I am referring to lumens...not wattage per foot.
A 400w HPS outputs 55,000 lumens at 1 foot distance on 1 square foot. At 2 feet it outputs 13,750 lumens, at 3 feet it outputs 55,000/9 = 5,555 lumens. At 4 feet it's covering 55,000/25 = 2,200 lumens.
So at 3 feet distance it's covering a 9 sq foot area, which is also 3 x 3 with 5,555 lumens per square foot.
So for vegetative growth (which only needs about 2,500 - 3,000 lumens per sq foot) a HPS light will work perfectly well at about 3 1/2 - 4 feet widths, so would cover a 4 x 4 area with 2,200 lumens per square foot or 3 1/2 feet at 4,489 lumens per sq foot.
For flowering the area will narrow if you want to get the optimum light to your plants, which is reckoned at about 8-10,000 lumens per sq foot. We know 2 feet puts out 13,750 and 3 feet 5,555, so 2 1/2 feet would give 8,800 lumens per square foot. So for flowering you should be looking at an area of about 2 1/2 feet square for optimum light per square foot.
A 400w isn't a particularly efferctive lamp in terms of lumens per watt, where 600's offer a much better option and cover a much wider area.