Free Lens Transposition Calculator
Convert plus cylinder to minus cylinder, or minus to plus, with easy 0.25 D controls. No account or download needed.
Free to use · No account · No upload
Start calculatingSPH & CYL: 0.25 D steps · Axis: whole degrees
Notation conversion only. It does not determine a prescription.
Lens transposition examples
| Entered prescription | Transposed prescription |
|---|---|
| −1.25 / +3.25 × 60° | +2.00 / −3.25 × 150° |
| −2.00 / −1.00 × 90° | −3.00 / +1.00 × 180° |
| +0.50 / −1.25 × 180° | −0.75 / +1.25 × 90° |
How to transpose a lens prescription
Use the signed sphere and cylinder values from the prescription. Transposition rewrites the notation; it keeps the same optical power.
- New sphere = sphere + cylinder.
- New cylinder = the original cylinder with its sign reversed.
- Rotate the axis by 90°: add 90° at 1–90°, subtract 90° at 91–180°.
Quarter-diopter controls, without the typing
Sphere and cylinder move in 0.25 D steps using + and −. You can type quarter-diopter values too, such as −1.25, 0.00 or +2.50. Axis uses whole degrees from 1 to 180.
A valid entry calculates immediately. Clear starts at plano, Load example restores the demonstration, and Transpose again reverses the conversion.
Plus cylinder, minus cylinder and plano
The same three rules work in both directions. At 90° the transposed axis is 180°; at 180° it is 90°. If cylinder is 0.00 D, sphere is unchanged and this tool retains the entered reference axis.
Free to use in your browser
No sign-in or subscription is required for this website calculator. Entered values stay in the browser; this tool does not send them to a server or save them to an IPDI customer record.
This is a notation-conversion aid. It does not perform refraction, diagnose eyesight or decide a prescription. Review the entered values before use.
How do I convert plus cylinder to minus cylinder?
Add sphere and cylinder for the new sphere, reverse the cylinder sign, then rotate the axis by 90° within 1–180°. For example, −1.25 / +3.25 ×60° becomes +2.00 / −3.25 ×150°.
Can I convert minus cylinder to plus cylinder too?
Yes. The same rule works both ways. For example, −2.00 / −1.00 ×90° becomes −3.00 / +1.00 ×180°.
Why are sphere and cylinder limited to 0.25 D steps?
This tool is designed for quarter-diopter entries. Tap + or − to move by 0.25 D, or type a valid quarter value. Axis uses a separate 1° step.
What happens if cylinder is zero?
A 0.00 D cylinder leaves the sphere unchanged. This calculator keeps your entered reference axis; there is no cylinder axis to rotate optically.
Is this lens transposition calculator free?
Yes. The browser calculator is free and does not need an account, app download or an IPDI subscription. The optical CRM app has its own yearly plan.
Are my prescription values uploaded or saved?
No. This website calculation stays in your browser. Copy result writes to your device clipboard only when you press it.
Formula reference: Opticianry training text (ERIC). Arithmetic aid; review the values before operational use.
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