Field of view calculator
Enter the lens and sensor, get the angle of view, the equivalent focal length and the scene you cover.
How do you calculate the angle of view of a lens?
Angle of view = 2 × arctan(d ÷ 2f), where d is the sensor width, height or diagonal and f is the focal length, with the lens focused at infinity. It follows from the rectilinear lens equation, image height = f × tan(field angle), which ZEISS gives in its technical article on distortion. A 50 mm lens on a 36 × 24 mm sensor sees 39.6° horizontally, 27.0° vertically and 46.8° diagonally.
What are crop factor and 35 mm equivalent focal length?
The crop factor is the diagonal of the 36 × 24 mm frame, 43.27 mm, divided by the diagonal of your sensor. Multiply the focal length by it to get the focal length that gives the same diagonal angle of view on a full-frame camera. A 35 mm lens on a 23.5 × 15.6 mm sensor has a crop factor of 1.53 and is about 54 mm equivalent. The Exif standard stores this value as the equivalent focal length assuming a 35 mm film camera.
How big a scene does a lens cover at a distance?
Scene width = sensor width × (distance − focal length) ÷ focal length, the same for the height. With a 50 mm lens on a 36 × 24 mm sensor at 20 feet, the scene is 14.3 feet wide and 9.5 feet tall. The picture is the sensor size divided by the magnification, and at 1:1 magnification the scene is as big as the sensor.
Why does the answer differ from sensor size × distance ÷ focal length?
That simple formula treats the distance as if the image formed exactly one focal length behind the lens, which is true only for a far-away subject. The thin-lens formula used here subtracts the focal length from the distance. The simple formula overstates the scene by focal length ÷ (distance − focal length): 5% for a 50 mm lens at 1 m, 0.5% at 10 m. Real lenses measure distance from principal planes that differ a little from the lens, which also only matters up close.
How far away should I stand to fit a subject in the frame?
Distance = focal length × (1 + subject size ÷ sensor side). To fit a 6-foot-tall subject along the 24 mm side of a full-frame sensor with a 50 mm lens, stand 12.7 feet away. Check that your lens can focus that close, and note that the angle of view narrows slightly when you focus near.
See also the depth of field calculator, the print size calculator and the PPI calculator.
Sources: ZEISS Camera Lens Division, B. Hönlinger and H. H. Nasse, “Distortion” (image equation of a rectilinear lens); Wikipedia, “Angle of view” and “Crop factor”; CIPA DC-X008-2019 (Exif 2.32), FocalLengthIn35mmFilm. Sensor sizes from the specifications of the Canon EOS R5 and R7, Sony α6400, Nikon D7500, Panasonic Lumix G9 and Fujifilm GFX100 II. How we check our calculators.