Lens Power and Base Curve: Front Curve, Back Curve, and Nominal Power

A diopter is one divided by the focal length in meters, so +2.00 D focuses at 50 cm. Each surface’s power depends on its index and radius, and Brooks and Borish add the two for a thin-lens estimate. The base curve sets the lens form and is chosen to suit the lens’s power range.

Last checked Nov 2, 2026. Confirm fees and dates with the certifying body. optical.education is independent and is not affiliated with or endorsed by the American Board of Opticianry and National Contact Lens Examiners (ABO-NCLE). Disclaimer.

Diopters and focal length

Lens power in diopters is the reciprocal of the focal length in meters: D = 1 ÷ f. Shorter focal length, stronger lens. A +2.00 D lens focuses parallel light 1 ÷ 2 = 0.50 m behind it; a −5.00 D lens diverges light as if from 0.20 m in front. Try values in the vergence calculator and see vergence.

Surface powers

Each surface has its own power. It depends on the material’s index and the surface’s radius: power = (n − 1) ÷ r for a surface in air, with r in meters. A surface with r = 0.10 m on n = 1.50 material: 0.50 ÷ 0.10 = 5.00 D. Convex surfaces are plus; concave surfaces are minus.

Nominal vs true power

Brooks and Borish describe nominal power as the sum of the two surface powers, F₁ + F₂, treating the lens as having no thickness. That works for thin, low-powered lenses. For stronger or thicker lenses, thickness changes the result, so the true power differs from the simple sum.

Using the Brooks method of adding surface powers:

• Front +6.00, back −4.00: +2.00 D.
• Need −3.00 D on a +4.00 front: back = −3.00 − 4.00 = −7.00 D.

Base curve basics

The base curve is the curve that sets the lens form, and base curves change with the power range. Brooks and Borish place the base curve of a single vision spectacle lens on the front, with the back curve ground to reach the prescription.

Practice set

Original problems.

1. Focal length of a +5.00 D lens?

   Show answer

   1 ÷ 5.00 = 0.20 m (20 cm).

2. A lens focuses parallel light 40 cm behind it. Power?

   Show answer

   1 ÷ 0.40 = +2.50 D.

3. Using the Brooks method, front +8.00, back −2.50. Nominal power?

   Show answer

   +8.00 + (−2.50) = +5.50 D.

4. Using the Brooks method, you need +1.00 D with a +6.00 base curve. What back curve?

   Show answer

   +1.00 − 6.00 = −5.00 D.

5. A surface on n = 1.60 material has r = 0.12 m. Its power?

   Show answer

   0.60 ÷ 0.12 = 5.00 D.

Keep studying: ABO certification overview, how to study for the ABO, ABO exam formulas, the last-week study plan and the free ABO practice test. Course options are on courses.

Standard text used for this page: Brooks CW, Borish IM. System for Ophthalmic Dispensing, 3rd ed. Butterworth-Heinemann, ch. 12 and 13 (nominal power, base curve), and ch. 18 (blank base curves by power). The NAO lens powers course and the Iowa optics review are linked under sources.

See ABO and NCLE courses ($89 bundle) →