRK/T¹⁰  and Hoffer Q¹¹). Predictions of ACD, which increases relative to the increase of AL, are based on initial and generally large datasets from which the formulas have been derived; however individual ACD measurements were not included in the prediction model. The Haigis formula therefore uses three measurements, AL, K and pre-operative ACD with the three IOL constants a0, a1 and a2.¹²  Olsen's formula is based on two additional measurements - pre-operative refraction and lens thickness - and delivers one IOL constant whereas the Holladay 2 formula is based on seven measurements, including the patient's age and the horizontal WTW measurement.^1,5  Finally, the Barrett formula uses a theoretical model eye whereby ACD is related to AL and K, and is also determined by the relationship between the A-constant and a ‘lens factor'. The position of the principle plane of the IOL is kept as a relevant variable.¹³

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.