Lens Thickness and the Sag Formula for Opticians

Sagitta is how deep a curve is over a given width, roughly y² × F ÷ (2000 × (n − 1)), with y the half-diameter in mm. Brooks and Borish use the sag to estimate how much thicker a minus edge or a plus center gets. A higher index material makes the edge thinner.

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.

Sagitta

Brooks and Borish define sagitta (sag) as the depth of a curve over a chord. For a given diameter, a steeper curve has more sag.

Approximate formula

s ≈ y² × F ÷ (2000 × (n − 1)), with s and y in millimeters (y is half the diameter), F in diopters and n the refractive index. It comes from the simpler s ≈ y² ÷ 2r and is most accurate for small diameters and weaker curves. Use the absolute value of F.

Minus edge vs plus center

Brooks and Borish (ch. 13) build thickness estimates from the sag:

Minus: edge ≈ center thickness + sag. −6.00 D, n 1.50, 50 mm (y 25), center 2.0 mm: 625 × 6 ÷ 1000 = 3.75, so the edge is about 5.75 mm.
Plus: center ≈ edge + sag. +4.00 D, n 1.50, 50 mm, 1.0 mm edge: 625 × 4 ÷ 1000 = 2.5, so the center is about 3.5 mm.

Materials

For the same −6.00 lens in n 1.60: 625 × 6 ÷ 1200 = 3.125, so the edge is about 5.13 mm, roughly 0.6 mm thinner. Compare materials in the lens materials comparison and read lens materials and Abbe value.

Frame size

In a 20/20 Magazine worked example, decentration added more edge thickness than the other factors compared. The arithmetic shows why: decentration moves the optical center off the middle, so one edge sits farther out. With the −6.00 lens decentered 4 mm, the far edge is 29 mm out: 841 × 6 ÷ 1000 = 5.05, so that edge is about 7.05 mm. 20/20 Magazine suggests choosing a frame that needs no decentration; see minimum blank size.

Practice set

Original problems.

Sag of a −4.00 D lens, n 1.50, at y = 25 mm?
Show answer
625 × 4 ÷ 1000 = 2.5 mm.
That lens with a 2.0 mm center. Edge thickness?
Show answer
2.0 + 2.5 = about 4.5 mm.
Same lens in n 1.67?
Show answer
625 × 4 ÷ (2000 × 0.67) = 2500 ÷ 1340 = 1.87; edge about 3.87 mm.
+3.00 D, n 1.50, 54 mm round, 1.0 mm edge. Center thickness?
Show answer
y = 27: 729 × 3 ÷ 1000 = 2.19; center about 3.19 mm.
A −5.00 D lens (n 1.50) has its far edge 30 mm from the OC instead of 25 mm. Extra sag?
Show answer
900 × 5 ÷ 1000 = 4.5 vs 625 × 5 ÷ 1000 = 3.125: about 1.4 mm more.

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. 13 (sag formula and its approximation, center and edge thickness) and ch. 4 (higher index thins edges). The NAO lens powers course and a 20/20 Magazine thickness article are linked under sources.

See ABO and NCLE courses ($89 bundle)

Frequently asked questions

Why do high index lenses look thinner?

A higher index bends light more, so the same power needs flatter curves, and flatter curves have less sag. Edges on a minus lens get thinner.

Sources: Brooks & Borish, System for Ophthalmic Dispensing, 3rd ed. (textbook), ch. 4 p. 49; ch. 13 pp. 323–325, 327 (opens in a new tab) ; 20/20 Magazine — Thick or Thin: What Matters Most When it Comes to Lens Thickness (opens in a new tab)

Official sources

Last reviewed Nov 2, 2026. 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.