Cylinder Transposition
Optics and Optometry
Minus cylinder to plus cylinder and back, with a meridian-by-meridian check that the lens is unchanged.
How it is calculated
- Add the cylinder to the sphere, flip the sign of the cylinder, and rotate the axis by 90°.
- The two written forms are the same lens. They have the same spherical equivalent and the same power in every single meridian — only the notation changes.
- Optometry is usually taught in minus cylinder and ophthalmology in plus cylinder, which is the only reason the conversion is needed so often.
- An axis of 0° is always written as 180°: a prescription is never written × 000.
- The tool shows the power in each principal meridian for both forms, because seeing them match is the quickest way to be sure a transposition is right.
References
- Standard ophthalmic optics. The transposition is verified meridian by meridian in OcuLearning's own optics test suite.
About these tools
OcuLearning Clinical Tools is part of an educational platform. These calculators are provided for learning and reference, and are not medical advice, a diagnosis, or a treatment recommendation.