Intraocular Lens (IOL) Power Calculation - Generations of Formulas

Background: What All Formulas Must Calculate

P = (1336 / [AL - ELP]) - (1336 / [1336/{1000/([1000/DPostRx] - V) + K} - ELP])

First Generation (1967 - late 1970s)

• Based on theoretical/geometric optics applied to the schematic eye
• Used fixed constants for ELP - it was assumed the same for all eyes
• Fyodorov's formula was the first to use keratometry and axial length
• In 1980, Sanders, Retzlaff, and Kraff published the landmark SRK regression formula:

P = A - 2.5L - 0.9K

• P = IOL power (D), A = lens-specific A-constant, L = axial length (mm), K = mean keratometry (D)
• First formula to introduce the lens-specific A-constant, accounting for IOL design and position
• Major limitation: used a fixed ELP for all eyes - inaccurate in short or long eyes

Second Generation (early 1980s)

• Recognized that the first-generation fixed ELP was the main source of error in extreme axial lengths
• SRK II added a correction factor (C-value) to the original SRK based on axial length:

P = A - 2.5L - 0.9K + C

• Still fundamentally a regression formula with limited anatomical basis
• Improved accuracy for outlier eyes but remained imprecise

Third Generation (late 1980s - 1990s)

SRK/T

• Hybrid: regression-derived constants combined with theoretical optics
• Optimizes ACD using a regression-derived formula incorporating AL and K
• Best for long eyes (AL >26 mm)

Holladay 1

• Divided ACD into: corneal thickness + endothelium-to-iris distance + iris-to-lens distance
• Introduced the Surgeon Factor (SF) - the distance from iris plane to IOL principal plane
• SF requires optimization per surgeon/lens combination

Hoffer Q

• Used a personalized ACD incorporating AL
• Particularly accurate in short eyes (AL <22 mm)
• Introduced a tangent function for the AL-ACD relationship

• Short eyes (<22 mm): Hoffer Q
• Normal eyes (22-26 mm): all three comparable
• Long eyes (>26 mm): SRK/T

Fourth Generation (1990s - 2010s)

Haigis Formula

• Replaced keratometry-derived ELP prediction with measured preoperative ACD
• Uses three constants (a0, a1, a2) that can all be individually optimized:
  • a0: shifts the prediction curve up/down
  • a1: weights the measured ACD
  • a2: weights the axial length
• Particularly useful when K is unreliable (e.g., post-LASIK corneas)

Holladay 2

• Uses 7 variables: AL, keratometry, ACD, white-to-white (WTW), lens thickness (LT), preoperative refraction, and patient age
• Most comprehensive formula of its era
• Requires the Holladay IOL Consultant software

Barrett Universal II

• Incorporates ACD plus a theoretical model of the lens
• Performs well across all AL ranges
• Widely considered one of the most accurate formulas currently in routine use
• Freely available online; now a benchmark comparator

Fifth Generation / AI & Machine Learning Era (2010s - present)

Hill-RBF (Radial Basis Function)

• Pure machine learning trained on thousands of postoperative outcomes
• Uses AL, K, ACD, and lens thickness
• Works within a "confidence interval" - flags cases outside its training data range

Kane Formula

• Combines theoretical optics with regression and AI elements
• Inputs: AL, K, ACD, LT, white-to-white, sex
• Multiple studies show it matches or outperforms Barrett Universal II
• Particularly effective in extreme AL eyes and post-refractive surgery cases

PEARL-DGS

• Neural network trained on a large European dataset
• Uses AL, K, ACD, LT, WTW, age, and sex

EVO Formula (Emmetropia Verifying Optical)

• Ray-tracing based, freely available online
• Strong performance for normal and extreme eyes

Summary Table

Special Situations

• Double-K method
• Masket formula
• Barrett True K
• ASCRS online calculator (consensus approach)

Key Concept: Constant Optimization