Vertex Distance: Formula, Examples and When It Matters
Last updated: October 2026
Short answer: vertex distance is the distance between the back of a spectacle lens and the cornea, usually about 12 mm. It matters for prescriptions stronger than about ±4.00 D. When a lens moves closer to the eye (for example, from glasses to contact lenses), a minus prescription becomes weaker and a plus prescription becomes stronger. Use Fnew = F ÷ (1 − dF).
The formula
Fc = F ÷ (1 − d × F)
- F = spectacle power (D)
- d = distance the lens moves towards the eye, in metres (for example, 12 mm = 0.012)
- Fc = equivalent power at the new position (for example, at the cornea)
Worked examples (vertex distance 12 mm)
| Spectacle power | Calculation | Corneal plane power |
|---|---|---|
| −4.00 D | −4 ÷ (1 + 0.048) | about −3.82 → −3.75 D |
| −10.00 D | −10 ÷ (1 + 0.12) | about −8.93 → −9.00 D |
| +10.00 D | +10 ÷ (1 − 0.12) | about +11.36 → +11.25 or +11.50 D |
Memory aid
- Moving closer to the eye: minus becomes less minus; plus becomes more plus.
- Moving further away: the opposite.
- This is why myopes often need weaker contact lenses than glasses, and aphakic patients need much stronger contact lenses than glasses.
Where it matters clinically
- Converting glasses to contact lens prescriptions
- Planning refractive surgery and phakic IOLs in high myopia (calculations are based on the corneal plane)
- Aphakia and high hyperopia
- Recording the vertex distance in the phoropter or trial frame when refracting high prescriptions, so the final glasses are made correctly
Frequently asked questions
When does vertex distance matter?
For prescriptions stronger than about ±4.00 D. Below that, the difference is usually smaller than a quarter of a dioptre.
What is the contact lens power for −10.00 D glasses?
At a 12 mm vertex distance, about −9.00 D: −10 ÷ (1 + 0.12) ≈ −8.93 D.
Why do aphakic patients need stronger contact lenses than glasses?
Moving a plus lens closer to the eye reduces its effectiveness, so a stronger plus lens is needed at the cornea to give the same correction.
Related: Prentice's rule, formulas in ophthalmology and contact lens clinic.
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