For educational and research purposes only. Not a medical device.
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IOL calculation formulas

A reference for every formula implemented in the calculator

The calculator implements the classic third-generation vergence formulas, the thick-lens PEARL-DGS, the proprietary APEX formula (spherical and toric modules), and a full set of post-refractive formulas.

Important notice

IOL Calculator is not a registered medical device. It is intended solely for educational and research purposes. All calculation results are for reference only and must be verified by the surgeon using certified instruments.

Standard formulas (third generation)

Classic formulas based on the vergence (thin-lens) optical model of the eye. They differ in how they predict ELP (effective lens position).

SRK/T

Retzlaff 1990
ELP via corneal height — regression of Cw on AL and K. The Retzlaff regression for AL > 24.2 mm corrects for long eyes. One of the most widely used formulas in the world.
AL: 20–30 mm

T2

Sheard 2010
A modification of SRK/T with a linear corneal height (no cusp effect). It removes the discontinuity at extreme K values, making the formula more stable.
AL: 20–30 mm

Hoffer Q

Hoffer 1993
ELP via pACD (ACD constant + AL, K). Traditionally considered best for short eyes (AL < 22 mm).
AL: 18–33 mm

Holladay 1

Holladay 1988
ELP via AG + Surgeon Factor. Wang-Koch correction for long eyes (AL > 26.5 mm).
AL: 20–30 mm

Haigis

Haigis 2000
The only standard formula that uses measured ACD. Triple regression: d = a0 + a1·ACD + a2·AL.
AL: 20–32 mm

Castrop

Langenbucher 2021
A thick-lens formula: ELP = ACD + C·LT + H. Models the cornea as a thick lens (Gullstrand). Three constants (C, H, R).
AL: 20–30 mm
Requires: LT

MIKOF

Takhchidi 2010
A Russian formula. ELP via corneal height + ADD_AC. Designed for IOL calculation across different axial-length ranges.
AL: 20–32 mm

Advanced formulas

Next-generation thick-lens formulas. All require a lens-thickness (LT) measurement.

APEX

Proprietary
A proprietary thick-lens formula for spherical IOL calculation. Works across the entire clinical axial-length range.
Requires: LT

PEARL-DGS

Debellemanière 2021
A four-surface thick-lens formula (JCRS 2021). Predicts the True Internal Lens Position from biometry.
Requires: LT

Post-refractive formulas

Formulas for IOL calculation after refractive surgery (LASIK, PRK, RK). Keratometry after refractive correction does not reflect the true corneal power.

APEX RK

Proprietary
A specialized formula for eyes after radial keratotomy. It accounts for the biomechanical features of the RK cornea and compensates for the long-term hyperopic shift (the PERK study). It activates automatically when the surgery type “Radial keratotomy” is selected in the post-refractive data.
No history
RK only

Haigis-L

Haigis 2008
Corneal-radius correction via regression. Works for myopic and hyperopic LASIK/PRK.
No history

Shammas-PL/PHL

Shammas 2007
Linear K correction: Kc = 1.14*K - 6.8. A simple no-history method.
No history

Shammas-Cooke

Shammas-Cooke 2024
K correction that includes AL: Kc = 0.9611*K - 0.2296*AL + 6.89. For post-myopic eyes only.
No history
Myopic only

WKM

Wang 2004
Wang-Koch-Maloney. K correction: Kc = 1.114*K - 5.59. For post-myopic eyes only.
No history
Myopic only

Clinical History + Double-K

Aramberri 2003
K_true from the clinical history. ELP from the pre-refractive K (Double-K method). The gold standard when a full history is available.
Requires history
K_pre, Rx_pre, Rx_post

Masket

Masket 2006
IOL power adjustment: adj = -0.326*SIRC + 0.101. Requires refraction before and after the refractive surgery.
Requires history
Rx_pre, Rx_post

Modified Masket

Hill
Updated coefficients: adj = -0.4385*SIRC + 0.0295. For myopic and hyperopic LASIK/PRK.
Requires history
Rx_pre, Rx_post

Toric module Toric

Toric IOL calculation for correcting corneal astigmatism. The primary recommendation is the proprietary APEX Toric module. The classic Abulafia-Koch selector runs in parallel and is shown as a confirmation line (with a warning when the models disagree).

Classic (Abulafia-Koch)

Abulafia et al. 2016
Vector decomposition of corneal astigmatism, posterior astigmatism via the Abulafia-Koch 2016 regression (JCRS 42:663), and SIA subtraction. Selects the optimal discrete toric model and implantation axis, with a table of correction lost on rotation.
Toric
Abulafia-Koch regression

APEX Toric

Proprietary
A proprietary toric module. It accounts for posterior corneal astigmatism — either from Pentacam measurements or from prediction. It runs automatically when LT and the K1/K2 axes are available.
Toric
Requires: LT + K axes
The clinical threshold for toric correction depends on the type of astigmatism (Koch et al., JCRS 2012). In 87% of cases the posterior corneal surface has against-the-rule astigmatism of ~0.3 D, which affects the total corneal cylinder differently:
• With-the-rule (WTR) ≥ 0.75 D — a toric IOL is indicated. Below this, the posterior cornea offsets the anterior cylinder, the total astigmatism is small, and the smallest toric (T2 ≈ 1.0 D) would overcorrect.
• Against-the-rule (ATR) ≥ 0.50 D — a toric IOL is indicated. The posterior cornea adds ~0.3 D to the anterior cylinder, so even 0.50 D by keratometry already amounts to ~0.80 D of total astigmatism.
• Oblique ≥ 0.50 D — a toric IOL is indicated. The posterior corneal contribution in oblique astigmatism varies between individuals, making the calculation less predictable.
For astigmatism > 4.0 D, rule out keratoconus.