# What is my contact lens vertex?

Converts a glasses prescription to contact lens power at the eye (or back) with the vertex formula Fc = F ÷ (1 − d·F), for the sphere and the cylinder, rounded to the 0.25 D steps lenses come in.

- Page: https://www.acalculator.org/health/contact-lens-vertex-calculator
- JSON spec: https://www.acalculator.org/health/contact-lens-vertex-calculator.json
- Version: 95efb28b4a55

## Default answer

Example with the default inputs (Convert from Glasses, Sphere (D) -6, Vertex distance (mm) 12): A -5.5 D sphere at the new plane.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| from | Convert from | Convert a glasses prescription to contact lenses, or contact lenses to glasses. |
| sph | Sphere (D) | The sphere power in diopters, minus for nearsighted and plus for farsighted. |
| cyl | Cylinder (D) | Optional: the cylinder power for astigmatism, in diopters, with its sign. |
| vd | Vertex distance (mm) | The distance from the back of the glasses lens to the front of the eye; 12 mm is usual. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| sphere | Sphere at the new plane | The sphere power after the vertex change, to the nearest 0.25 D. |
| cylinder | Cylinder at the new plane | The cylinder power after the vertex change, to the nearest 0.25 D. |
| sphereExact | Sphere, unrounded | The sphere after the vertex change before rounding to 0.25 D. |
| cylinderExact | Cylinder, unrounded | The cylinder after the vertex change before rounding to 0.25 D. |
| matters | Does vertex matter? | Vertex changes the power noticeably when a meridian is stronger than ±4.00 D. |

## Method

Glasses to contacts: Fc = F ÷ (1 − d × F); contacts to glasses: F = Fc ÷ (1 + d × Fc); d is the vertex distance in metres. The cylinder converts both meridians (S and S + C) and subtracts.

## Assumptions

- A soft contact lens sits on the cornea, so its vertex distance is 0.
- The cylinder axis does not change.
- Contact lenses come in 0.25 D steps here; strong powers are often made in 0.50 D steps.
- This is an optical conversion, not a fitting; an eye care professional fits and prescribes contact lenses.

## Worked examples

1. from = glasses, sph = -6, vd = 12 gives sph = -5.5, sphereExact = -5.597015. Source: It matters beyond about ±4.00 D, https://en.wikipedia.org/wiki/Vertex_distance (retrieved 2026-10-05).
2. from = glasses, sph = 8, vd = 12 gives sph = 8.75, sphereExact = 8.849558. Source: It matters beyond about ±4.00 D, https://en.wikipedia.org/wiki/Vertex_distance (retrieved 2026-10-05).
3. from = glasses, sph = -5, cyl = -2, vd = 12 gives sph = -4.75, cyl = -1.75, sphereExact = -4.716981, cylinderExact = -1.740583. Source: It matters beyond about ±4.00 D, https://en.wikipedia.org/wiki/Vertex_distance (retrieved 2026-10-05).
4. from = contacts, sph = -5.5, vd = 12 gives sph = -6, sphereExact = -5.888651. Source: It matters beyond about ±4.00 D, https://en.wikipedia.org/wiki/Vertex_distance (retrieved 2026-10-05).

## FAQ

### What is vertex distance?

The gap between the back of a glasses lens and the front of the eye, usually 12 to 14 mm. A contact lens sits on the eye, so its vertex distance is 0. Moving a lens changes the power the eye gets, so a strong glasses prescription needs a different contact lens power.

### How do I convert glasses power to contact lens power?

Use Fc = F ÷ (1 − d × F), with F the glasses power in diopters and d the vertex distance in metres. A −6.00 D lens at 12 mm gives −6 ÷ (1 + 0.072) = −5.60 D, so about −5.50 D in a contact lens.

### When does vertex distance matter?

Beyond about ±4.00 D. Below that, the change is under a quarter diopter, so the contact lens power is the same as the glasses power in 0.25 D steps.

### Why is my contact lens prescription weaker than my glasses?

If you are nearsighted (a minus prescription), a lens closer to the eye needs less minus power for the same effect. If you are farsighted (a plus prescription), it needs more plus power. So minus contacts are weaker and plus contacts are stronger than the glasses.

### How does the cylinder convert?

A toric prescription has two principal meridians: the sphere, and the sphere plus the cylinder. Each converts on its own; the new cylinder is the difference of the two rounded meridians. The axis stays the same.

### Can I order contact lenses from this result?

No. A contact lens prescription also needs the base curve, diameter, lens material and a fitting check by an eye care professional. In the United States, you need a contact lens prescription to buy lenses.

## Sources

- Wikipedia. Vertex distance: the effective power formula Fc = F ÷ (1 − xF), 12 to 14 mm usual, significant beyond about ±4.00 D, retrieved 2026-10-05. https://en.wikipedia.org/wiki/Vertex_distance
- Federal Trade Commission. Buying Prescription Glasses or Contact Lenses: Your Rights (sellers may sell contact lenses only with a valid prescription), retrieved 2026-10-05. https://consumer.ftc.gov/articles/buying-prescription-glasses-or-contact-lenses-your-rights