Vertex Distance Calculator: Spectacle Rx to Contact Lens Power
This calculator converts a glasses prescription to contact lens power at the cornea, or moves a lens from one vertex distance to another, such as from the refraction to a new frame. Enter the power, the original vertex distance and the new one (0 mm for a contact lens), and it returns the compensated power. It is a tool for opticians, contact lens fitters and students, and it does not replace a contact lens fitting or prescription: the fitter chooses the lens and confirms the power on the eye.
Vertex Distance Compensation
Adjust prescription power when the lens is moved closer to or farther from the eye (e.g. spectacles → contact lenses).
Formula
F' = F / (1 − x · F), where x is the vertex-distance reduction (old VD − new VD) in meters.
Vertex distance formula
The formula is Fc = F ÷ (1 − d × F), where F is the original power in diopters, d is the reduction in vertex distance in meters (original minus new), and Fc is the compensated power. Moving a lens closer makes d positive; moving it farther away makes d negative.
The rule to remember: closer to the eye, a minus lens needs less minus and a plus lens needs more plus. Moving lenses away does the reverse.
Worked examples
Glasses to contact lens: -6.50 D at 12 mm. Fc = -6.50 ÷ (1 − 0.012 × -6.50) = -6.50 ÷ 1.078 = -6.03 D, about -6.00 D at the cornea.
Plus: +11.00 D at 13 mm. Fc = +11.00 ÷ (1 − 0.013 × 11.00) = +11.00 ÷ 0.857 = +12.84 D.
Toric: -5.00 -1.50 × 180 at 12 mm. Convert each principal meridian, running the calculator once for each: -5.00 D becomes -4.72 D and -6.50 D becomes -6.03 D. Recombined, that is -4.72 -1.31 × 180, which rounds to an available toric power such as -4.75 -1.25 × 180.
Glasses to glasses: +9.50 D refracted at 12 mm, in a frame that sits at 15 mm. Enter 12 and 15: the lens is 3 mm farther away, so it needs less plus, +9.24 D. To go from a contact lens back to glasses, enter 0 as the original distance.
When vertex compensation matters
The effect rises roughly as the square of the power. At 12 mm, -4.00 D becomes -3.82 D and +4.00 D becomes +4.20 D, about 0.20 D, which is why compensation usually starts at ±4.00 D. At high powers the vertex distance itself matters: +12.00 D works out to +14.02 D at the cornea from 12 mm but +14.42 D from 14 mm, so measure it rather than assume it.
Common mistakes
Using millimeters in the formula (12 instead of 0.012). Getting the sign of d wrong, which makes a myope more minus at the cornea instead of less. Running the cylinder value through the formula by itself instead of each principal meridian. And forgetting that the result still has to be rounded to a power the lens is made in.
Vertex distance on the NCLE and ABO exams
Vertex compensation is core material for the NCLE contact lens exam (the CLRE) and also comes up in ABO prep. Practice the formula by hand and use the rule above to rule out answers that move the wrong way. Review Converting Spectacle Rx to Contact Lens Power and Vertex Distance and Other Measurements.
Vertex distance chart: spectacle Rx to contact lens power (±4.00 to ±20.00 D)
Spectacle power converted to the corneal plane (contact lens power) from vertex distances of 10, 12 and 14 mm, computed with the calculator's formula Fc = F ÷ (1 − d × F). Each cell shows the result to 0.01 D and, in parentheses, the nearest 0.25 D step. The one value that falls exactly halfway, -15.625 D (-20.00 D at 14 mm), is printed to three decimals and rounded toward plus. Above ±6.00 D many soft lenses come only in 0.50 D steps, so use the nearest power the lens is made in.
