Enter the values of Sphere, Cylinder (in plus-cylinder notation), and Axis into the calculator to convert your prescription into the equivalent minus-cylinder form.
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Plus To Minus Cyl Formula
The following formulas are used to transpose (convert) a prescription from plus-cylinder notation to minus-cylinder notation:
\begin{aligned}
S_{-} &= S_{+} + C_{+} \\
C_{-} &= -C_{+} \\
A_{-} &= A_{+} + 90^\circ \pmod{180^\circ}
\end{aligned}Variables:
- S+ is the sphere power in plus-cylinder notation (diopters).
- C+ is the cylinder power in plus-cylinder notation (diopters, typically written as a positive value).
- A+ is the axis in degrees (typically 1–180).
- S–, C–, and A– are the equivalent values in minus-cylinder notation.
To convert from plus-cylinder to minus-cylinder, add the plus-cylinder value to the sphere to get the new sphere, change the sign of the cylinder, and rotate the axis by 90° (keeping the axis within 1–180; if the result exceeds 180, subtract 180).
| Sphere (Plus Cyl) | Cylinder (Plus Cyl) | Axis (°) | Sphere (Minus Cyl) | Cylinder (Minus Cyl) | Axis (°) |
|---|---|---|---|---|---|
| +0.00 | +0.50 | 90 | +0.50 | -0.50 | 180 |
| -1.00 | +0.50 | 20 | -0.50 | -0.50 | 110 |
| -2.00 | +1.00 | 45 | -1.00 | -1.00 | 135 |
| -0.50 | +0.75 | 80 | +0.25 | -0.75 | 170 |
| +1.00 | +0.25 | 10 | +1.25 | -0.25 | 100 |
| +2.00 | +1.00 | 120 | +3.00 | -1.00 | 30 |
| -3.00 | +1.50 | 75 | -1.50 | -1.50 | 165 |
| +0.50 | +0.50 | 60 | +1.00 | -0.50 | 150 |
| +1.50 | +0.75 | 150 | +2.25 | -0.75 | 60 |
| -1.50 | +2.00 | 95 | +0.50 | -2.00 | 5 |
| +0.00 | +1.25 | 30 | +1.25 | -1.25 | 120 |
| +2.50 | +0.50 | 135 | +3.00 | -0.50 | 45 |
| -2.50 | +0.25 | 5 | -2.25 | -0.25 | 95 |
| -0.25 | +1.25 | 160 | +1.00 | -1.25 | 70 |
| +3.00 | +0.75 | 110 | +3.75 | -0.75 | 20 |
| -1.25 | +1.00 | 180 | -0.25 | -1.00 | 90 |
| +0.75 | +1.50 | 140 | +2.25 | -1.50 | 50 |
| -0.75 | +0.25 | 70 | -0.50 | -0.25 | 160 |
| +1.25 | +2.00 | 25 | +3.25 | -2.00 | 115 |
| -3.50 | +0.50 | 100 | -3.00 | -0.50 | 10 |
| Formulas: Sphere(minus) = Sphere(plus) + Cylinder(plus); Cylinder(minus) = -Cylinder(plus); Axis(minus) = Axis(plus) + 90; if result > 180, subtract 180 (axis is typically written 1–180). | |||||
What is a Plus To Minus Cyl?
A Plus to Minus Cyl (often called prescription transposition) is a method used in optometry to rewrite an eyeglass or contact lens prescription from plus-cylinder notation to minus-cylinder notation (or vice versa). In plus-cylinder notation, the cylinder value is written as a positive number; in minus-cylinder notation, the cylinder value is written as a negative number. The conversion changes the written form by adding the cylinder to the sphere, changing the sign of the cylinder, and rotating the axis by 90 degrees (keeping the axis within 1–180). This conversion does not change the optical power of the prescription—it only represents the same two principal meridian powers in a different format.
How to Calculate Plus To Minus Cyl?
The following steps outline how to calculate the Plus To Minus Cyl.
- Start with the prescription in plus-cylinder form: Sphere (S+), Cylinder (C+), and Axis (A+).
- Calculate the new sphere: S– = S+ + C+.
- Change the sign of the cylinder: C– = -C+.
- Rotate the axis by 90°: A– = A+ + 90; if the result is greater than 180, subtract 180 (axis is typically written 1–180).
- Review the converted prescription to confirm it is written in standard minus-cylinder form (negative cylinder).
Example Problem:
Use the following values as an example problem to test your knowledge.
Sphere (plus cyl) = +2.00
Cylinder (plus cyl) = +1.00
Axis (plus cyl) = 120°
Converted (minus cyl): Sphere = +3.00, Cylinder = -1.00, Axis = 30°
