Contact Lens Vertex Calculator (glasses prescription to contact lens power)

Understanding the contact lens vertex calculator — concept and principle

This calculator converts a glasses prescription to the power needed at the eye for a contact lens, correcting for vertex distance. It handles sphere and cylinder, shows the results rounded to the nearest 0.25 D, the spherical equivalent and the change in sphere, and says whether a vertex correction is usually needed. Optometry students and contact lens wearers curious about their prescription use it.

12 mm closer to the eye — with the default inputs: −5.50 −0.75 × 180.

How it is calculated

Effective power at the eye: Fc = F ÷ (1 − d × F), with F in dioptres and d in metres
Meridian 1 = sphere; meridian 2 = sphere + cylinder; each is converted separately
Contact lens sphere = converted meridian 1; cylinder = converted meridian 2 − converted meridian 1; the axis is unchanged
Spherical equivalent = average of the two converted meridians
Vertex correction is usually needed when either meridian exceeds ±4.00 D

The principle

A spectacle lens sits about 12 mm in front of the eye, while a contact lens sits on it. Moving a lens closer to the eye changes the power needed to focus light at the same point: minus powers for short sight become weaker, and plus powers for long sight become stronger. The effect grows with the power and the distance; below about ±4.00 D it is smaller than a quarter dioptre, the usual prescribing step, and is ignored.

Worked example

Defaults: −6.00 −1.00 × 180, vertex distance 12 mm.

Meridian 1: −6.00 ÷ (1 + 0.012 × 6) = −6.00 ÷ 1.072 = -5.6 D.
Meridian 2: −7.00 ÷ 1.084 = −6.458 D; cylinder = −6.458 − (−5.597) = -0.86 D; axis 180.
Rounded: sphere -5.5, cylinder -0.75.
Spherical equivalent = -6.03 D; change in sphere = 0.4 D.
Over ±4.00 D: Yes — over ±4.00 D.

Each point is the calculator re-run with only “Glasses sphere (D)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Glasses sphere (D)	Contact lens sphere (D)
-1.5	-1.47
-3	-2.9
-4.5	-4.27
-6	-5.6
-7.5	-6.88
-9	-8.12
-12	-10.49

How to read the result

This is the optical starting point only. The final contact lens power, base curve, diameter and toric design are set by an eye-care professional after a trial fitting and over-refraction. Small cylinders are sometimes left uncorrected with spherical lenses, depending on vision and comfort.

Common mistakes

Converting the cylinder directly instead of each meridian.
Using millimetres instead of metres in the formula.
Ordering lenses from a glasses prescription without a fitting.
Forgetting that the axis does not change.

Keep in mind: Not a contact lens prescription. Contact lenses must be fitted by a qualified eye-care professional to avoid eye damage.

Frequently asked questions

Why is my contact lens power lower than my glasses?

For minus prescriptions, moving the lens closer to the eye reduces the power needed.

When does vertex distance matter?

Usually when the power is above ±4.00 D in either meridian.

Can I use my glasses prescription to buy contacts?

No. A contact lens fitting is needed to set power, fit and design.

Sources: Effective-power (vertex distance) formula of geometric optics, F₂ = F₁ ÷ (1 − x·F₁), and the ±4.00 D rule ("Vertex distance conversion" chart, Eyes On Eyecare)

Checked 9 Nov 2026. Effective-power (vertex distance) formula of geometric optics, F₂ = F₁ ÷ (1 − x·F₁), and the ±4.00 D rule, as given in “Vertex distance conversion: downloadable cheat sheet”, Eyes On Eyecare (12 mm vertex distance chart); meridian-by-meridian conversion of cylinders is standard optics.

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