What sign convention does this use?

The standard Cartesian sign convention: R1 is positive if the center of curvature is to the right of the surface (surface curves toward incoming light), and R2 is positive if its center of curvature is also to the right. For a typical biconvex lens, R1 > 0 and R2 < 0.

What is a plano-convex lens?

One surface is flat (radius = ∞). Enter a very large number like 1,000,000 mm for the flat surface, or use the preset buttons. Mathematically 1/∞ = 0, so that surface contributes nothing.

What refractive index should I use?

Crown glass is about 1.52, flint glass 1.62, polycarbonate 1.59, water 1.33, and acrylic 1.49. The surrounding medium is assumed to be air (n = 1.0).

Why do I get a negative focal length?

A negative focal length means the lens is diverging — parallel rays spread out after passing through it. This happens when (1/R1 − 1/R2) is negative, e.g. a biconcave lens with R1 0.

What is optical power in diopters?

Power = 1/f where f is in meters. A 50 mm focal length lens has a power of 20 diopters. Optometrists use diopters directly for prescriptions.

Lensmaker Equation Calculator

Name: Lensmaker Equation Calculator
Availability: InStock
Author: Nham Vu

Enter the two radii of curvature and the refractive index to compute the focal length of a thin lens.

Lens Parameters

Quick Presets

R₁ — First Radius of Curvature

Positive = center of curvature to the right (convex surface)

R₂ — Second Radius of Curvature

Negative = center of curvature to the left (convex rear surface)

Refractive Index (n)

Crown glass: 1.52 Flint glass: 1.62 Polycarbonate: 1.59 Acrylic: 1.49

Results

Enter lens parameters and click Calculate

Summary

Enter the two radii of curvature and the refractive index to compute the focal length of a thin lens.

How it works

Enter the first radius of curvature (R1) — positive if the surface curves toward the incoming light.
Enter the second radius of curvature (R2) — negative if it curves away from the incoming light.
Enter the refractive index of the lens material (e.g. 1.5 for crown glass).
The calculator applies 1/f = (n − 1) × (1/R1 − 1/R2) and displays the focal length.
A positive focal length means a converging lens; negative means a diverging lens.
Optical power in diopters (1/f in meters) is shown alongside the focal length.

Use cases

Design eyeglass or contact lens prescriptions from given curvature parameters.
Verify focal lengths for camera or microscope objective lens prototypes.
Solve optics homework problems involving the lensmaker's equation.
Compare converging vs. diverging behavior for different glass types.
Understand how lens shape (biconvex, plano-convex, concave) affects focal length.
Convert focal length to optical power (diopters) for clinical optics.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu