A spectacle lens sits roughly 12 mm in front of the eye; a contact lens sits directly on it. Over that small gap the light continues to converge or diverge, so the power that actually reaches the eye changes. That means the contact lens power is not the same as the spectacle prescription. For low prescriptions the difference is negligible, but as power rises it becomes clinically significant. Our vertex conversion tool does the maths instantly; this guide explains what it is doing and how to apply it correctly.
The short version
- Convert whenever any meridian is at or above ±4.00 D.
- Formula: Fc = Fs / (1 − d · Fs), with d in metres.
- Minus powers become less minus; plus powers become more plus.
- For torics, convert each principal meridian separately.
- Always confirm the final power with a trial-lens over-refraction.
Why the power changes
Light leaving a correcting lens forms a focus at a fixed point (its focal length from the lens). Move the lens closer to or further from the eye and the vergence of the light arriving at the eye changes, an effect called lens effectivity. To keep the focus on the retina, the power must be adjusted for the new position. Moving from the spectacle plane to the corneal plane is exactly this situation.
The formula
The effective power at the new (corneal) plane is:
Fc = Fs / (1 − d × Fs)
where Fs is the spectacle power in dioptres, Fc is the required contact lens power, and d is the vertex distance in metres (so 12 mm = 0.012 m). Use the true sign of the power throughout: minus for myopia, plus for hyperopia. The term (1 − d · Fs) is the reason a positive and a negative power of the same magnitude convert by different amounts.
Which way does it go?
- Minus (myopic) powers become less minus at the cornea; you need a weaker minus contact lens than the spectacle Rx.
- Plus (hyperopic) powers become more plus at the cornea; you need a stronger plus contact lens than the spectacle Rx.
The effect is also asymmetric: for a given magnitude, the plus conversion is larger than the minus conversion (compare +8.00 and −8.00 in the table below).
Worked examples (12 mm vertex)
−8.00 D spectacle: Fc = −8.00 / (1 − 0.012 × −8.00) = −8.00 / 1.096 = −7.30 D → order −7.25 D.
+8.00 D spectacle: Fc = +8.00 / (1 − 0.012 × +8.00) = +8.00 / 0.904 = +8.85 D → order +8.75 D.
−12.00 D spectacle: Fc = −12.00 / 1.144 = −10.49 D → order −10.50 D, a difference of 1.5 D from the spectacle Rx.
Quick reference: spectacle → contact lens at 12 mm
| Spectacle Rx (D) | Myopia (minus) | Hyperopia (plus) |
|---|---|---|
| 4.00 | −3.75 | +4.25 |
| 5.00 | −4.75 | +5.25 |
| 6.00 | −5.50 | +6.50 |
| 7.00 | −6.50 | +7.75 |
| 8.00 | −7.25 | +8.75 |
| 9.00 | −8.00 | +10.00 |
| 10.00 | −9.00 | +11.25 |
| 12.00 | −10.50 | +14.00 |
| 15.00 | −12.75 | +18.25 |
Need a value not shown, or a different vertex distance? Use the vertex conversion tool.
Toric (astigmatic) prescriptions
With significant cylinder, the two principal meridians have different powers and therefore convert by different amounts. The correct approach is to resolve the prescription into its two meridional powers, vertex- convert each meridian separately, then rebuild the sphere and cylinder from the converted meridians. Doing this by hand is error-prone, so the spectacle-to-contact calculator handles sphere and cylinder together. See also the toric fitting guide.
When do you actually need to bother?
The widely used rule of thumb is to apply vertex correction for any component of the prescription at or above ±4.00 D. Below that, the change is within a single 0.25 D step and is normally ignored. Above it, always convert. As the table shows, by ±10.00 D the difference is around a dioptre or more, far too much to leave uncorrected.
Measuring vertex distance & pitfalls
- Confirm the distance used to refract. 12 mm is a common default, but the actual back vertex distance varies with frame and fit; a distometer or a well-set trial frame improves accuracy.
- Round to the nearest available lens step (usually 0.25 D, with 0.50 D steps in high powers).
- Don't forget the plus/minus asymmetry. Converting a hyperope's Rx as if it were a myope's underestimates the change.
- Always over-refract the trial lens on the eye; the conversion gives a starting point, not the final answer.