# Contact Lens Vertex Calculator

URL: https://speedycalculator.com/calculators/physics/contact-lens-vertex/
Last updated: 2026-10-30

> The contact lens vertex calculator converts a spectacle prescription to the equivalent contact lens power for each eye, correcting for the vertex distance – for spherical and toric (astigmatic) prescriptions.

## Inputs

- Vertex distance (mm, cm, m, in, µm)
- Right eye sphere (D)
- Right eye cylinder (D)
- Left eye sphere (D)
- Left eye cylinder (D)

## Results

- Right eye contact lens sphere
- Right eye contact lens cylinder
- Left eye contact lens sphere
- Left eye contact lens cylinder

## Formula

```
F_c = F_s / (1 − d·F_s)  (d in metres; applied to each principal meridian)
```

## Explanation

Glasses sit about 12 mm in front of the eye, contact lenses directly on it. For prescriptions stronger than about ±4 D this distance matters: a −8.00 D spectacle lens corresponds to about −7.30 D in a contact lens. Eye-care professionals make this vertex conversion when fitting lenses.

### How to use the Contact Lens Vertex Calculator

- **Vertex distance**
- **Right eye sphere (D)**
- **Right eye cylinder (D)**
- **Left eye sphere (D)**
- **Left eye cylinder (D)**

This is an optics conversion for education. Contact lenses must be fitted and prescribed by an eye-care professional. Everything is calculated in your browser.

### How it works

Enter the sphere and cylinder for each eye and the vertex distance of the spectacles (usually 12 mm). Each principal meridian is converted separately and the cylinder recombined.

### Inputs explained

FieldWhat to enterVertex distanceUnits: mm, cm, m, in, µmRight eye sphere (D)A numberRight eye cylinder (D)A numberLeft eye sphere (D)A numberLeft eye cylinder (D)A number

### What each result means

- **Right eye contact lens sphere** = [Right eye sphere (D)]÷(1 - [Vertex distance]×[Right eye sphere (D)])
- **Right eye contact lens cylinder** = ([Right eye sphere (D)] + [Right eye cylinder (D)])÷(1 - [Vertex distance]×([Right eye sphere (D)] + [Right eye cylinder (D)])) - [Right eye contact lens sphere]
- **Left eye contact lens sphere** = [Left eye sphere (D)]÷(1 - [Vertex distance]×[Left eye sphere (D)])
- **Left eye contact lens cylinder** = ([Left eye sphere (D)] + [Left eye cylinder (D)])÷(1 - [Vertex distance]×([Left eye sphere (D)] + [Left eye cylinder (D)])) - [Left eye contact lens sphere]

### Example values

How the main result changes when **Vertex distance** changes and everything else stays at the example values above:

Vertex distance (mm)Right eye contact lens sphere (D)6-5.799-5.6912-5.615-5.518-5.4224-5.24

## Worked example

Inputs — Vertex distance: 12 mm; Right eye sphere (D): -6; Right eye cylinder (D): -1.5; Left eye sphere (D): -5.5; Left eye cylinder (D): 0.

Results — **Right eye contact lens sphere = -5.6 D**; Right eye contact lens cylinder = -1.28 D; Left eye contact lens sphere = -5.16 D; Left eye contact lens cylinder = 0 D.

## Key terms

- **Vertex distance**: Distance from the back of a spectacle lens to the cornea.

## FAQ

**When does vertex distance matter?**
For powers above about ±4.00 D.

**Why are minus contact lenses weaker than glasses?**
Moving a minus lens closer to the eye increases its effective power.

**Can I order contact lenses with this?**
No – contact lenses need a fitting and prescription from an eye-care professional.

**What is a toric lens?**
A lens with different powers in two meridians, correcting astigmatism.


## Sources

- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)
- [American Academy of Ophthalmology – Optics](https://www.aao.org/)