Live Result
Results update while valid values are entered.
OD Optical Cross
OS Optical Cross
Formula Used
New Sphere = Original Sphere + Original Cylinder
New Cylinder = Original Cylinder × −1
New Axis = Original Axis ± 90°, normalized to 1°–180°
Spherical equivalent remains unchanged. Principal meridian powers also remain unchanged. These checks verify equivalent optical notation.
How to Use This Calculator
- Enter sphere, cylinder, and axis for either eye.
- Select automatic or a required cylinder conversion direction.
- Add optional ADD, prism, base, PD, and notes.
- Review live calculations and optical verification details.
- Copy, print, share, or export the final result.
Worked Examples
| Original Rx | Transposed Rx | Direction |
|---|---|---|
| −2.00 −1.00 × 180° | −3.00 +1.00 × 90° | Minus to plus |
| +1.50 +0.50 × 45° | +2.00 −0.50 × 135° | Plus to minus |
| PL −2.00 × 170° | −2.00 +2.00 × 80° | Minus to plus |
| −1.25 PL | −1.25 PL | No transposition |
Saved Calculation History
Prescription Terms
| Term | Meaning |
|---|---|
| SPH | Spherical lens power in diopters. |
| CYL | Astigmatism correction power in diopters. |
| AXIS | Cylinder orientation from 1° through 180°. |
| OD | Right eye prescription. |
| OS | Left eye prescription. |
| ADD | Additional near power for multifocal lenses. |
| PD | Pupillary distance measured in millimeters. |
| Prism | Prismatic correction with a base direction. |
Frequently Asked Questions
What does prescription transposition change?
It changes cylinder notation only. Optical lens power remains equivalent. Sphere, cylinder, and axis are rewritten.
How is the new sphere calculated?
Add the original cylinder to sphere. Keep all algebraic signs during addition. The result becomes the new sphere.
How is the cylinder changed?
Reverse the cylinder sign. Positive becomes negative, and negative becomes positive. Its absolute size remains unchanged.
How is the new axis calculated?
Move the axis by ninety degrees. Normalize the answer within one through 180. Equivalent orientations remain optically identical.
Is an axis needed for zero cylinder?
No axis is required. Zero cylinder has no directional component. The calculator leaves axis blank.
What does plano mean?
Plano means zero spherical power. It may appear as PL or 0.00. Both forms indicate no sphere power.
Why verify spherical equivalent?
Spherical equivalent should remain unchanged. It provides a useful arithmetic verification. It does not replace clinical assessment.
Are ADD and prism values transposed?
No, those values remain unchanged. Transposition affects sphere, cylinder, and axis. The calculator preserves additional fields.
Can both eyes use different cylinder signs?
Yes, each eye is processed independently. Automatic mode detects each cylinder sign. Forced modes warn about mismatches.
Can I use unusual diopter increments?
Yes, decimal inputs are accepted. The step selector guides common increments. Display precision controls visible rounding.
Does this calculator create a prescription?
No, it only rewrites notation. It cannot diagnose or prescribe lenses. Consult a qualified eye-care professional.
Important Disclaimer
This calculator transposes existing spectacle notation. It does not create medical prescriptions. Professional verification remains essential before lens fabrication.