What is my contact lens vertex?
Type the sphere, the cylinder if you have one, and the vertex distance. The contact lens vertex calculator moves the power from the glasses plane to the eye (or back) and rounds it to the 0.25 D steps lenses come in. It is an optical conversion, not a contact lens fitting.
- Sphere at the new plane
- -5.5
A -5.5 D sphere at the new plane.
- Sphere, unrounded
- -5.597
- Does vertex matter?
- Yes: the power is over ±4.00 D
Sphere at the new plane: -5.5. A -5.5 D sphere at the new plane.
This calculator gives general information only. It is not medical advice and does not replace a doctor or other health care provider. Talk with a professional about your results. Terms of use
How to calculate
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.
Example with the default inputs (Convert from Glasses, Sphere (D) -6, Vertex distance (mm) 12): A -5.5 D sphere at the new plane.
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.
- 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
Each example is checked against the calculator on every build.
- Convert from Glasses, Sphere (D) -6, Vertex distance (mm) 12 gives Sphere (D) -5.5, Sphere, unrounded -5.597015.Source: It matters beyond about ±4.00 D, https://en.wikipedia.org/wiki/Vertex_distance (retrieved 2026-10-05)
- Convert from Glasses, Sphere (D) 8, Vertex distance (mm) 12 gives Sphere (D) 8.75, Sphere, unrounded 8.849558.Source: It matters beyond about ±4.00 D, https://en.wikipedia.org/wiki/Vertex_distance (retrieved 2026-10-05)
- Convert from Glasses, Sphere (D) -5, Cylinder (D) -2, Vertex distance (mm) 12 gives Sphere (D) -4.75, Cylinder (D) -1.75, Sphere, unrounded -4.716981, Cylinder, unrounded -1.740583.Source: It matters beyond about ±4.00 D, https://en.wikipedia.org/wiki/Vertex_distance (retrieved 2026-10-05)
- Convert from Contacts, Sphere (D) -5.5, Vertex distance (mm) 12 gives Sphere (D) -6, Sphere, unrounded -5.888651.Source: It matters beyond about ±4.00 D, https://en.wikipedia.org/wiki/Vertex_distance (retrieved 2026-10-05)
How it works
Powers are in diopters (D). The vertex distance d is typed in millimetres and used in metres (d = mm ÷ 1000).
- Glasses to contacts (moving the lens d metres toward the eye): Fc = F ÷ (1 − d × F).
- Contacts to glasses (moving it d metres away): F = Fc ÷ (1 + d × Fc).
- Cylinder. The two principal meridians are the sphere S and S + C. Each is converted with the formula above. The new sphere is the converted S, rounded. The new cylinder is (converted S + C, rounded) − (converted S, rounded). With no cylinder, or a cylinder of 0, no cylinder is shown. The axis does not change.
- Rounding. Each converted meridian rounds to the nearest 0.25 D. A value exactly halfway between two steps rounds away from zero (−5.125 becomes −5.25). The unrounded values also show, to 3 decimals, rounded half up (away from zero).
- Does vertex matter? “Yes” when the sphere, or the second meridian S + C, is stronger than ±4.00 D (above +4 or below −4); “Little” otherwise.
Rules. Sphere from −25 to +25 D; cylinder from −10 to +10 D; vertex distance from 5 to 20 mm. If 1 − d × F (or 1 + d × Fc) is 0 or less, there is no answer.
Exact arithmetic. The typed powers and distance are exact decimals; the conversion is done in exact fractions and rounded once.
Assumptions
- Thin-lens optics; the contact lens sits on the cornea (vertex 0).
- Lenses in 0.25 D steps; very strong lenses are often made only in 0.50 D steps.
Worked examples by hand
−6.00 D glasses at 12 mm. d = 0.012. Fc = −6 ÷ (1 − 0.012 × (−6)) = −6 ÷ 1.072 = −5.597 D. Nearest step: −5.50 (0.097 away) rather than −5.75 (0.153 away), so −5.50 D. The power is over ±4.00 D, so vertex matters.
+8.00 D glasses at 12 mm. Fc = 8 ÷ (1 − 0.096) = 8 ÷ 0.904 = 8.850 D. Nearest step 8.75 D.
−5.00 −2.00 at 12 mm. Meridians −5 and −7. −5 ÷ 1.06 = −4.717, rounded −4.75. −7 ÷ 1.084 = −6.458, rounded −6.50. Cylinder = −6.50 − (−4.75) = −1.75. Unrounded: sphere −4.717, cylinder −6.458 − (−4.717) = −1.741.
−5.50 D contact lens back to glasses at 12 mm. F = −5.5 ÷ (1 + 0.012 × (−5.5)) = −5.5 ÷ 0.934 = −5.889 D. Nearest step −6.00 D.
Other questions people ask
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.