The one line of arithmetic behind all of it
For any distance much larger than the focal length, the framed width is distance × sensor width ÷ focal length. That is the thin-lens approximation, and it is what this page uses. It is not a shortcut around the trigonometric version — it is algebraically identical to 2 × distance × tan(½ × angle of view) when the angle of view is defined as 2 × arctan(sensor width ÷ 2f), which is how it is defined. The two forms agree exactly; the trigonometric one is just harder to do in your head on a location scout.
Where it stops being exact is close focus. The real object distance is measured from the front principal plane, not the sensor, and at high magnification the lens extends and the effective focal length shifts. For portraits, interiors, sports and landscape work — anything where the subject is more than a few feet away — the error is far below the accuracy of your distance estimate. For macro, use magnification directly instead.
The angle of view is reported three ways because the industry quotes all three. Cinema tends to quote horizontal, stills lens marketing tends to quote diagonal, which is the largest of the three and therefore the most flattering.
Crop factor, honestly
Crop factor is the ratio of the full-frame diagonal, 43.27 mm, to the diagonal of your sensor. It answers exactly one question: what full-frame focal length would frame the same scene from the same spot. It answers that question well, and it is routinely stretched to answer questions it cannot.
| Format | Diagonal | Crop factor | 50 mm frames like |
|---|---|---|---|
| Medium format 44 x 33 | 55.0 mm | 0.79x | 40 mm |
| Full frame 36 x 24 | 43.3 mm | 1.00x | 50 mm |
| APS-C 23.5 x 15.6 | 28.2 mm | 1.53x | 77 mm |
| Micro Four Thirds 17.3 x 13 | 21.6 mm | 2.00x | 100 mm |
| One inch type 13.2 x 8.8 | 15.9 mm | 2.73x | 136 mm |
What crop factor does not change is the marked focal length, which still governs depth of field and perspective compression through the actual optics. A 25 mm lens on Micro Four Thirds frames like a 50 mm on full frame and renders depth like a 25 mm, which is the whole difference between the two formats in one sentence. The depth of field calculator handles that side of it.
Distance sets perspective, focal length only sets framing
This is the part that survives no amount of gear talk. The relative size of a nose and an ear, or a building and the hill behind it, is set entirely by where the camera stands. Change the lens and you change how much of the scene fits; change your position and you change how the scene looks. The reason a 24 mm portrait looks distorted is not the lens — it is that you had to walk to within two feet of the face to fill the frame with it.
So the working order is: choose the distance that makes the subject look right, then pick the focal length that frames what you want from there. If the room will not allow that distance, the honest options are a wider lens with the distortion it brings, a different angle, or a different room. The reverse solver in this calculator exists precisely for the moment when you have a fixed width to cover and a fixed wall to stand against.
Video crops that nobody mentions until you are on set
A stills sensor is often not fully used in video. A 16:9 recording mode takes a shorter slice of a 3:2 sensor, some high-frame-rate modes read out a smaller window, and electronic stabilisation crops in again on top of whatever the mode already did. Each of those makes your wide lens less wide, and they stack. The crop selector here lets you apply the main ones before the arithmetic runs, so the number you get out is what the file will actually contain.
If you are planning the delivery side too, the video file size calculator covers bitrate and running time, and the shoot storage calculator covers cards and copies for the day.
Questions people ask
Is the framed width formula exact or an approximation?
Width = distance × sensor width ÷ focal length is exact under the thin-lens model, and it is identical to the trigonometric form 2 × distance × tan(half the angle of view). The approximation lies in the thin-lens model itself, which treats the lens as a single plane and ignores the fact that focus distance is measured to the sensor while the geometry works from the front principal plane. At ordinary shooting distances the difference is far smaller than the error in pacing out the distance. At close focus and macro it matters, and magnification-based math is the right tool there.
Does a longer lens actually compress perspective?
No. Distance compresses perspective, and long lenses are what you use when you are far away. Shoot the same subject with a 200 mm from far back and a 50 mm from close in, then crop the 50 mm shot to match the framing, and the spatial relationships in the two images will be the same. The compression people describe is real, it is just caused by the walk backwards, not by the glass. This is why moving your feet is the strongest compositional control you have.
How wide can I go before a room shot looks wrong?
Straight lines stay straight in a rectilinear lens, so the giveaway is not curvature but stretching: objects near the frame edge get pulled outward, and anything close to the camera looms. Past roughly 90 degrees diagonal that becomes obvious in interiors, and past about 100 degrees it dominates. The interior photography convention is to stay around 20 to 24 mm on full frame and accept that the room will not fit in one frame, rather than go wider and hand over an image where the near corner of the sofa is the size of the far wall.
Why do two lenses of the same marked focal length frame differently?
Marked focal lengths are nominal and rounded, real focal lengths drift with focus distance on many designs, and zoom lenses in particular can lose a noticeable amount of focal length at close focus — the behaviour usually called focus breathing. Two 50 mm lenses can differ by a few percent at infinity and by a lot more at close range. Use the calculator to decide which lens to bring, then frame with your eyes.
Should I plan around the sensor size or the recording mode?
The recording mode, always, because that is what ends up in the file. A camera with a full-frame sensor recording in a cropped video mode is, for framing purposes, a smaller-format camera for the duration of that mode. Set the crop option to match what you will actually record in, and if you use electronic stabilisation, check its crop factor in the manual and add it — the two multiply rather than adding.