What is the formula for percent of frame filled at a specific distance and focal length?

Question

I am thinking about buying a new lens specifically to take photos of distant targets (birds, bears, etc). I currently own the Canon 70-300 IS USM, which is a nice lens, but I find that if I want to take a photo of anything further away than about 10 meters, the target does not fill a large amount of the frame (meaning I have to significantly crop in post production).

I am currently looking at the Canon prime 400mm, however I would like to determine at what distance an object will fill a reasonable proportion of the frame.

Is there a formula or rule of thumb I can apply that will help me in this situation? I realise the size of the target I am shooting will play a role here, so if we need to make an assumption about the size of the target please let me know.

Answer

The formula for the percentage of image filled is

focal_length x subject_size x 100
_________________________________distance x sensor size

All units are millimeters. Use the width of the subject/sensor to work out the horizontal fill % and the height of the object/sensor to work out the vertical fill %

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