Focal Length Calculator

Focal length describes how strongly an optical system converges or diverges light. For a thin converging lens, the object distance, image distance, and focal length are linked by the thin lens equation: one divided by focal length equals one divided by object distance plus one divided by image distance. Rearranging that relationship gives focal length as object distance multiplied by image distance, divided by their sum. This calculator applies that equation when both distances are positive and expressed in meters. The result also includes lateral magnification. Magnification is the image distance divided by the object distance, and its magnitude tells you how large the image is relative to the object. A value of 0.2 means the image is one fifth of the object's size, while a value above 1 indicates enlargement. In a complete sign-convention treatment, a real image formed by a converging lens is inverted and magnification carries a negative sign. This practical calculator reports the magnitude so the relative size is easy to read. Lens power is the reciprocal of focal length in meters and is measured in diopters. A lens with a focal length of 0.5 meter has a power of 2 diopters, while a 0.1-meter lens has a power of 10 diopters. Shorter focal lengths therefore correspond to stronger optical power. Diopters are widely used for eyeglass prescriptions, magnifiers, and other optical systems because powers of thin lenses placed close together can often be added directly. Accurate inputs depend on measuring from the lens's optical center rather than from the front of a housing or camera body. The thin lens model also assumes that lens thickness is small compared with the relevant distances and that rays remain near the optical axis. Real photographic objectives contain multiple elements, so their marked focal length refers to an effective optical model rather than a simple physical distance. Use this tool for classroom optics, photography experiments, microscopy planning, projector setups, and preliminary lens selection. It is most reliable for ideal thin lenses in air. For thick lenses, strongly curved elements, virtual objects, or virtual images, use the appropriate signed distances and a full optical design model.