Calculating approx Focal Length when image cropped.

Sootchucker

Sootchucker

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Just thinking recently, is there a calculation that will allow you to approximate the focal length of an image after cropping ?

I.e. if I start with a 20mp image shot with a 300mm lens, then crop it to 12mp - what would the "effective" focal length be.

I want to use this as a sort of lens simulator to see what sort of "magnification" bigger lenses would have on my various cameras ?
 
Thanks all, appreciate the input, but what I was looking for was a formula so that I can play around with cropping my own images to see what sort of focal length I would need to capture it "full frame" so to speak.

For instance, this image below was originally captured by my OMD EM1 MK II and 300mm F4 Pro lens.



The image originally started off at 20mp (5184 x 3888 pixels), and now it's cropped it's only 5.72mp (2929 x 1953).

I've just read something on line that said you take the longest side dimension (before cropping) -so in this case 5184 divided by the long side of the cropped image (so 2929) x focal length of the lens used (in this case my 300mm F4 Pro).

If that's true then it would be (5184/2929) x 300 = 531mm - so the "equivalent" FL for this shot would be 531 x 2 (the crop factor of M4/3 = 1,062mm

Does that sound right ?
 
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Taking a ratio of longer sides will only work if you keep the aspect ratio (i.e. 3x2), which you don't

For a general case you need a ratio between diagonals, so:

EFL = 300 * (sqrt(5184^2 + 3888^2) / sqrt(2929^2 + 1953^2)) = 522mm

(EDIT: sorry it's 300* not 531*)
 
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Sootchucker said:
I've just read something on line that said you take the longest side dimension (before cropping) -so in this case 5184 divided by the long side of the cropped image (so 2929) x focal length of the lens used (in this case my 300mm F4 Pro).

If that's true then it would be (5184/2929) x 300 = 531mm - so the "equivalent" FL for this shot would be 531 x 2 (the crop factor of M4/3 = 1,062mm
Click to expand...
gunnar said:
Taking a ratio of longer sides will only work if you keep the aspect ratio (i.e. 3x2), which you don't

For a general case you need a ratio between diagonals, so:

EFL = 300 * (sqrt(5184^2 + 3888^2) / sqrt(2929^2 + 1953^2)) = 522mm
Click to expand...
These are both useful methods. As has been pointed out, the first method only works when the aspect ratio hasn't changed; if the aspect ratio has changed then the second method is better. But the first method is much easier, so if the aspect ratio hasn't changed too much and you don't need an exact answer then I'd suggest it's fine.

HOWEVER, there is one limitation: both of these methods only really work when you're using long lenses. You can't do the same maths with wide angles. The formula is fine for (35mm full frame equivalent) focal lengths over about 100mm, and not too bad for (35mm full frame equivalent) focal lengths over about 50mm, but anything shorter/wider than that and the formula breaks down.

(Why? High school trigonometry. You're looking at a planar representation of an angular field of view. For narrow fields of view they scale proportionately, because for small angles sin θ ≈ tan θ ≈ θ. But for larger angles the relationship doesn't hold.)
 
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