| Spectacle power (D) | Minus Rx at 10 mm | Minus Rx at 12 mm | Minus Rx at 14 mm | Plus Rx at 10 mm | Plus Rx at 12 mm | Plus Rx at 14 mm |
|---|---|---|---|---|---|---|
| ±4.00 | -3.85 (-3.75) | -3.82 (-3.75) | -3.79 (-3.75) | +4.17 (+4.25) | +4.20 (+4.25) | +4.24 (+4.25) |
| ±4.50 | -4.31 (-4.25) | -4.27 (-4.25) | -4.23 (-4.25) | +4.71 (+4.75) | +4.76 (+4.75) | +4.80 (+4.75) |
| ±5.00 | -4.76 (-4.75) | -4.72 (-4.75) | -4.67 (-4.75) | +5.26 (+5.25) | +5.32 (+5.25) | +5.38 (+5.50) |
| ±5.50 | -5.21 (-5.25) | -5.16 (-5.25) | -5.11 (-5.00) | +5.82 (+5.75) | +5.89 (+6.00) | +5.96 (+6.00) |
| ±6.00 | -5.66 (-5.75) | -5.60 (-5.50) | -5.54 (-5.50) | +6.38 (+6.50) | +6.47 (+6.50) | +6.55 (+6.50) |
| ±6.50 | -6.10 (-6.00) | -6.03 (-6.00) | -5.96 (-6.00) | +6.95 (+7.00) | +7.05 (+7.00) | +7.15 (+7.25) |
| ±7.00 | -6.54 (-6.50) | -6.46 (-6.50) | -6.38 (-6.50) | +7.53 (+7.50) | +7.64 (+7.75) | +7.76 (+7.75) |
| ±7.50 | -6.98 (-7.00) | -6.88 (-7.00) | -6.79 (-6.75) | +8.11 (+8.00) | +8.24 (+8.25) | +8.38 (+8.50) |
| ±8.00 | -7.41 (-7.50) | -7.30 (-7.25) | -7.19 (-7.25) | +8.70 (+8.75) | +8.85 (+8.75) | +9.01 (+9.00) |
| ±8.50 | -7.83 (-7.75) | -7.71 (-7.75) | -7.60 (-7.50) | +9.29 (+9.25) | +9.47 (+9.50) | +9.65 (+9.75) |
| ±9.00 | -8.26 (-8.25) | -8.12 (-8.00) | -7.99 (-8.00) | +9.89 (+10.00) | +10.09 (+10.00) | +10.30 (+10.25) |
| ±9.50 | -8.68 (-8.75) | -8.53 (-8.50) | -8.38 (-8.50) | +10.50 (+10.50) | +10.72 (+10.75) | +10.96 (+11.00) |
| ±10.00 | -9.09 (-9.00) | -8.93 (-9.00) | -8.77 (-8.75) | +11.11 (+11.00) | +11.36 (+11.25) | +11.63 (+11.75) |
| ±10.50 | -9.50 (-9.50) | -9.33 (-9.25) | -9.15 (-9.25) | +11.73 (+11.75) | +12.01 (+12.00) | +12.31 (+12.25) |
| ±11.00 | -9.91 (-10.00) | -9.72 (-9.75) | -9.53 (-9.50) | +12.36 (+12.25) | +12.67 (+12.75) | +13.00 (+13.00) |
| ±11.50 | -10.31 (-10.25) | -10.11 (-10.00) | -9.91 (-10.00) | +12.99 (+13.00) | +13.34 (+13.25) | +13.71 (+13.75) |
| ±12.00 | -10.71 (-10.75) | -10.49 (-10.50) | -10.27 (-10.25) | +13.64 (+13.75) | +14.02 (+14.00) | +14.42 (+14.50) |
| ±12.50 | -11.11 (-11.00) | -10.87 (-10.75) | -10.64 (-10.75) | +14.29 (+14.25) | +14.71 (+14.75) | +15.15 (+15.25) |
| ±13.00 | -11.50 (-11.50) | -11.25 (-11.25) | -11.00 (-11.00) | +14.94 (+15.00) | +15.40 (+15.50) | +15.89 (+16.00) |
| ±13.50 | -11.89 (-12.00) | -11.62 (-11.50) | -11.35 (-11.25) | +15.61 (+15.50) | +16.11 (+16.00) | +16.65 (+16.75) |
| ±14.00 | -12.28 (-12.25) | -11.99 (-12.00) | -11.71 (-11.75) | +16.28 (+16.25) | +16.83 (+16.75) | +17.41 (+17.50) |
| ±14.50 | -12.66 (-12.75) | -12.35 (-12.25) | -12.05 (-12.00) | +16.96 (+17.00) | +17.55 (+17.50) | +18.19 (+18.25) |
| ±15.00 | -13.04 (-13.00) | -12.71 (-12.75) | -12.40 (-12.50) | +17.65 (+17.75) | +18.29 (+18.25) | +18.99 (+19.00) |
| ±15.50 | -13.42 (-13.50) | -13.07 (-13.00) | -12.74 (-12.75) | +18.34 (+18.25) | +19.04 (+19.00) | +19.80 (+19.75) |
