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I read (in a user comment) that the iPhone's focal length is longer when shooting video because the frame is cropped slightly to enable video stabilization. I'm having difficulty finding info online about it though.

Is this true? And if so, how can we calculate the "new" focal length that takes this cropping into account?

  • While this question might be about the video aspect of a particular camera's function, the elements of the question do have relevance or interest to still photography. This is basic focal length / field of view calculation stuff, which is simply lens geometry. In fact, to determine the answer, a still image (i.e., photo) must be extracted from the video, which puts it back in the realm of photography. – scottbb Jan 8 '17 at 4:22
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TL;DR: yes, the video mode is cropped by approx. 1.28× (calculated by measurement). The effective video focal length is 36mm (in 35mm equivalent).

I read (in a user comment) that the iPhone's focal length is longer when shooting video because the frame is cropped slightly to enable video stabilization. Is this true?

It appears to be true that the video mode is cropped. I set up my iPhone 7 on a tripod aimed directly at a measuring tape, and took both a photo and and video of the tape. I did not move my phone or the measuring tape between shots.

iPhone 7 photo mode width test
Width measurement of iPhone 7 photo mode

iPhone 7 video mode width test
Width measurement of iPhone 7 video mode (exported still frame)

From these images, I estimate the width of the photo mode wP = 49.6 cm, and the width of the video mode wV = 42.2 cm.

And if so, how can we calculate the "new" focal length that takes this cropping into account?

If we think of the video mode as its own crop factor with respect to the photo mode, then we only need to compute how much the image circle was reduced by as a result of cropping. The image circle of an image is just the cicumcircle, or smallest circle that will fit around a shape.

If the video image were cropped by the same factor in both dimensions (i.e., keeping the same aspect ratio), then we could just divide the measured image widths. But because the aspect ratio also change, we must compute the diameters of the images.

iPhone 7 video mode image overlaid on photo mode, with image circles drawn
Video mode sized and overlaid on photo mode, with image circles and measurements

Recall that Pythagoras told us that the diameter of a rectangle is given by d = √(w² + h²). But I didn't measure height. However, we do know height relative to width, from the aspect ratios: h = w/A.

Putting them together, we have d = (w/A) * √(A² + 1).

The aspect ratio of the photo mode is 4032:3024 = 4/3. The aspect ratio of the video mode is 1920:1080 = 16/9.

Dividing the diagonal of the photo mode (dP) by the diagonal of the video mode (dV), I calculate the video mode's image circle is 1.28 times smaller than the photo mode's image circle.

This diagonal crop ratio is exactly what crop factor is, and is applied to focal lengths (as a multiplier) to get "35mm equivalent focal length".

So, since the iPhone 7's photo-mode uses the lens's full area, and that lens provides a field-of-view equivalent the FoV of a 28mm lens on a 35mm format body, then the iPhone 7's video-mode FoV is equivalent to 1.28 * 28 ≈ 36mm lens (in 35mm equivalent).


See also:

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    Thank you for this thoroughly explained answer! Just one further question: How can we calculate the "actual focal length" (as opposed to the 35mm equivalent)? – Mentalist Jan 8 '17 at 6:10
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    @Mentalist Just to be clear, the "actual focal length" is a property of the lens, whether or not a camera is attached to it. In my iPhone's images EXIF data, it says "Lens Info: 3.99mm f/1.8". So the actual focal length of the lens is 3.99mm. Now, in terms of equivalent field of view, if a different lens were in the iPhone such that uncropped it looked like the current cropped video field of view, then that lens would hypothetically be 1.28 * 3.99 = 5.11mm. But that's not actual focal length, any more than a 50mm lens on a 1.5x crop DSLR (APS-C) would "actually" be 75mm. – scottbb Jan 8 '17 at 6:24
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    Very good point about the angle of view being absolute. I appreciate you taking the time to explain all this. – Mentalist Jan 8 '17 at 8:03
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    My pleasure. Your question was new to me — it hadn't occurred to me that the video mode was cropped, so I learned something new as well. Thank you! – scottbb Jan 8 '17 at 8:27
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    One more thing. Normally this crop is needed when digital image stabilization is in place. Not always present on phisical mechanical image stabilization. – Rafael Jan 8 '17 at 11:08

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