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Calculate the diagonal of the uncropped image:
Diag = SQRT(Power([image X dimension],2)+Power([image Y dimension],2))
Then calculate the diagonal of the cropped image, using the X and Y pixel dimensions of the crop. Divide the original number by the smaller number to get the crop factor.
The effective focal length you used was 400 * crop factor.
Thanks for the detail, perfect. I'll crop as I wish and see what focal length would have been ideal.
You can do this with a formula based on the megapixels. I don't know what camera you have but let's say it's 24MP and I am assuming you are using a full frame camera, otherwise that 400mm lens will have a different FOV depending on exactly the camera body you are using - for example 600mm or 640mm if it's an APS-C body. Also note all lens focal lengths are rated at infinity focus, and magnification changes near minimum focus distance are common and can result in a different effective focal length depending on lens design.
This how the math works:
(Desired focal length / actual focal length) squared
Then take your megapixel count and divide it by that value.
EXAMPLE Now let's say you want to see what 600mm would be like, using your 400mm lens and your 24MP full frame camera (feel free to correct my assumptions). Find something far in the distance to take a picture of to eliminate any magnification change caused by the specific lens design.
600/400 = 1.5. Square that (resolution is a square function) and you get 2.25. Now divide your megapixels by 2.25 (24 / 2.25) and you get 10.67MP.
Go into your editor of choice and make a 3:2 crop (the aspect ratio of a full frame camera sensor) that gives you a ~10MP final image. Crop wherever you want and that is what the image would look like if taken with a 600mm lens instead of a 400mm lens. Hope I explained that clearly.
Here's the simplest (and easiest to remember) formula:
Crop factor equals ratio of focal lengths.
That's it. To simulate a 600mm lens by cropping an image shot on a 400mm, calculate the ratio of the focal lengths: 400mm/600mm = 2/3. Then multiply the image size by that factor (e.g., a 4500x3000 px image would become a 3000x2000 px image), and crop accordingly.
Obviously this ignores things like lens distortion, and you do lose a fair amount of pixels, but if your subject isn't too close, and all you want is an idea of the kind of reach you'd get from a longer lens, then this is perfectly fine.
Oh, and calculating the effective focal length of a lens on a crop sensor works the same way, only in reverse: say you're using a 400mm on an APS-C sensor with a crop factor of 1.5; c = f1/f2 means that f1 = c * f2, so you just multiply: 400mm x 1.5 = 600mm; that's your effective focal length.
The only caveat is that it might not be immediately obvious which focal length goes where in the fraction, but since cropping always makes an image smaller (and the subject larger in the frame), it's easy to figure out whether you got it right.