Understanding Modern IOL Power Calculation Formulas Haigis, Barrett, EVO and Kane Explained
- Sep 4, 2025
- 13 min read
In this article I will explain how the different IOL calculation formulas like Haigis, Barrett universal II, Kane, EVO and Olsen formula work.
To begin with, if you ask that what is the difference between the older generation IOL calculation formulas like SRK T or Holladay I, Haigis, and the current generation modern formulas, the first thing that comes to mind is the difference of IOL power calculation by thin and thick optics.
What is thin and thick optics formula? This is explained in detail in the article, Gaussian optics, Gullstrand eye, & Biometry ( https://www.quickguide.org/post/all-about-gaussian-optics-gullstrand-eye-theoretical-and-ray-tracing-formula ). Basically, a thin lens is such that its thickness is so negligible that all refraction is considered to happen only at one plane. However, no lens, be it IOL or any other, will have some finite thickness. A thick lens formula considers the lens optic to have separate pairs of refracting plane - one anterior and the other posterior refracting plane.
The first principal plane is where light rays appear to refract as they enter the lens or system from the object side.
The second principal plane is where rays appear to emerge after they have refracted through the system and exit towards the image side.
Older two variable formulas like the Holladay I, SRK T, or the Hoffer Q have calculated the IOL power and ELP of the IOL based on thin lens optics. The new generation formulas like the Barrett, EVO or Kane are however based on the thick optics approximation. In such formulas, both IOL power and ELP are based on the two refracting planes.
Here you can access a calculator that helps you understand IOL power based on thick lens formula. https://sheet.zoho.com/sheet/open/oxim98090819123a94bd99435f9a6bc62eed2?sheetid=0&range=F15
Let us know how these individual formulas are different from each other. Let us start with the modern thick lens IOL calculation formulas.
This is how Barrett Universal II formula work:
The Barrett is an unpublished formula. However, I have given a brief explanation of the formula in the below video:
https://www.youtube.com/watch?v=1JDDL1la0Gw ( click to link)
In brief, the Barrett Universal formula being based on thick lens formula, determines the principal planes of refraction through input variables like corneal power (K readings), axial length (AL), horizontal white to white (HWTW), anterior chamber depth (ACD). It uses Lens Factor (LF) to determine the final principal planes of refraction and thus the ELP of the IOL. The LF is the distance from the iris plane to the second principal plane of the IOL. The LF however is mostly influenced by the anatomical pre surgery ACD and the A constant of the IOL. For this a relationship between the A constant of IOL and the Lens Factor was derived.
Thus Barrett Universal formula is based on paraxial rays (rays that travel close to the optical axis of the lens) and is based on thick lens mathematical calculation.
The Barrett Universal formula is a theoretical formula that divides the entire eye globe into two spheres, the anterior and posterior spheres. The interaction of the two spheres is based on the patient data you input (AL, K, LT ,etc.) which would determine the position of the ciliary root, which in turn will determine the lens position through the Lens Factor or LF.
The Barrett Toric Calculator provides an option to enter measured posterior cornea values. If you have values of posterior cornea then you may select the appropriate biometry/topography device from the drop down menu and input only posterior corneal values (see image1). For IOL Master 700 TK, only PK1 and PK2 values to be input. If you are working for post lasik patients, then Barrett True K should be used for determining IOL power. In this case also, you may enter the measured posterior cornea power in the same way.
This is how Emmetropia Verifying Optical (EVO) formula work:
The brain behind this formula is Dr Tun Kuan Yeo, a doctor based out of Singapore. When the formula was conceived in 2015, a lot of attention was being given to posterior corneal astigmatism (PCA), and Dr Douglas Koch and his team's work that showed that the risk of not considering the PCA was under correcting against-the-rule astigmatism or over correcting with-the-rule astigmatism. While Douglas Koch's findings published in 2011 came at a time when not many devices measured PCA, yet there was the promise that biometry and IOL power prediction would take a leapfrog with a IOL calculation formula that would take measured PCA into account once such measurement was available.
The EVO formula was launched in 2016 that took into account axial length, corneal power, anterior chamber depth, lens thickness, horizontal white to white. In 2019 the EVO next version was launched that provided post Lasik IOL power calculation. In the advanced options, notice you can input the measured posterior corneal values and choose from the drop down menu the device used to measure. Do not enter IOL Master TK values in place of measured posterior cornea but only the posterior corneal values from the IOL Master 700. In the 2019 version, you can enter the central corneal thickness (CCT) values to help determine the ELP of the IOL more precisely.
Like the Barrett, EVO is a thick lens formula based on Gaussian optics (refer to my article Gaussian optics, Gullstrand eye, & Biometry ( https://www.quickguide.org/post/all-about-gaussian-optics-gullstrand-eye-theoretical-and-ray-tracing-formula ) for more details on Gaussian optics. As indicated in the article, Gaussian optics is based on paraxial rays only, and it does not take into account the spherical aberration associated with marginal rays. Unlike Olsen formula, both EVO and Barrett are theoretical paraxial ray formula.
In Cooke Modified Axial Length or CMAL ( available at https://www.quickguide.org/post/cooke-modified-axial-length-cmal ) I had provided an idea how CMAL uses sum of segments to convert axial length with group refractive index to an axial length based on actual refractive index of each of the mediums of eye. The CMAL axial length is the distance from the cornea to the retinal pigment epithelium (RPE). The concept of sum of segment based axial length (example Argos) as opposed to group refractive index based axial length ( IOL Master or Lenstar) is explained in the article Optical Biometry- Myth & Science ( https://www.quickguide.org/post/optical-biometry-myth-science ).
In image 3 (above) the axial length (27 mm) has been derived from an optical biometry machine that is based on group refractive index. The converted CMAL axial length that mimics axial length measured with segmented refractive index is 26.87 mm. You may be thinking what would be the importance of this conversion. Studies by Koch and others have shown that axial length measured in myopes may overestimate the length of the vitreous chamber if based on group refractive index, thus leading to a hyperopic surprise.