| ±16.00 | -13.79 (-13.75) | -13.42 (-13.50) | -13.07 (-13.00) | +19.05 (+19.00) | +19.80 (+19.75) | +20.62 (+20.50) |
| ±16.50 | -14.16 (-14.25) | -13.77 (-13.75) | -13.40 (-13.50) | +19.76 (+19.75) | +20.57 (+20.50) | +21.46 (+21.50) |
| ±17.00 | -14.53 (-14.50) | -14.12 (-14.00) | -13.73 (-13.75) | +20.48 (+20.50) | +21.36 (+21.25) | +22.31 (+22.25) |
| ±17.50 | -14.89 (-15.00) | -14.46 (-14.50) | -14.06 (-14.00) | +21.21 (+21.25) | +22.15 (+22.25) | +23.18 (+23.25) |
| ±18.00 | -15.25 (-15.25) | -14.80 (-14.75) | -14.38 (-14.50) | +21.95 (+22.00) | +22.96 (+23.00) | +24.06 (+24.00) |
| ±18.50 | -15.61 (-15.50) | -15.14 (-15.25) | -14.69 (-14.75) | +22.70 (+22.75) | +23.78 (+23.75) | +24.97 (+25.00) |
| ±19.00 | -15.97 (-16.00) | -15.47 (-15.50) | -15.01 (-15.00) | +23.46 (+23.50) | +24.61 (+24.50) | +25.89 (+26.00) |
| ±19.50 | -16.32 (-16.25) | -15.80 (-15.75) | -15.32 (-15.25) | +24.22 (+24.25) | +25.46 (+25.50) | +26.82 (+26.75) |
| ±20.00 | -16.67 (-16.75) | -16.13 (-16.25) | -15.625 (-15.50) | +25.00 (+25.00) | +26.32 (+26.25) | +27.78 (+27.75) |
Frequently asked questions
How do I convert a glasses prescription to contact lens power?
Convert each principal meridian with Fc = F ÷ (1 − d × F), using the vertex distance in meters, then round to a power the lens is made in. Below ±4.00 D the change is usually too small to matter. A contact lens prescription also requires a fitting by an eye care practitioner, who chooses the lens, base curve and diameter and checks the power on the eye.
What is a normal vertex distance?
Most spectacle lenses sit about 12 to 14 mm from the cornea. For high prescriptions, the vertex distance used during the refraction should be recorded, because the prescribed power gives the intended correction only at that distance.
Why does a nearsighted person need less minus in contact lenses?
A minus lens has a stronger effect the closer it is to the eye, so less minus power gives the same correction at the cornea. At a 12 mm vertex distance, -9.00 D in glasses works out to about -8.12 D at the cornea.
How do I convert a toric prescription to contact lens power?
Convert each principal meridian separately, then recombine them. At 12 mm, -5.00 -1.50 × 180 has meridians of -5.00 D and -6.50 D, which become -4.72 D and -6.03 D at the cornea: -4.72 -1.31 × 180, ordered as the nearest toric power made, such as -4.75 -1.25 × 180. The axis does not change with vertex distance, but a soft toric lens can rotate on the eye, which the fitter checks and corrects for.
Does vertex distance matter for plus lenses?
Yes, and the effect grows with the plus power: +10.00 D at 12 mm is +11.36 D at the cornea. It matters between frames too. A strong plus lens that sits farther from the eye than the refraction did acts stronger, so the ordered power may need to come down.
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