# Transposition: another notation for the same prescription

Transposition adds cylinder to sphere, reverses the cylinder sign and rotates the axis by 90°, preserving the optical equivalence of the representation.

## Example

−2.00 −1.00 × 180° is equivalent to −3.00 +1.00 × 90°. The operation changes notation; it does not determine a new prescription.

## Units and axis

Sphere and cylinder are in dioptres; axis is in degrees. The calculator accepts axes from 0° to 180° and reports 1° through 180° for integer axes. With zero cylinder, axis has no optical effect and is preserved, normalizing 0° to 180°.

## Verification

Reverse transposition should recover the original representation, accounting for the equivalence of 0° and 180°. It does not fill missing fields or calculate addition or prism.

## References

- [Ohio Optometric Association — Optometric Math](https://www.ooa.org/aws/OOA/asset_manager/get_file/110761?ver=83)

## Related topics

- [Prentice’s rule: approximate prism magnitude](https://lensas.com.br/en/knowledge/prentice-rule/)
- [Lens thickness: inputs needed for an estimate](https://lensas.com.br/en/knowledge/lens-thickness/)

Educational content · Fictional examples · Automated technical review, no claimed clinical validation.

Canonical: https://lensas.com.br/en/knowledge/prescription-transposition/
Version: 2026-09-15.1