Spectacle Transposition and Contact Lens Power Tool
Last updated: October 2026
Enter a spectacle prescription to get its transposed form, spherical equivalent and the equivalent power at the cornea (for contact lenses), corrected for vertex distance.
How it works
- Transposition: new sphere = sphere + cylinder; new cylinder = the same number with the opposite sign; new axis = axis ± 90°.
- Spherical equivalent: sphere + half the cylinder.
- Vertex conversion: each principal meridian is converted separately with Fc = F / (1 − dF), where d is the vertex distance in metres. Minus lenses need less power at the cornea; plus lenses need more.
- The effect becomes clinically important at about ±4.00 D and above. See vertex distance for worked examples.
For contact lenses: this gives the power needed at the corneal plane. Soft toric lenses come in limited cylinder steps and axes, and rigid lenses correct corneal astigmatism through the tear lens, so the final lens still needs fitting and over-refraction.
Related: Prentice's rule, Jackson cross-cylinder, duochrome test and retinoscopy tips.
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