How cylinder transposition works
- Add the cylinder power to the sphere power to get the new sphere.
- Reverse the sign of the cylinder, changing minus to plus or plus to minus.
- Rotate the axis by 90 degrees, keeping the result within 1 to 180 degrees.
Vision tools
Prescription notation calculator
Cylinder Transposition Calculator
Convert a spectacle prescription between minus-cylinder and plus-cylinder notation while preserving the same optical power.
Enter SPH, CYL, and AXIS
Include the plus or minus sign shown on the prescription. Axis uses degrees from 1 to 180.
Transposed prescription
Enter all three values and select “Transpose prescription” to see the equivalent notation and calculation steps.
Why prescriptions use different cylinder forms
Optometrists, ophthalmologists, laboratories, and instruments may record astigmatism correction in different conventions. A correctly transposed pair is optically equivalent; it is another way to write the same lens power rather than a new or stronger prescription.
Important limits
This calculator performs notation arithmetic only. It does not verify that a prescription belongs to you, account for prism or multifocal fields, convert a glasses prescription to contact lenses, or determine whether the prescription is clinically appropriate. Confirm eyewear orders with the prescribing professional or dispensing optician.
These tools provide general education only. They do not diagnose an eye condition, replace a comprehensive eye exam, or provide a prescription for glasses or contact lenses.
Editorial responsibility and sources
Maintained by the AstigmatismTest.com Editorial Team. Last reviewed and updated . The team checks the method, limits, and wording against the references below; this byline does not claim review by a licensed clinician. Read our editorial policy.
Methodology references
- Lensometry - NCBI Bookshelf / StatPearls
- Optical Theory II: Course Content and Outcomes - Portland Community College