I\'m trying to resize a larger video to fit an area that I have. In order to achieve this I calculate first the dimensions of the resized video so That it fits my area, and
try -vf "scale=iw*min(405/iw\,320/ih):ih*min(405/iw\,320/ih),pad=405:320:(405-iw)/2:(320-ih)/2"
Edit to clarify what's going on in that line: you are asking how to scale one box to fit inside another box. The boxes might have different aspect ratios. If they do, you want to fill one dimension, and center along the other dimension.
# you defined the max width and max height in your original question
max_width = 405
max_height = 320
# first, scale the image to fit along one dimension
scale = min(max_width/input_width, max_height/input_height)
scaled_width = input_width * scale
scaled_height = input_height * scale
# then, position the image on the padded background
padding_ofs_x = (max_width - input_width) / 2
padding_ofs_y = (max_height - input_height) / 2