This calculator allows you to determine and visualize the optimal rotation angle
of a toric pseudophakic intraocular lens for the correction of corneal astigmatism.
It takes into account the orientation relative to the corneal dome (K1/K2 axes) and the
cornea–IOL distance (ELP), with precise conversion of powers between
the IOL plane and the corneal plane.
What the tool calculates & displays
The rotations θCmin (minimal cylinder) and θCtarget (minimal deviation from target), with the optimal rotation zone.
The expected refraction after rotation (S, C, A) and the SE difference (spherical equivalent) achieved vs. targeted.
The IOL plane → corneal plane conversion for cylinder, taking ELP into account.
Educational visualizations: optimization curve, frontal and surgical views,
cylinder profiles (SE=0) and J0/J45 diagrams (−/+ cylinder conventions).
⚠️ Warnings & Terms of Use
Decision support software intended for healthcare professionals. It
does not replace clinical examination or the surgeon’s judgment.
The results depend on the entered measurements and on simplified models (ELP, posterior corneal astigmatism, SIA, vergence conversions).
Expect deviations due to measurement and manufacturing tolerances, decentration, secondary rotation, etc.
Caution in cases of irregular cornea (keratoconus, scars), corneal history (PRK/LASIK, rings, keratoplasty), or marked lenticular astigmatism: adjust the strategy and inputs accordingly.
This module is provided “as is”, for teaching/evaluation purposes.
It is not a medical device (MDR/CE) in the absence of regulatory validation. The user remains solely responsible for clinical decisions.
Data: in this version, calculations are performed in the browser and no data is transmitted by the provided script.
In case of online hosting, ensure compliance with local regulations (GDPR, consent) and security.
📏 1/5 DISTANCES
2/5 KERATOMETRY
(K1 = least curved meridian, K2 = most curved)
<
→ K2 axis: 90° (perpendicular to K1)
🔧 POSTERIOR SURFACE CORRECTION
3/5 TARGET REFRACTION
4/5 TORIC IMPLANT
Enter the toric IOL parameters. The predicted postoperative refraction will be calculated automatically.
5/5 MEASURED POSTOP REFRACTION
Enter the actual measured refraction after surgery to calculate optimal IOL rotation
FINAL RESULTS
FIGURES
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Export Information
Note: The files will be downloaded sequentially.
Figure 1: Optimization Curve
Description: This curve shows the amplitude of the total refractive cylinder as a function of IOL rotation. The vertical lines indicate the optimal positions θ_Cmin (minimal cylinder) and θ_Ctarget (minimal error relative to the target).
Figure 2: Frontal Views
Description: Frontal representation of the eye showing the keratometric axes (K1, K2) and the IOL axis before and after optimal rotation.
Figure 3: Surgical View
Description: Surgical view: the angular scale reads 180°–0° (reversed from the anatomical convention) tomatch the surgeon's operative view The rotation angle and direction remain the same.
Figure 4: Vector Cylinder Profiles
Description: Pure cylindrical power profiles (SE=0) showing the contributions of the cornea, the IOL, and their resultant before/after rotation.
Figure 5: J0/J45 Vector Diagram
Description: Vector representation of astigmatism in J0/J45 coordinates showing the vector addition of corneal and IOL components.
Glossary – Terms Used
SE (Spherical Equivalent)
SE = S + C/2. Used to compare the achieved and the targeted values.
Spectacle plane / Corneal plane / IOL plane
Optical planes where powers are expressed. Conversions use the vertex distance and the ELP.
K1 / K2 and A1 / A2
Keratometric radii (K1 is the flattest, K2 the steepest) and their orthogonal axes (A2 = A1 + 90°).
PCA / Posterior Corneal Astigmatism
Contribution from the posterior surface of the cornea. Can be estimated using different methods (Koch/Baylor, Abulafia, etc.).
SIA
Surgically Induced Astigmatism: astigmatism induced by the incision, entered as magnitude/axis.
Negative / Positive cylinder conventions
Same astigmatism expressed in C− or C+. Conversion: C+ = −C−, A+ = A− + 90°.
J0 / J45
Vector coordinates: J0 = −(C/2)·cos(2A), J45 = −(C/2)·sin(2A).
Useful for vector addition of components (cornea, IOL, etc.).
θCmin / θCtarget
Rotations producing the minimal cylinder and the minimal deviation from target (SE/J0/J45), respectively.
Ps / Pc (IOL)
Spherical power (Ps) and cylindrical power (Pc) at the IOL plane.
ΔSE / ΔC
Differences between the expected post-rotation refraction and the measured (or targeted) refraction, at the spectacle plane.
Cornea–IOL distance
Distance used to convert powers between the IOL plane and the corneal plane.
It is involved in the “IOL-plane / corneal-plane” ratio for cylinder conversion.
Subsidiary astigmatism
Astigmatism component not explained by the anterior/posterior cornea and the IOL
(e.g., internal effects, small inaccuracies).
Estimated vectorially from the measured refraction; it influences the residual cylinder and sometimes the axis.
Optimal zone
Range of rotations where the refractive cylinder remains ≤ the chosen threshold (e.g., 0.75 D).