Lens Maker's Equation Calculator

It gives the focal length of a thin lens from its material and shape: 1/f = (n - 1)(1/R1 - 1/R2), where n is the refractive index and R1, R2 are the two surface radii in meters. The reciprocal of the focal length is the optical power in diopters.

A surface that bulges toward the incoming light has a positive radius, while one that curves away has a negative radius. For a symmetric biconvex lens R1 is positive and R2 is negative, as in the 0.1 m and -0.1 m example.

Type inf (or infinity, flat, or leave the box empty) for a flat side. A flat surface has an infinite radius, so its 1/R term becomes zero, which is exactly right for a plano lens.

Optical power is the reciprocal of the focal length in meters, P = 1/f, measured in diopters (D). A lens with a 0.1 m focal length has a power of 10 D, and a 0.4 m focal length gives 2.5 D.

The factor (n - 1) would be zero or negative for n of 1 or less, meaning the lens could not focus light in air. The calculator rejects any index at or below 1, and it also rejects two flat surfaces since that lens has no power.

No. This is the thin lens form, which ignores the center thickness of the glass. For a thick lens you need the extra term that adds the thickness divided by n times the product of the radii, which this tool does not include.

Meters. Because power is 1/f, entering radii in meters gives the focal length in meters and the power directly in diopters. If you have millimeters, convert to meters first (divide by 1000).

Yes. If the radii make the bracket negative, the focal length and power come out negative, which is a diverging lens. The tool reports whatever sign the formula produces as long as the result is not zero.

No. The computation runs in your browser with the same engine the tests use, so your index and radii stay on your device and are never sent to a server.