Prescription Analysis and Lens Power Calculations
Reading a prescription
A prescription lists sphere, cylinder, axis, prism, add, and sometimes base curve and PD. Sphere corrects all meridians equally; cylinder corrects the difference between meridians and must be paired with an axis from 1 to 180.
Transposition and equivalents
Transposition changes form without changing power: new sphere = sphere + cylinder; new cylinder = −cylinder; new axis = axis ± 90°. Spherical equivalent = sphere + ½ cylinder, used for approximating refractive error and contact lens comparisons, never as a legal substitute for the full toric power.
Prism and vertex distance
Oblique prism is resolved into horizontal and vertical components, or components are combined with the Pythagorean theorem plus arctangent for direction. Vertex distance changes effective power above roughly ±4.00 D: F_new = F / (1 − d·F), with d in meters.
Traps
- Transposing the axis but forgetting to subtract the cylinder.
- Forgetting the axis must land between 1 and 180 after adding or subtracting 90 (0 is written as 180).
- Ignoring slab-off or bicentric needs in high anisometropia, which causes vertical prism imbalance at the reading level.
Worked examples
+2.00 −1.00 × 180 transposes to +1.00 +1.00 × 090; the spherical equivalent is +1.50 either way. Combine +3.00 BI with +4.00 BU: resultant = √(3² + 4²) = 5Δ, directed arctan(4/3) ≈ 53° above the horizontal, toward the base-up side.