Enter the sphere, cylinder (minus), and axis values into the calculator to convert the prescription to plus cylinder form.
Important: This tool only transposes spectacle (eyeglass) lens notation and does not validate whether a prescription is accurate or appropriate. Do not use it to self-prescribe—verify the converted values with your optometrist/ophthalmologist or dispensing optician. Not for contact lens prescriptions. If you have eye pain or sudden vision changes, seek professional care promptly.
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Minus Cyl To Plus Formula
The following formulas are used to convert a prescription from minus cylinder form to plus cylinder form:
D_{sphere}^{new} = D_{sphere}^{old} + D_{cyl}^{old}
D_{cyl}^{new} = -D_{cyl}^{old}
Axis^{new} = \begin{cases}Axis^{old} + 90, & Axis^{old} ≤ 90 \\ Axis^{old} - 90, & Axis^{old} > 90\end{cases}- D_{sphere}^{new} is the new sphere power in diopters (D).
- D_{cyl}^{new} is the new cylinder power in diopters (D).
- D_{sphere}^{old} and D_{cyl}^{old} are the original sphere and cylinder powers.
- Axis^{old} and Axis^{new} are the cylinder axes in degrees (°).
To perform the conversion, apply the formulas above to your original sphere, cylinder, and axis values.
| Sphere (D) | Cylinder (D, minus) | Axis (°) | Sphere (D, plus form) | Cylinder (D, plus) | Axis (°) |
|---|---|---|---|---|---|
| 0.00 | -0.50 | 180 | -0.50 | +0.50 | 90 |
| -0.50 | -0.50 | 45 | -1.00 | +0.50 | 135 |
| -1.00 | -0.25 | 90 | -1.25 | +0.25 | 180 |
| -1.25 | -0.75 | 10 | -2.00 | +0.75 | 100 |
| -1.50 | -1.00 | 60 | -2.50 | +1.00 | 150 |
| -2.00 | -0.50 | 120 | -2.50 | +0.50 | 30 |
| -2.50 | -1.25 | 75 | -3.75 | +1.25 | 165 |
| -3.00 | -2.00 | 20 | -5.00 | +2.00 | 110 |
| -3.25 | -1.50 | 135 | -4.75 | +1.50 | 45 |
| -3.50 | -0.75 | 150 | -4.25 | +0.75 | 60 |
| -4.00 | -2.25 | 25 | -6.25 | +2.25 | 115 |
| -4.50 | -1.00 | 80 | -5.50 | +1.00 | 170 |
| -5.00 | -0.50 | 180 | -5.50 | +0.50 | 90 |
| +0.50 | -0.75 | 90 | -0.25 | +0.75 | 180 |
| +1.00 | -1.00 | 45 | 0.00 | +1.00 | 135 |
| +2.00 | -0.50 | 100 | +1.50 | +0.50 | 10 |
| -0.25 | -0.25 | 160 | -0.50 | +0.25 | 70 |
| -2.25 | -2.50 | 30 | -4.75 | +2.50 | 120 |
| -0.75 | -1.25 | 110 | -2.00 | +1.25 | 20 |
| -1.75 | -0.50 | 140 | -2.25 | +0.50 | 50 |
| Conversion (minus cyl to plus cyl): Sphere’ = Sphere + Cylinder; Cylinder’ = −Cylinder; Axis’ = Axis ± 90 (normalize to 1–180; use 180 instead of 0). | |||||
What is Minus Cylinder To Plus Cylinder?
In eyeglass prescriptions, cylinder notation can be written in minus or plus form. Minus cylinder form is commonly used in some regions, while plus cylinder form is used in others. Converting between the two does not change the optical correction, only the format of the prescription.
How to Convert Minus Cylinder To Plus Cylinder?
Follow these steps to convert your prescription from minus cylinder notation to plus cylinder notation.
- Record your original sphere (D_{sphere}^{old}), cylinder (D_{cyl}^{old}), and axis (Axis^{old}).
- Calculate the new sphere: D_{sphere}^{new} = D_{sphere}^{old} + D_{cyl}^{old}.
- Calculate the new cylinder: D_{cyl}^{new} = -D_{cyl}^{old}.
- Adjust the axis: if Axis^{old} ≤ 90, Axis^{new} = Axis^{old} + 90; if Axis^{old} > 90, Axis^{new} = Axis^{old} – 90.
- Verify your new prescription values match the converted notation.
Example Problem:
Original sphere (D_{sphere}^{old}) = -2.00
Original cylinder (D_{cyl}^{old}) = -1.50
Original axis (Axis^{old}) = 180°
Converted sphere (D_{sphere}^{new}) = -2.00 + (-1.50) = -3.50
Converted cylinder (D_{cyl}^{new}) = -(-1.50) = +1.50
Converted axis (Axis^{new}) = 180° – 90° = 90°
