What this calculator does
A spectacles prescription and a contact lens prescription for the same eye are not the same number once the lens power is strong enough. Spectacle lenses sit a short distance in front of the eye, called the vertex distance, while a contact lens sits directly on the cornea, so the effective power the eye actually receives changes when that distance disappears.
This calculator applies the standard contact lens vertex distance correction to convert a spectacle power into the equivalent contact lens power. It is an informational conversion for understanding the maths behind the correction, not a substitute for an optometrist's actual contact lens fitting and prescription, which also accounts for corneal curvature and other factors this formula does not.
The formula
The corrected power is the spectacle power divided by one minus the vertex distance (in metres) multiplied by the spectacle power. The correction is small for weak prescriptions and grows quickly for strong ones, which is why it is usually only applied clinically from around plus or minus 4.00 dioptres and stronger.
| Term | Meaning |
|---|---|
| Fsp | Spectacle lens power, in dioptres, as written on the spectacles prescription. |
| Fcl | The equivalent contact lens power once the vertex distance is removed. |
| d | Vertex distance: the gap between the back of the spectacle lens and the front of the eye, converted to metres for the formula. |
The inputs explained
| Field | What to enter |
|---|---|
| Spectacle lens power (Fsp) (D) | The spectacle lens power from the prescription, in dioptres. Negative for short-sightedness, positive for long-sightedness. |
| Vertex distance (mm) | The vertex distance, in millimetres, typically measured by the optometrist and often around 12mm for standard spectacle frames. |
When to use it
Understanding why a contact lens prescription differs from a spectacle one
Seeing the two numbers side by side, and by how much they diverge, explains why an optometrist does not simply hand over the spectacle prescription for contact lenses at higher powers.
Checking the direction of the correction
For short-sighted (negative) prescriptions, the contact lens power comes out weaker in magnitude than the spectacle power; for long-sighted (positive) prescriptions, it comes out stronger, and seeing both cases side by side makes that pattern clear.
Seeing why the correction barely matters for mild prescriptions
Running a low power such as -1.50D through the calculator shows a correction of only a small fraction of a dioptre, which is why vertex correction is usually ignored below about plus or minus 4.00D.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the vertex correction grows with a stronger short-sighted prescription
The same 12mm vertex distance applied to a range of short-sighted (negative) spectacle powers.
| Spectacle power | Equivalent contact lens power | Correction applied |
|---|---|---|
| -2 D | -1.95 D | +0.05 D |
| -4 D | -3.82 D | +0.18 D |
| -6 D | -5.60 D | +0.40 D |
| -8 D | -7.30 D | +0.70 D |
| -10 D | -8.93 D | +1.07 D |
| -14 D | -11.99 D | +2.01 D |
How the vertex correction changes with vertex distance at a fixed power
A fixed -10.00D spectacle lens, measured at a range of vertex distances.
| Vertex distance | Equivalent contact lens power | Correction applied |
|---|---|---|
| 8 mm | -9.26 D | +0.74 D |
| 10 mm | -9.09 D | +0.91 D |
| 12 mm | -8.93 D | +1.07 D |
| 14 mm | -8.77 D | +1.23 D |
| 16 mm | -8.62 D | +1.38 D |
| 18 mm | -8.47 D | +1.53 D |
Questions
Why does contact lens power come out weaker for short-sighted prescriptions?
Moving a negative (diverging) lens closer to the eye, from the spectacle plane to the cornea, means the eye no longer needs as much divergence to compensate, so the contact lens needs a smaller magnitude of negative power than the spectacle lens.
At what power does vertex distance correction actually matter?
It is usually applied clinically from around plus or minus 4.00 dioptres and stronger. Below that, the correction is small enough that most practitioners prescribe the same power for contacts as for spectacles.
Can I use this instead of seeing an optometrist for contact lenses?
No. This calculator only applies the vertex distance formula to a spectacle power. An actual contact lens fitting also involves corneal curvature, lens material, tear film and a trial fitting on the eye, none of which this simple conversion accounts for.
What happens if the correction formula gives an undefined result?
That happens only in an extreme edge case where the denominator becomes zero, which would require an unrealistically strong prescription combined with that specific vertex distance. In ordinary prescriptions this never occurs.
For unrelated everyday percentage-style conversions, see the percentage calculator. For the underlying dioptre-and-distance relationship in optics generally, this calculator applies the same vertex formula used across ophthalmic optics.