NCLE math is a short list: convert glasses power to the eye (vertex) above about ±4.00 D, convert keratometry between diopters and millimeters (337.5 ÷ value), work out the tear lens for rigid lenses (steeper add minus, flatter add plus), and correct toric rotation with LARS. These skills sit inside ABO-NCLE’s Prefitting, Diagnostic Fitting and Follow-Up domains.
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Where the math shows up
ABO-NCLE’s CLRE outline has eight domains. The math below mostly sits in Prefitting (15 questions), Diagnostic Fitting (11) and Follow-Up (20). Distances in formulas are in meters unless it says otherwise.
Vertex conversion
Contact lens power = F ÷ (1 − d × F), where F is the glasses power and d is the vertex distance in meters (12 mm = 0.012). Do each main meridian separately.
- −6.00 D at 12 mm: −6 ÷ (1 + 0.072) = −5.60 D, so about −5.50 D.
- +6.00 D at 12 mm: 6 ÷ (1 − 0.072) = +6.47 D, so about +6.50 D.
- Rule of thumb: myopes need less minus in a contact lens; hyperopes need more plus.
Try it: vertex distance calculator.
Keratometry: diopters and millimeters
- Radius (mm) = 337.5 ÷ K (D), and K = 337.5 ÷ radius. 44.00 D ≈ 7.67 mm.
- Corneal cylinder = steep K − flat K. Readings of 43.00 @ 180 and 44.50 @ 090 mean 1.50 D of corneal cylinder, with-the-rule (steepest near 90).
- Near 7.50–8.00 mm, a 0.05 mm change is about 0.25 D.
Practice reading mires: keratometer simulator · keratometry basics.
Tear lens (SAM-FAP)
A rigid lens traps a layer of tears that acts like its own lens. Steeper Add Minus, Flatter Add Plus. Each diopter the base curve is steeper than flat K adds about +1.00 D of tear lens, so the contact lens needs about 1.00 D more minus.
Example: flat K 43.00 D, glasses −3.00 D (no vertexing needed), base curve 43.50 D (0.50 D steeper). Tear lens ≈ +0.50 D, so lens power ≈ −3.00 + (−0.50) = −3.50 D.
Toric rotation (LARS)
Left Add, Right Subtract. Look at the lens marking from your side of the slit lamp. If it has rotated 10 degrees to your left, add 10 to the prescribed axis; if it has rotated 10 degrees to your right, subtract 10. Example: prescribed axis 180, marking rotates 10 degrees right: order axis 170.
Other numbers to know
- Spherical equivalent = sphere + (cylinder ÷ 2), often used for a soft spherical lens when the cylinder is small. Calculator.
- Oxygen transmissibility (Dk/t) = the material’s permeability (Dk) ÷ its thickness. Thinner lenses or higher-Dk materials let more oxygen through.
- Residual astigmatism (rough check) with a rigid spherical lens ≈ refractive cylinder − corneal cylinder, after both are compared at the same plane.
Frequently asked questions
Is there a lot of math on the NCLE exam?
ABO-NCLE does not publish a count of math questions. Its CLRE outline is organized by tasks such as prefitting, diagnostic fitting, dispensing and follow-up, and contact lens calculations come up inside those tasks.
When do you need to vertex a prescription for contact lenses?
When the glasses power is stronger than about ±4.00 D in a meridian. Below that, the change from moving the correction to the eye is less than a quarter diopter. Use F ÷ (1 − d × F) with d in meters.
See also: Vertex distance calculator
What does SAM-FAP mean?
Steeper Add Minus, Flatter Add Plus. If a rigid lens base curve is steeper than K, the tear lens is plus, so you add minus to the lens power. If it is flatter than K, add plus.
What does LARS mean for toric lenses?
Left Add, Right Subtract. Look at the lens on the eye: if the marking rotates to your left (clockwise from your view), add the amount of rotation to the axis; if it rotates to your right, subtract it.
How do you convert keratometry from diopters to millimeters?
Divide 337.5 by the value. 337.5 ÷ 45.00 D = 7.50 mm, and 337.5 ÷ 7.50 mm = 45.00 D.
See also: Keratometer simulator
Official sources
- ABO-NCLE Exam Handbooks page: Basic Exam Handbook (October 2026 edition, linked from the Oct–Dec 2026 registration pages) (opens in a new tab)
- ABO-NCLE — Basic Exam overview (opens in a new tab)
- ABO-NCLE — NCLE Basic Examination, Oct–Dec 2026 registration (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.