Lens Thickness Calculator

Lens thickness from sagitta: where the geometry comes from

Students, optics hobbyists, and prototyping engineers often need a fast check: if a spherical surface has radius R and a clear circular aperture of diameter D, how much does the glass “bulge” between center and edge? That bulge is the sagitta (sag). This page explains the idealized formula the widget uses, why prescription eyewear is a different software stack, and how to avoid impossible chords.

The sagitta formula in one breath

For a spherical surface convex toward the surrounding medium, with half-aperture y = D⁄2 measured along the tangent plane at the vertex, the sag is sag = R − √(R² − y²) when y < R. If y ≥ R, the chord would lie outside what a single sphere can span—your numbers describe something else (a different surface type, a smaller usable aperture, or a measurement convention mismatch).

The calculator then adds one or two identical sag contributions to an edge thickness to mimic a simple plano–convex or symmetric biconvex sketch. Real biconvex lenses often use different radii; treat “two equal faces” as a teaching default, not a universal blank model.

What this intentionally does not do

Eyeglass thickness depends on refractive index, prism, decentration, base curve policy, minimum blank geometry, and safety standards. Contact lenses add tear layers and flexure. Microscope objectives add multiple elements and glued interfaces. None of that belongs in a single sag box. If you are ordering finished optics, send CAD and tolerances to a vendor who signs the metrology report.

How to read the scenario table

Small perturbations in R swing sag quickly when you are already “steep” relative to diameter. A +1 mm diameter change can push an already-tight radius into the invalid y ≥ R region—when a scenario row disappears, that is the model telling you the perturbation crossed a feasibility line, not a bug.