New sphere = SPH + CYL
+2.00 + (+1.00) = +3.00
Add algebraically, keeping the signs. A negative cylinder reduces the sphere value; a positive cylinder increases it.
Plus cylinder ↔ minus cylinder
Cylinder Transposition Calculator
Convert plus cylinder to minus cylinder, or vice versa. Enter SPH, CYL and axis to see the equivalent prescription and each calculation step.
Transpose Your Prescription
One eye at a time. The cylinder sign determines the conversion direction.
Notation conversion only. This does not apply vertex correction, determine lens fit or issue a new prescription.
Both directionsNo power roundingStep-by-step result
Three simple rules
How to Convert Plus Cylinder to Minus Cylinder
The same method works for minus-to-plus cylinder transposition. Add the signed powers, reverse CYL’s sign, then shift the axis by 90°.
New cylinder = −CYL
+1.00 → −1.00
Change only the cylinder’s sign. Its magnitude stays the same, so +1.00 D becomes −1.00 D.
New axis = AXIS ± 90°
90° + 90° = 180°
Add 90° when the original axis is 90° or less. Otherwise subtract 90°, keeping the result between 1° and 180°.
+2.00 / +1.00 × 90° = +3.00 / −1.00 × 180°
These are two descriptions of the same optical correction. The changed numbers do not mean the prescription became stronger.
A visual check
Why Cylinder Transposition Keeps the Same Power
The two principal meridian powers stay the same. Transposition changes which is written as the sphere and which axis is assigned to the cylinder.
Compare the optical powers
Transposition, SE or vertex conversion?
CYL transposition
Rewrites the full SPH/CYL/axis combination in the opposite cylinder notation.
Spherical equivalent
Averages SPH and CYL into one power. Use the spherical equivalent calculator for that separate calculation.
Vertex conversion
Adjusts power for a change in lens position. Use the contact lens vertex calculator for theoretical glasses–contacts conversion.
Plus and minus cylinder examples
Prescription Transposition Examples
Read each prescription as SPH / CYL × AXIS. Powers are in diopters; axis is in degrees. No rounding is needed.
| Example | Original prescription | Transposed prescription |
|---|---|---|
| Plus → minus | +2.00 / +1.00 × 90° | +3.00 / −1.00 × 180° |
| Minus → plus | −4.00 / −1.50 × 180° | −5.50 / +1.50 × 90° |
| Mixed signs | −2.00 / +0.75 × 30° | −1.25 / −0.75 × 120° |
| Plano result | +1.00 / −1.00 × 135° | 0.00 / +1.00 × 45° |
Quick answers
Cylinder Transposition Calculator FAQ
Is a CYL converter the same as a cylinder transposition calculator?
For plus-to-minus and minus-to-plus prescription notation, yes. This tool changes sphere, cylinder sign and axis together; changing only the CYL sign would not describe the same correction.
What happens at axis 90 or 180?
Axis 90° becomes 180°. Axis 180° becomes 90°. The calculator uses the 1–180° convention and does not output 0° or 270°.
Can I transpose a prescription with zero cylinder?
When CYL is 0.00 D, there is no cylinder component to transpose. The sphere stays the same and axis is not applicable. Leave the axis blank; the tool will explain why no conversion is needed.
What does plano mean in the sphere field?
Plano or PL means 0.00 D sphere. The calculator accepts either term in SPH. It does not mean that cylinder must also be zero.
Does transposition convert glasses to contact lenses?
No. It preserves optical power at the same lens position. For a glasses prescription with astigmatism, the toric contact lens calculator applies vertex conversion to both principal meridians. Neither calculation determines a contact lens product, base curve, diameter or fit.
Should I transpose each eye separately?
Yes. Use SPH, CYL and axis from a single eye’s prescription. Reset the form before entering the other eye so values are not mixed.
Method reference
The three transposition rules are documented in Foundations in Dispensing, Chapter 6 (printed page 74). This tool applies those rules without rounding the powers and treats zero cylinder as a sphere-only prescription.
Keep Exploring Contact Lens Tools
More free tools: prescription conversion, lens prices, exam & fitting costs, and astigmatism conversion. No sign-up.
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