Lens Maker Equation Calculator

The lens maker equation connects a lens's material and surface curvature to its focal length. For a thin lens surrounded by air, optical power is one over focal length and equals the refractive index minus one multiplied by the difference between the reciprocals of the first and second surface radii. The calculator uses 1/f = (n - 1) times (1/R1 - 1/R2), with all distances entered in meters. The resulting focal length is in meters and its reciprocal is optical power in diopters. Signs are essential. Under the Cartesian convention used here, a radius is positive when its center of curvature lies to the right of the surface as light travels from left to right, and negative when it lies to the left. A common biconvex lens therefore has a positive first radius and a negative second radius. With refractive index 1.5 and radii of positive 0.2 meter and negative 0.2 meter, the power is 5 diopters and the focal length is 0.2 meter. Reversing the curvatures produces a negative focal length, describing a diverging lens. Refractive index measures how strongly light slows in a material compared with vacuum. Typical visible-light values are about 1.49 for acrylic and around 1.5 to 1.9 for optical glasses. A larger index difference from the surrounding medium gives greater power for the same surface shapes. Because refractive index varies with wavelength, real lenses focus colors at slightly different points, an effect called chromatic aberration. The value entered should correspond to the material and wavelength relevant to the design. This thin-lens form assumes lens thickness is negligible compared with the radii and focal length, and it assumes air outside the lens. Thick lenses require an additional center-thickness term, while lenses immersed in water or another medium require a relative refractive index. Surface asphericity, manufacturing tolerances, and higher-order aberrations also affect practical performance but are outside this paraxial approximation. Optical designers use the equation as a first estimate for eyeglasses, cameras, telescopes, magnifiers, and laboratory optics. It also helps students understand how steeper curvature, material index, and sign convention alter convergence. Enter radii in the same unit if you only need focal length in that unit, but meters are recommended because the displayed diopter value is defined as inverse meters. A zero radius is invalid, while equal signed radii can yield zero power and an infinite focal length.