Field of View Calculator - Camera

Angular field of view follows from triangle geometry at the image plane: the half-angle is the arctangent of half the sensor dimension divided by the focal length, so the full angle is twice that. Because each sensor edge and the diagonal differ in length, one lens yields three different numbers, and the diagonal figure is always largest. The arctangent is why the relationship compresses at long focal lengths: 24mm to 50mm on full frame drops the horizontal angle from about 74 degrees to about 40, while 200mm to 400mm only takes it from about 10 degrees to 5. Crop factor is the ratio of the 43.27mm diagonal of the 36 by 24mm frame to the diagonal in use, giving about 1.5x for a 23.5 by 15.6mm APS-C sensor, 1.6x for the 22.3 by 14.9mm Canon variant, 2.0x for Micro Four Thirds, 2.7x for a 1-inch sensor and 0.79x for a 43.8 by 32.9mm medium format frame. Linear coverage at a working distance is twice the distance times the tangent of half the angle, the calculation used for security camera placement, machine vision layouts, drone survey overlap and architectural planning. Three caveats apply. The formula assumes focus at infinity; at close range the optics extend and the true angle narrows, an effect called focus breathing. It assumes rectilinear projection, so it fails for fisheye lenses, which use equidistant or equisolid mappings and can exceed 180 degrees where an arctangent never can. And marked focal lengths are nominal, often deviating a few percent from the physical value.

The reference frame behind every crop factor is an accident of cinema. Oskar Barnack, working at Ernst Leitz in Wetzlar, built a compact prototype around 1913 and 1914 that ran perforated 35mm motion picture film horizontally, doubling the standard 18 by 24mm cine frame to 24 by 36mm to get enough negative area for enlargement. The Leica I reached the market in 1925 and the format spread widely enough that its 43.27mm diagonal became the yardstick against which other formats are still measured. The convention that a normal lens has a focal length near the frame diagonal, and the fact that 50mm rather than 43mm became the standard normal lens, both descend from this frame. The language of crop factors belongs to the digital transition. Early professional digital SLRs such as the Nikon D1 of 1999 and the Canon D30 of 2000 used sensors smaller than 24 by 36mm because large wafers were expensive, so photographers needed a way to translate the familiar angular behaviour of existing lenses. The terms crop factor and focal length multiplier entered common use then, along with quoting 35mm equivalent focal lengths for compact cameras. Olympus and Kodak announced the Four Thirds system in 2002 as an open standard designed for digital from the start, and Micro Four Thirds followed in 2008. Equivalent focal length reporting is now standard in Exif metadata and in phone camera specifications.