Vertex distance calculator

Vertex conversion finds the power a lens needs at a new distance from the eye, using Fc = F ÷ (1 − d·F) with d in meters, so a spectacle prescription can be changed to a contact lens power at the cornea, or back.

Calculator

Vertex conversion

Enter the prescription and vertex distance. Each meridian is converted, then rounded to the nearest 0.25 D.

0 if none.
Ignored with 0 cyl.
Back of the spectacle lens to the cornea. Use the measured distance.

Works on your device: nothing you type is saved or sent anywhere.

When vertex distance matters

As a rule of thumb, vertex distance matters for higher powers and can be ignored for low ones. The calculator shows whether the converted power rounds to a different 0.25 D step. Minus powers need less minus at the cornea; plus powers need more plus. Use the vertex distance actually measured for the patient.

Worked example

A −10.00 D spectacle lens worn at 12 mm (0.012 m):

  • Fc = −10.00 ÷ (1 − 0.012 × −10.00) = −10.00 ÷ 1.12 = −8.93 D
  • Nearest 0.25 D: −9.00 D at the cornea

For a toric prescription, convert each meridian. −6.00 −2.00 × 180 at 12 mm: −6.00 → −5.60 (−5.50) and −8.00 → −7.30 (−7.25), so the result is −5.50 −1.75 × 180.

Common mistakes

  • Using millimeters in the formula. Change 12 mm to 0.012 m first.
  • Vertexing only the sphere of an astigmatic prescription. Convert both meridians.
  • Getting the sign wrong in 1 − d·F: with a minus lens the denominator is more than 1.
  • Rounding the cylinder on its own. Round each meridian, then take the difference.
  • Treating the converted number as the final order. Confirm with the fit and over-refraction.

Frequently asked questions

What is vertex distance?

Vertex distance is the gap between the back of the spectacle lens and the front of the eye (the cornea). Use the distance actually measured for that patient and frame.

When does vertex distance matter for contact lenses?

As a rule of thumb, it matters for higher powers and can be ignored for low ones. A quick test: if the converted power rounds to a different 0.25 D step than the spectacle power, the change matters. −3.00 D at 12 mm stays −3.00 D; −10.00 D becomes −9.00 D.

What is the vertex distance formula?

Fc = F ÷ (1 − d × F), where F is the spectacle power, d is the vertex distance in meters and Fc is the effective power at the cornea. For example, −10.00 D at 12 mm gives −10.00 ÷ (1 + 0.12) = −8.93 D.

Why do nearsighted people need less minus in contact lenses?

Because a minus lens acts stronger as it moves closer to the eye, so the contact lens needs less minus than the glasses. A plus lens acts weaker as it moves closer, so a farsighted patient needs more plus in contacts: +10.00 D at 12 mm becomes about +11.36 D at the cornea.

How do you vertex an astigmatic (toric) prescription?

Convert each principal meridian separately, then rebuild the prescription. For −6.00 −2.00 × 180 at 12 mm, the meridians −6.00 and −8.00 become about −5.60 and −7.30, which rounds to −5.50 −1.75 × 180. Do not vertex only the sphere.

How do you convert a contact lens power back to a spectacle power?

Use the reverse formula: Fs = F ÷ (1 + d × F), with d in meters. For example, a −8.93 D power at the cornea is about −10.00 D in a spectacle lens worn at 12 mm.

Is the vertex-converted power the final contact lens power?

No. It is a starting point. The final contact lens power depends on the lens design, the fit and an over-refraction, and the prescriber decides what is ordered.

More free optician tools

Studying for certification? See the ABO certification guide and the NCLE certification guide.

References

Calculators are study aids. Always verify finished eyewear with your instruments and follow your practice's procedures. More optical calculators.

Independent study resource

Not affiliated with or endorsed by ABO-NCLE, IJCAHPO, or any state board. Not medical advice. Practice questions are original and don't guarantee a passing score. Verify current requirements with the official source. Read the full disclaimer.

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