What this calculator does
Back vertex distance is the gap between the back surface of a spectacle lens and the front of the cornea. This back vertex calculator estimates how a lens power in dioptres changes when that gap is moved closer to or further from the eye, using the standard optics relationship between lens power and vertex distance.
The effect is small for weak lenses and grows quickly for strong ones. A pair of reading glasses moved a few millimetres barely changes anything useful, but a strong prescription, such as one used after cataract surgery or for high myopia, can shift by a meaningful fraction of a dioptre for the same few millimetres of movement.
The formula
Effective power equals the original power divided by one minus the shift in vertex distance, in metres, multiplied by the original power. Moving the lens closer to the eye is treated as a negative shift and moving it further away as a positive one, which is why the effective power moves in opposite directions depending on which way the lens moves.
| Term | Meaning |
|---|---|
| Vertex distance | The distance between the back surface of a lens and the front of the eye. |
| Original power (F) | The lens power as prescribed at its original fitting distance, in dioptres. |
| Effective power | The power the lens effectively delivers once its distance from the eye changes. |
The inputs explained
| Field | What to enter |
|---|---|
| Original lens power (F) (D) | The lens power as originally prescribed, in dioptres. Use a negative number for a minus (myopia) lens if your own records use that convention. |
| Change in vertex distance (mm) | How far the vertex distance changes, in millimetres. |
| Lens moved | Whether the lens moves closer to the eye or further away from it at the new fitting. |
When to use it
Switching between glasses and contact lenses
Contact lenses sit directly on the eye with effectively zero vertex distance, so a spectacle prescription needs adjusting before it applies to a contact lens fitting, particularly for stronger prescriptions.
Refitting frames with a different bridge or pantoscopic tilt
A new frame style can change how far the lens sits from the eye even at the same prescription, which shifts the effective power delivered.
Understanding why a strong prescription is sensitive to fit
This calculator makes it concrete why a high-powered lens loses accuracy if it slips down the nose or sits at an unusual distance, while a mild prescription barely notices the same movement.
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 effective power changes with vertex distance shift, for a range of lens powers
A 3 mm shift closer to the eye, across a range of original lens powers.
| Original power | Effective power at new vertex distance | Change in power |
|---|---|---|
| -8 D | -8.20 D | -0.20 D |
| -4 D | -4.05 D | -0.05 D |
| -2 D | -2.01 D | -0.01 D |
| 2 D | 1.99 D | -0.01 D |
| 4 D | 3.95 D | -0.05 D |
| 8 D | 7.81 D | -0.19 D |
Questions
Does back vertex distance matter for a mild prescription?
Barely. For lenses under about 4 dioptres, a few millimetres of vertex distance change shifts the effective power by only a small fraction of a dioptre, well within normal fitting tolerance.
Why does moving a lens closer to the eye increase its effective power for a plus lens?
A converging (plus) lens brings light to a focus at a fixed distance behind the lens; moving the lens closer to the eye moves that focus relatively further behind the cornea, which the eye compensates for as if the lens were slightly stronger.
Is this the same calculation an optometrist uses?
It uses the same standard vertex-distance formula taught in optics, but an actual fitting also accounts for frame tilt, lens design and individual eye measurements. Treat this as an educational estimate, not a substitute for a proper fitting by an eye-care professional.
At what lens power does vertex distance start to matter clinically?
As a rough guide, opticians start paying close attention above about 4 to 5 dioptres, with the effect becoming clinically significant for high prescriptions such as those above 10 dioptres.
For the sine, cosine and tangent relationships used elsewhere in optics and geometry, see the sine, cosine and tangent calculator.