To move a lens power to a new position, use Fc = F ÷ (1 − dF), with d in meters. Moving a plus lens closer to the eye needs more plus; a minus lens needs less minus. Conversion is usually considered from about ±4.00 D, a common practice convention. Example: −6.00 D at 12 mm becomes −5.50 D.
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The short version, with the formula and threshold, is on NCLE exam formulas and ABO exam formulas. This guide works through toric lenses, the reverse direction, and the mistakes that cost points.
What vertex distance is
Vertex distance is the gap between the back surface of a spectacle lens and the front of the cornea, in millimeters. A contact lens sits at 0 mm. Because a lens’s effect depends on where it sits, the same prescription needs a different power at a different distance.
The formula and the sign of d
Spectacle plane to contact lens plane (moving the lens closer): Fc = F ÷ (1 − dF). Contact lens plane back to the spectacle plane (moving it farther): Fs = F ÷ (1 + dF). In both, d is the vertex distance in meters (12 mm = 0.012 m) and F keeps its sign.
Check your hand answers with the vertex distance calculator. It uses the same formulas, converts each meridian, and rounds to the nearest 0.25 D.
Worked examples
Sphere, both signs (12 mm)
- −6.00 ÷ (1 − 0.012 × −6.00) = −6.00 ÷ 1.072 = −5.60 → −5.50 D
- +6.00 ÷ (1 − 0.072) = +6.00 ÷ 0.928 = +6.47 → +6.50 D
Toric: −5.00 −1.50 × 180 at 12 mm
- Find each meridian: 180 meridian −5.00 D; 090 meridian −5.00 + (−1.50) = −6.50 D.
- Convert each: −5.00 ÷ 1.060 = −4.72 → −4.75 D; −6.50 ÷ 1.078 = −6.03 → −6.00 D.
- Rewrite: sphere −4.75, cylinder −6.00 − (−4.75) = −1.25. Result −4.75 −1.25 × 180.
The cylinder dropped from −1.50 to −1.25. Converting −1.50 on its own would have left it unchanged, which is wrong.
Contact lens back to spectacles
+10.00 D at the cornea, glasses at 12 mm: +10.00 ÷ (1 + 0.12) = +8.93 → +9.00 D.
Common mistakes
- Using 12 instead of 0.012. Millimeters must become meters.
- Dropping the sign of F inside the bracket.
- Converting the cylinder instead of each meridian.
- Using the spectacle-to-contact formula in the reverse direction.
- Treating the converted power as the final lens order. Fitting and over-refraction still decide it.
Practice problems
Original problems. Round to the nearest 0.25 D.
−4.00 D spectacle at 12 mm, to the contact lens plane
Show answer
−4.00 ÷ (1 − 0.012 × −4.00) = −4.00 ÷ 1.048 = −3.82 → −3.75 D
+4.00 D spectacle at 12 mm, to the contact lens plane
Show answer
+4.00 ÷ (1 − 0.048) = +4.00 ÷ 0.952 = +4.20 → +4.25 D
−8.00 D spectacle at 10 mm, to the contact lens plane
Show answer
−8.00 ÷ (1 + 0.080) = −7.41 → −7.50 D
+12.00 D spectacle at 14 mm, to the contact lens plane
Show answer
+12.00 ÷ (1 − 0.168) = +12.00 ÷ 0.832 = +14.42 → +14.50 D
−10.00 D spectacle at 12 mm, to the contact lens plane
Show answer
−10.00 ÷ (1 + 0.120) = −8.93 → −9.00 D
Frequently asked questions
What vertex distance is assumed if none is written?
There is no official default. Many clinics and calculators, including ours, start at 12 mm, but that is a convention. If the prescription lists a vertex distance, use it; for high powers, measure it.
Does moving glasses down the nose change their power?
The lens doesn’t change, but its effect on the eye does. Sliding a plus lens farther from the eye increases its effective power; sliding a minus lens farther away decreases its effective minus. That is why some high-plus wearers push glasses down to read.
Why convert each meridian instead of the cylinder?
The formula works on total power along a line. A cylinder value is a difference between two meridians, so converting it alone gives the wrong answer. Convert both meridians, then rewrite the sphere and cylinder.
Official sources
- ABO-NCLE — ABO (NOCE) test specifications (opens in a new tab)
- ABO-NCLE — ABO and NCLE Basic exams (opens in a new tab)
Last reviewed . Requirements, fees, and dates change — always confirm with the official source before you register or apply. ABO-NCLE and IJCAHPO are the only authorities for their own exam facts, so those facts rest on a single source.