Vertex distance calculator

What vertex distance does

The power printed on a pair of glasses is measured at the back surface of the lens, about a centimeter in front of the eye. A contact lens sits on the eye itself. For weak prescriptions the difference is too small to matter, but for strong ones it is large enough to change what the eye sees, so the power has to be converted. The usual direction is glasses to contact lens; the reverse is needed when someone who wears contacts orders their first strong glasses.

The formula

For a lens of power F (in diopters) moved a distance d (in meters) toward the eye, the equivalent power is Fc = F ÷ (1 − d × F). It follows from vergence: light that the glasses bring to a focus at 1/F meters behind the lens is already 1/F − d meters from the new position, so the new lens needs 1/(1/F − d). Moving the lens away from the eye changes the sign of d, giving F ÷ (1 + d × F). Because power differs between meridians, the formula is applied to each principal meridian: the sphere (along the axis) and sphere plus cylinder (at right angles). The new cylinder is the difference, the axis is unchanged, and the results are rounded to the nearest 0.25 D.

Worked example

Contact Lens Spectrum’s toric-lens article uses −3.00 −3.00 × 015 at 12 mm. The meridian along 15° is −3.00 D: below 4.00 D, so it stays as written (the exact value, −2.90 D, rounds back to −3.00 D). The other meridian is −6.00 D: 0.012 × 6 = 0.072, so Fc = −6 ÷ 1.072 = −5.60 D, which rounds to −5.50 D. The cylinder is the difference, −5.50 − (−3.00) = −2.50, so the lens is −3.00 −2.50 × 015, the same figure the article reports. A pure sphere works the same way: −5.00 D at 12 mm gives −4.72 D, rounded to −4.75 D. A plus lens strengthens: +10.00 D becomes +11.36 D, or +11.25 D.

How big the change is at 12 mm

The shift grows roughly with the square of the power (it is d × F² for small d), which is why it is negligible at 2 D and large at 10 D or more. Below the 4.00 D mark the exact difference stays under a quarter diopter at 12 mm; above it, the difference passes the 0.25 D step of most contact lens powers.

Limits and common mistakes

• Converting the cylinder directly. Applying the formula to the cylinder number alone gives the wrong answer, because the cylinder is a difference of two meridian powers. Convert the meridians, then subtract.
• Compensating weak lenses. Below 4.00 D the shift is under a quarter diopter at 12 mm; for example −2.00 D moves by only 0.05 D. Lai (2019) advises vertexing only the meridians stronger than 4.00 D, and the calculator tells you which case you are in.
• Assuming 12 mm for everyone. The distance depends on the frame and the nose. A few millimeters off barely matters at 5 D, but it matters at 12 D.
• Treating a conversion as a lens order. A contact lens also depends on curve, diameter, toric stabilization and available powers. Cylinder choices may be limited to what the manufacturer makes, and Lai suggests choosing the lower available cylinder to avoid overcorrecting astigmatism. The conversion is a starting number for a trained fitter.

Common questions

What is vertex distance?

It is the distance between the back surface of a spectacle lens and the front of the cornea. Because the power of a strong lens depends on where it sits relative to the eye, the same lens moved closer to the eye or farther from it focuses differently. A contact lens sits on the cornea, so its distance is effectively zero.

Why do minus glasses become weaker as contact lenses?

Moving a minus lens toward the eye makes its effect on the eye stronger than its label, so a weaker lens is needed to do the same job. For −5.00 D at 12 mm the exact figure is −4.72 D, which rounds to −4.75 D. Plus lenses go the other way: +10.00 D in glasses becomes about +11.36 D, or +11.25 D rounded, as a contact lens.

Do I need vertex compensation below 4 diopters?

Usually not. Contact Lens Spectrum (Lai, 2019) says compensation is required for each meridian stronger than 4.00 D. The reason is size: at 12 mm a −2.00 D lens shifts by only 0.05 D, below the 0.25 D step contact lenses are made in. The calculator still shows the exact numbers so you can see how small the change is.

How is the cylinder handled?

Each principal meridian is converted on its own, because each has its own power: the sphere along the axis and sphere plus cylinder at right angles. The new cylinder is the difference between the two converted meridians, and the axis stays the same. That is why the cylinder of a −3.00 −3.00 prescription does not shrink by the same amount as the sphere.

What vertex distance should I enter?

The measured distance from your own frame and face. The worked examples here use 12 mm, the value in the Contact Lens Spectrum example, and the calculator accepts 0 to 30 mm. A distance is measured by your eye-care professional; the vertex distance of a frame sitting differently on the nose changes with fit.

Can I go from contact lens power back to glasses?

Yes, choose “Contact lens to glasses.” The lens moves away from the eye, so the formula becomes F ÷ (1 + d × F). Round-tripping −5.00 D through −4.75 D and back gives −5.00 D, within a quarter-diopter of where it started, because of the rounding to 0.25 D.

See also the spherical equivalent calculator for plus and minus cylinder forms, the lens thickness calculator and the thin lens calculator for the optics behind the formula.

For general information only — not medical advice. Conversions here are educational; they are not a prescription or a contact lens fitting, and a prescription must come from an eye-care professional. Sources: the vergence relation F ÷ (1 − d × F) from standard geometric optics; the 4.00 D threshold and the −3.00 −3.00 × 015 worked example from “Take a Turn With Soft Toric Lenses for Astigmatism,” Contact Lens Spectrum, September 2019 (vol. 34, pp. 25–30). How we check our calculators.