Formula used
New Sphere = Sphere + Cylinder New Cylinder = −Cylinder New Axis = Axis ± 90° Spherical Equivalent = Sphere + Cylinder ÷ 2
The axis must remain from 1° through 180°. Add 90° to the original axis. Subtract 180° when the result exceeds 180°.
How to use
- Enter sphere, cylinder, and axis values.
- Select automatic or a directed conversion mode.
- Choose both eyes or one selected eye.
- Add optional ADD, prism, base, PD, and notes.
- Choose precision, increment, and rounding controls.
- Submit the form and review each calculation step.
- Use copy, CSV, PDF, or print controls.
Example data
| Original prescription | Transposed prescription |
|---|---|
| −2.00 −1.50 × 30 | −3.50 +1.50 × 120 |
| +1.25 +0.75 × 45 | +2.00 −0.75 × 135 |
| Plano −1.00 × 180 | −1.00 +1.00 × 90 |
| +2.50 −0.50 × 110 | +2.00 +0.50 × 20 |
Understanding prescription transposition
Transposition changes cylinder notation without changing optical power. Plus-cylinder and minus-cylinder forms describe equivalent lenses. The sphere, cylinder, and axis values all change together.
Sphere represents the main focusing power of the lens. Cylinder describes astigmatism correction strength. Axis identifies the cylinder orientation from 1° through 180°.
Plano means zero dioptres for the related field. A zero cylinder usually needs no meaningful axis. The calculator still preserves optional prescription details.
Frequently asked questions
What does transposing an eye prescription mean?
It converts plus-cylinder notation into minus-cylinder notation, or reverses it. The optical effect stays equivalent. Only the written form changes.
Why does the sphere value change?
The original cylinder is added to the original sphere. This preserves total lens power. The cylinder sign then reverses.
How is the new axis calculated?
Add or subtract 90° from the original axis. Keep the answer from 1° through 180°. Both directions produce the same final orientation.
What happens when cylinder is zero?
The prescription remains effectively unchanged. An axis is normally unnecessary. The calculator displays a warning.
What is the spherical equivalent?
It estimates the average focusing power. Add half the cylinder to the sphere. It does not replace a complete prescription.
Can I enter Plano?
Yes, enter PL, Plano, or 0.00. Each value is treated as zero dioptres. Positive signs remain visible in results.
Are ADD and prism values transposed?
No, those values are preserved exactly. Transposition changes sphere, cylinder, and axis only. Other details remain attached to the eye.
How does the equivalence checker work?
Both entries are normalised to one cylinder form. Their powers and axes are then compared. Small rounding tolerance is allowed.
Does this calculator replace an eye professional?
No, it performs mathematical notation changes only. It cannot diagnose vision or modify treatment. Confirm clinical decisions with a qualified eye professional.
Safety notice
This tool performs mathematical prescription transposition only. It does not diagnose vision problems or authorise prescription changes. Consult an optometrist or ophthalmologist for clinical guidance.