Vertex Calculator for Contact Lenses

1. Choose the direction. Most people convert a glasses prescription to contact lens power.
2. Enter the vertex distance in millimetres. Use the figure on your prescription, or 12 mm as a common default.
3. Type the sphere for each eye. Add cylinder and axis only for a prescription with astigmatism.

Results are written as sphere / cylinder x axis. A blank cylinder gives a single sphere power.

Vertex distance is the gap between the back surface of a glasses lens and the front of the cornea. Most eye tests measure the prescription with a lens held 12 to 14 mm from the eye. A contact lens sits on the tear film of the cornea, so its vertex distance is close to zero.

Moving a lens changes the power the eye receives, even though the lens itself stays the same. A minus lens moved closer to the eye acts stronger. A plus lens moved closer acts weaker. A contact lens therefore needs less minus power, or more plus power, than the glasses lens it replaces.

The effect grows with the strength of the lens. Optics references treat it as significant beyond about 4.00 D in either direction. Below that, the change is usually smaller than one 0.25 D lens step.

Vertex distance is one part of a contact lens fitting. It is not the whole fitting, and this page does not replace one.

The calculator applies the vertex correction formula to each principal meridian of the lens.

1. It turns the vertex distance from millimetres into metres.
2. It converts the sphere power with the formula. That is the first meridian.
3. For astigmatism it adds sphere and cylinder to get the second meridian, and converts that power too.
4. The new cylinder is the second converted power minus the first. The axis stays the same.
5. It rounds sphere and cylinder to the nearest 0.25 D and shows the exact values beside them.

Converting each meridian matters. Putting the cylinder number alone through the formula gives a wrong answer, because a cylinder is a difference between two powers, not a power of its own.

A glasses prescription reads -8.00 -2.50 x 90 for the right eye. The vertex distance is 13 mm, so d = 0.013.

The sphere drops by 0.75 D and the cylinder by about 0.50 D. Converting the cylinder on its own would give -2.42 D and round to -2.50 D, which overstates the astigmatism by two lens steps.

Glasses to Contact Lens Chart at 12 Mm

The chart covers sphere powers only. Plus powers change faster than minus powers of the same size.

Lens Power

Power is the largest factor. At 12 mm, -3.00 D changes by 0.10 D and stays at -3.00 D after rounding. At -10.00 D the change is 1.07 D.

Vertex Distance

A longer distance means a larger change. A -10.00 D lens gives -8.93 D at 12 mm and -8.77 D at 14 mm. Those round to -9.00 D and -8.75 D, one full lens step apart.

Sign of the Lens

Minus lenses lose power at the eye and plus lenses gain it. +4.00 D becomes +4.20 D at 12 mm, while -4.00 D becomes -3.82 D.

Astigmatism

Each meridian changes by its own amount, so the cylinder shrinks or grows with the sphere. Toric lenses are also made in a limited set of cylinder and axis steps, which a professional matches to your eye.

Rounding

The tool rounds to 0.25 D. Lens ranges differ by maker, and some high powers come only in 0.50 D steps. The exact value is shown so the rounding is visible. The rounding calculator shows the same step rounding on any number.

The two prescriptions are separate documents. A converted power is only one line of a contact lens prescription.

US consumer rules require a contact lens prescription to list the power, the base curve and, where appropriate, the diameter. Buying lenses needs a current, valid prescription.

Understanding Your Own Prescription

People often ask why their contact lens boxes show a weaker minus number than their glasses. The calculator shows the size of that gap. The percentage calculator turns the change into a share of the original power.

Studying Optics

Students of optics and optical dispensing practise this formula by hand. The exact output lets you check each step of your own working.

Checking a Change of Frame

A new frame that sits further from the eye changes the effective power of a strong lens. Enter the difference in distance to see the size of the effect. Convert small lengths with the mm to cm converter.

1. Entering Millimetres as Metres

The formula needs metres. Using 12 instead of 0.012 gives a result 1,000 times off. The tool converts the units for you.

2. Converting the Cylinder Alone

The cylinder is the gap between two meridians. Convert both meridians, then subtract.

3. Changing the Axis

Vertex distance does not rotate the lens. The axis number carries across as written.

4. Using the Wrong Direction

Glasses to contacts makes minus powers weaker. Contacts to glasses makes them stronger. A result that moves the wrong way means the direction is reversed.

5. Treating the Answer as a Prescription

The power is a starting point for a fitting. Lens shape, material and how the lens sits on the eye are set in the exam room.

The arithmetic is exact for thin lenses in air. Real fittings add factors that no power formula covers.

No. They are separate prescriptions. The contact lens power is adjusted for vertex distance, and the prescription also lists details such as base curve and diameter that glasses do not have.

Optics references treat it as significant beyond about 4.00 D. At 12 mm, -4.00 D becomes -3.82 D and rounds to -3.75 D, while -3.00 D stays at -3.00 D after rounding.

A minus lens acts stronger when it sits closer to the eye. The contact lens therefore needs less minus power to give the same focus. A -6.50 D glasses lens equals about -6.00 D on the eye at 12 mm.

They go up. A plus lens acts weaker when moved closer to the eye, so +5.00 D in glasses at 13 mm becomes +5.35 D, which rounds to +5.25 D.

An eye-care professional measures it with a small gauge called a distometer. Many prescriptions for strong lenses note it. Without a figure, 12 mm is a common default for study purposes.

No. The axis marks the direction of the astigmatism, and moving the lens along the line of sight does not rotate it. Only sphere and cylinder change.

Yes. Choose contact lenses to glasses. The tool uses F / (1 + d x F), so -5.50 D on the eye becomes -5.89 D at 12 mm and rounds to -6.00 D.

No. Contact lenses need a valid prescription written after a fitting. The result here is an educational estimate and leaves out base curve, diameter and lens type.

Most lenses are made in quarter-dioptre steps, so a prescriber picks the nearest available power. The exact value is shown beside it so you can see the rounding.

No. The maths runs in your browser and nothing is sent to us. Save keeps a result only in this browser.

• Vertex distance: definition, formula and derivation (Wikipedia; vertex correction formula, the 12 to 14 mm refraction distance and the 4.00 D threshold).
• Vertex distance lesson with a sphero-cylinder example (OpticianWorks optician training; meridian by meridian method and contact lens compensation).
• Buying Contact Lenses (US Food and Drug Administration; need for a current, valid prescription and what to check on a lens order).
• Buying Prescription Glasses or Contact Lenses: Your Rights (US Federal Trade Commission; what a contact lens prescription must include and when it is released).
• Contact Lenses for Vision Correction (American Academy of Ophthalmology; lens types, toric lenses and the need for a professional fitting).