AccuLens Oblique Cross Cylinder Calculator
Vector-based cross-cylinder math with rotation handling, optional vertexing, and a clean workflow for specialty lenses.
Quick start
1
Enter the **original lens** Sphere / Cylinder / Axis worn on-eye.
2
Enter any **on-eye rotation** amount and pick the **LARS** direction (CW = Left Add, CCW = Right Subtract).
3
Enter the **over-refraction** (Sphere / Cylinder / Axis). Adjust **vertex distance** if needed (default 12 mm).
4
Choose a **Lens Rotation Handling** mode:
- Rotate lens — design allows pre-rotation (e.g., Maxim3D/back-surface control). We’ll align the toric interface.
- Keep original rotation — rotation is expected to remain (e.g., soft toric/standard toric haptic).
5
Click Calculate. The **Final Rx** appears in a card. Use Copy Final Rx to paste into your order or chart.
What the calculator does
- Automatic transposition to minus cylinder for any plus-cyl inputs (both the original lens and the O.R.).
- Rotation correction with LARS. If you choose “Rotate lens,” we provide a clear adjust offset by ±XX° instruction and reflect it in the output note.
- Optional vertex compensation when |power| > 4.00 D (sphere and/or cylinder meridian), using the distance you specify (default 12 mm).
- Clinically clean output. Results are rounded to twelfths (0.12 D) for S and C, and axis is normalized to 001–180.
Math (brief)
We combine the original lens and the over-refraction in power-vector space and convert back to standard notation.
\( J_0 = -\frac{C}{2}\cos(2\theta), \quad J_{45} = -\frac{C}{2}\sin(2\theta) \)
After vector addition \( (M, J_0, J_{45}) \), we resolve:
- \( C = -2\sqrt{J_0^{\,2}+J_{45}^{\,2}} \)
- \( \text{Axis} = \operatorname{atan2}(J_{45}, J_0)\cdot\frac{90}{\pi} \) (normalized to 001–180)
- \( S = M - \frac{C}{2} \)
We transpose any plus-cyl inputs first to keep vertexing and UI consistent; the vector math itself is sign-agnostic.
Rotation & LARS specifics
- CW – Left Add (LARS): subtract the entered degrees from the original axis.
- CCW – Right Subtract (LARS): add the entered degrees to the original axis.
When Rotate lens is selected, we assume the design can pre-align the toric optic. You’ll see a badge on the card (e.g., adjust offset by −30°) and a matching note under the final Rx.
Vertex compensation
For high powers, we apply effective power at the chosen vertex distance \(d\) (meters):
\( F_{\text{eff}} = \frac{F}{1 - dF} \)
We evaluate both principal meridians for the O.R. and adjust sphere/cylinder as appropriate. Default \(d=0.012\) m (12 mm).
Output & copying
- Final Rx is highlighted at the top of the results card.
- The note beneath tells you whether we assumed the lens stays in the same rotation or if you should pre-rotate (with the exact degree and sign).
- Copy Final Rx copies only the bold Rx line (e.g., +2.25 −1.75 × 165). You’ll get a brief “Copied!” confirmation.
Rounding & conventions
- Sphere & Cylinder: rounded to nearest 0.12 D (twelfths).
- Axis: integer degrees, normalized to 001–180.
- Signs: explicit + and − in output for clarity.
Tips
- If your design cannot be pre-rotated, pick Keep original rotation to avoid mis-aligning the cylinder meridian.
- Double-check the rotation direction (LARS) if your result looks off by ~2× the entered rotation.
- Use the vertex box for significant O.R.s; leave it at 12 mm for typical refractions.
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