How much you'll fit in frame
Angle of view for any sensor and focal length, how wide a scene that covers at a given distance, and the reverse — what lens fills the frame with a subject of a known size.
Field of view
What lens do I need?
The question the other way round: you know how wide the subject is and how far back you can stand.
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Nothing leaves this device
The formulas
horizontal FOV = 2 · atan(sensor width / 2f)
scene width = 2 · d · tan(FOV / 2)
focal needed = sensor width · distance / subject width
This is the geometry of a rectilinear lens — the ordinary kind that keeps straight lines straight. Fisheyes deliberately do not obey it and will show considerably more than these figures suggest.
Two smaller caveats. Focal lengths are quoted at infinity focus, and many lenses get slightly wider as they focus closer — a "50mm" at minimum focus may behave like 45mm. And manufacturers round: a lens sold as 50mm is often 51.4mm or 48.6mm.
Why "equivalent focal length" causes so many arguments
Crop factor is a diagonal ratio. Micro Four Thirds is 2× full frame on the diagonal, so a 25mm lens is called "50mm equivalent" — and diagonally that is exactly right. But Micro Four Thirds is 4:3 and full frame is 3:2, so the two do not frame identically. The 25mm sees a little less horizontally and a little more vertically than a 50mm on full frame. The diagonal matches; the rectangle does not.
This page reports all three angles for that reason. If you are matching a shot across two formats, match the one along the dimension you care about.
What equivalence does and does not carry over
Framing: yes. A 25mm on Micro Four Thirds and a 50mm on full frame at the same spot capture near enough the same scene.
Depth of field: no, not at the same f-number. Matching the framing means the smaller format gives more depth of field at the same aperture — about the crop factor in stops. See the depth of field calculator.
Exposure: yes. f/4 is f/4 on any format. The same shutter speed and ISO give the same brightness, whatever the sensor size.
Perspective: no — and this is the one people get wrong. Perspective is set by where you stand, not by the lens. A wide lens does not "distort" faces; standing close does. Shoot the same subject from the same spot with a wide lens and crop to match a long one, and the perspective is identical.
Related
Panorama planner uses these angles to work out frame counts. Depth of field covers the sharpness half.
Questions people actually ask
What focal length matches human vision?
There is no single answer, which is why the claim that 50mm is “normal” causes so much argument. Our sharp central vision covers only a degree or two; our full field is close to 180 degrees but mostly peripheral. The 50mm convention comes from its diagonal angle roughly matching the diagonal of a print viewed at a comfortable distance — a statement about looking at photographs, not about eyes.
Why is my lens wider than the figures here?
Three usual reasons. It may be a fisheye, which is designed not to follow this geometry. It may be focused close, since most lenses widen slightly as they focus nearer. Or the marked focal length is rounded — a “50mm” is rarely exactly 50.
Does a longer lens compress perspective?
No — distance does. Perspective is fixed entirely by where the camera stands. A long lens makes you stand further back, and that is what flattens the relationship between near and far. Shoot from one spot with a wide lens, crop to match a telephoto, and the perspective is identical.
How do I match framing between two cameras?
Multiply the focal length by the ratio of the crop factors. Going from full frame to Micro Four Thirds, halve it. But match the angle you actually care about — the diagonal matches exactly, the horizontal and vertical do not, because the two formats are different shapes.