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Cross-Cylinder Calculator

Toric refinement, Rx combination, and power cross

Cross-Cylinder Tool

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Mode

Trial Contact Lens Rx

Over-Refraction

Lens Rotation

Direction

How to Apply Cross-Cylinder Results in Clinic

What this calculator does

This cross-cylinder calculator supports three common tasks in clinic: toric refinement (trial toric lens + rotation + over-refraction), Rx combination (dioptric power sum of two spherocyl prescriptions), and power cross (principal meridian powers). It is designed for quick verification of axis, cylinder effect, and how rotation changes the effective on-eye correction.

If you also need to switch between plus- and minus-cylinder notation, use the Plus/Minus Cylinder Transposition Calculator.

Note: outputs are a mathematical target. Final ordering may require available parameters, trial confirmation, and clinical judgment.

Toric refinement: trial lens rotation and LARS

Toric refinement combines the trial contact lens Rx, the observed rotation direction (clinician left/right), and the over-refraction to compute a suggested lens power: the ideal on-eye spherocyl under the measured rotation. Conceptually, it answers: given how the trial lens rotates and what residual spherocyl remains on over-refraction, what on-eye spherocyl would best correct the eye?

Rotation is commonly interpreted using LARS (Left Add, Right Subtract) from the clinician’s viewpoint. If your clinic documents rotation from the patient’s viewpoint, convert accordingly.

If you want a broader fitting workflow, see the Contact Lens Hub for related clinical tools and references.

Rx combination (dioptric power sum)

Rx combination returns the single sphero-cylinder that matches the optical effect of stacking two prescriptions as a true dioptric power sum. This is useful for trial-lens math, lens-stacking demonstrations, and understanding how cylinders interact when axes are not aligned.

Tip: for a quick starting point when moving from glasses to soft lenses, the Glasses to Contact Lens Conversion Calculator can help (then refine clinically).

Power cross and principal meridians

A sphero-cylinder prescription has two principal meridians that are 90° apart. The cylinder axis identifies one principal meridian. Along the axis meridian, the power equals Sphere. Along the meridian 90° away, the power equals Sphere + Cylinder (with cylinder signed). Writing these two perpendicular powers as a pair is the power cross.

Principal meridian powers (power cross)

Axis meridian power = Sphere
Meridian 90° away = Sphere + Cylinder

Example: Rx Plano / -1.50 x 090 has principal meridians of 090°: 0.00 D and 180°: -1.50 D.

Cross-Cylinder FAQs

What is a power cross?

A power cross expresses lens power in two perpendicular meridians. For a sphero-cylinder prescription, the principal meridians are the axis meridian and the meridian 90° away.

How do I get the principal meridian powers from an Rx?

Along the cylinder axis meridian, power equals the sphere. In the meridian 90° away, power equals sphere + cylinder (with cylinder signed).

Does plus-cylinder versus minus-cylinder change the optics?

No. Transposition changes how the prescription is written, but it does not change the principal meridional powers.

What does Rx combination mean clinically?

It returns the single sphero-cylinder equivalent to stacking Rx1 and Rx2 together, meaning the lenses are combined as a true dioptric power sum.

What does toric refinement output represent?

It represents the suggested lens power (the ideal on-eye spherocyl) based on observed toric lens rotation and the measured residual over-refraction.

How should I interpret left vs right rotation (LARS)?

Many clinicians use LARS from the clinician’s viewpoint: Left Add, Right Subtract.

What does “ideal on-eye spherocyl” mean?

It is the mathematical target spherocyl that would best correct the eye under the measured rotation and residual over-refraction. Final ordered parameters may differ based on available lens options and clinical confirmation.