Lensmaker's Equation Calculator

How it is calculated

The tool evaluates 1/f = (n − 1) × (1/R₁ − 1/R₂) and then takes f = 1 / (1/f). n is the refractive index of the lens material (must be greater than 1), R₁ and R₂ are the radii of curvature of the first and second surface in centimetres, and f is the focal length in centimetres. Optical power in dioptres is P = 100 / f with f in cm (equivalently 1 / f in metres).

Signs matter: a surface bulging toward the incoming light has a positive radius. A positive f means a converging lens, a negative f a diverging one. The tool returns nothing if n ≤ 1, if either radius is 0, or if the two terms cancel (1/R₁ = 1/R₂, a zero-power lens). It uses the thin-lens form and ignores lens thickness.

Common mistakes

• Giving both radii the same sign for a biconvex lens. The second surface curves the other way, so it needs the opposite sign (20 and −20, not 20 and 20, which gives no result).
• Entering radii in millimetres or metres. The focal length is reported in cm, so radii should be in cm too.
• Typing the refractive index as 1 or lower. Air has n = 1, and a lens needs a value above it, such as 1.5 for typical glass.
• Ignoring a negative answer. A negative focal length and negative dioptres mean the lens diverges light, as in a lens for short-sightedness.
• Using the result for a thick lens or a lens in water. The formula assumes a thin lens surrounded by air.