Lens Focal Length Calculator

The focal length needed to frame a subject follows from similar triangles in the thin lens model. The ratio of image height on the sensor to subject height in the world equals the ratio of focal length to subject distance, so focal length equals sensor dimension multiplied by distance and divided by subject size. Filling 80 percent of the 24 mm height of a full-frame sensor with a 1.8 m person standing 5 m away gives 19.2 times 5000 divided by 1800, or about 53 mm, which is why a 50 mm lens is the classic full-length portrait choice at conversational distance. The approximation holds while subject distance greatly exceeds focal length; at macro distances the simple form understates the required lens extension. Field of view follows from the same geometry as twice the arctangent of half the sensor dimension over focal length, about 39.6 degrees horizontally for a 50 mm lens on a 36 mm wide sensor. Sensor size enters twice. It sets the numerator in the framing formula, and it sets the crop factor, defined as the ratio of the 43.27 mm full-frame diagonal to the diagonal of the sensor in question: 1.5x for most APS-C, 1.6x for Canon APS-C, and 2.0x for Micro Four Thirds. Crop factor converts a focal length into the full-frame equivalent giving the same angle of view, but does not change the actual focal length, so depth of field behaves according to the real value. Perspective depends only on camera-to-subject distance, which is why 85 mm to 135 mm lenses flatter faces: they force a working distance that renders facial proportions naturally.

The geometry behind lens selection is classical Gaussian optics, formalized in the early nineteenth century by Carl Friedrich Gauss and colleagues, who reduced complex multi-element systems to principal planes and a single focal length. That abstraction is what allows a photographer to treat a modern retrofocus zoom as if it were a thin lens for framing purposes. Angle of view tables appeared in photographic manuals throughout the plate era, but they were tied to whatever plate size a photographer used, since focal length alone means nothing without a frame size to project onto. A common reference frame arrived with 35 mm still photography. Oskar Barnack built his prototype camera at Ernst Leitz in Wetzlar around 1913, using perforated 35 mm cine film in a doubled 24 by 36 mm frame, and the Leica I released in 1925 made that format a commercial standard. Its 43.3 mm diagonal defined the notion of a normal lens, though manufacturers settled on the rounder 50 mm. When digital single lens reflex cameras arrived with sensors smaller than the film frame, notably the Nikon D1 in 1999 and Canon models that followed, photographers needed a way to translate their existing lens intuitions, and the crop factor or focal length multiplier entered common vocabulary. It remains an equivalence device rather than a physical change, a point of persistent confusion in discussions of sensor formats.