Plus/Minus Cylinder Transposition
Convert between (+) and (−) cylinder notation without changing power
Transpose an astigmatic prescription between plus-cylinder and minus-cylinder notation without changing the correction.
Transpose prescription
Enter sphere, cylinder, and axis. The result preserves optical power in every meridian.
Transposition rules
1. New sphere = original sphere + original cylinder
2. New cylinder = same magnitude, opposite sign
3. New axis = original axis ± 90° (kept 001–180)
Example: +2.00 +1.00 ×090 → +3.00 −1.00 ×180. Both notations describe the same refractive error; soft toric ordering and most optometric charting use minus cylinder.
Transposing between plus and minus cylinder
The same astigmatic prescription can be written in plus-cylinder or minus-cylinder form, and different instruments, records and manufacturers favour different conventions. Transposition converts between them without changing the actual correction. This tool does the three-step transposition for you so you can match whichever notation you need.
The rule it applies: add the cylinder to the sphere, flip the sign of the cylinder, and rotate the axis by 90°. The resulting prescription is optically identical to the original.
Does transposition change the correction?
No. Plus-cyl and minus-cyl forms describe exactly the same lens; only the notation differs. Transposing is purely a rewriting step.
Why do I need it for contact lenses?
Soft toric lenses are conventionally specified in minus-cylinder form. If your refraction is in plus-cyl, transpose before selecting a toric. See the toric fitting guide.
For more on cylinder and axis, see Toric lenses & astigmatism basics and reading a lens specification. See our disclaimer.