Today’s Question: Imagine you are using a 100mm lens on a full frame camera body. This combination makes images that are 3000×2000 pixels. When you crop the image to be 1500×1000 pixels what is the “implied” focal length of the lens. How is this computed?
Tim’s Quick Answer: You can calculate effective focal length in this type of situation by calculating the ratio represented by the starting and ending dimensions, and then multiplying that value by the focal length used to capture the original image to determine the effective focal length for the field of view of the cropped image.
More Detail: Calculating the effective focal length for an image you’ve cropped can be helpful in terms of knowing what lens focal length would have been required to achieve the field of view of the cropped image, for example.
To calculate the ratio represented by the crop, you can divide the pixel dimensions for the original image by the pixel dimensions for the cropped image, being sure to use the pixel count for the same side (such as calculating for only the width or only the height) for both images.
With the example above, you could divide the original width (3,000 pixels) by the cropped width (1,500 pixels) to calculate the ratio of 2 (3000 / 1500 = 2). This ratio represents the crop factor. Since the original image was captured with a lens focal length of 100mm, you could multiply that focal length by the ratio you determined, which in this example gives an effective focal length of 200mm (100 X 2 = 200).
So, with the example outlined above, to achieve the same field of view from the cropped image in an original capture you would need to use a 200mm lens rather than a 100mm lens.
