how many plants under a 400 WATT HPS

If you want to grow them fairly large, I would say 4 or 5. If you put the light on a light rail 6 to 8. You wont get maximum yield like you would with a 1000 watt system or even a 600 watt.
But you would get a pretty good final product.

I started growing in a box (#1) 7'x3'x6' with a 400 watts MH for veg light in vertical no reflector , very tight and double to 800 watts HPS for flower, two 400 vertical no reflector for box (#2) 8'x46"x6'. 21 Girls 4 feet tall cut lollipop style which also gave me a ton of clones, I guess it all depends on how you plan and build your box and the kind of food and how offend you feed and i do rotate, all inside of boxes are reflective.

I have 14 plants in 4*4 room with the light hung at an angle and the walls covered in shiny insulation. There is a fan blowing air onto them and i created a co2 bottle with sugar baking soda and yeast mixed with water. Is this enough space and light

I grow 6 plants in two dwc reservoirs with 6 gal of water each. 2 gal water for each plant. I veg them to about 5 inches then flower. I grow northern lights. Plants grow to about 3 ft. I don't trim or anything. This is under a 400w hps. I get a pound per grow which is a little over 2.5 oz per plant.

i see that urv got all those plants in there now in only a space of 4x4, they look small and in early flowering stage ,am i right? if so ul have trouble when they get few more weeks in to flower as they bush out like mad and all the bottoms branches will not get much light so best to lollipop em , ul have trouble getting to ya plant also ,

for anyone to answer the OP's question, would have know more about how you wanted to grow, but a few things to remember about a 400HPS it will only give coverage to a 4'x4' space but 3'x3' will be getting the best of it with the outside foot getting secondary light...and it does not penetrate very far about 18"-24" max...with that being said in my autoflower grow in my 2'x2' tent I use a 400HPS in a homemade cooltube and use 9 x 2gal pots, but in my box thats 5'x2' I use the same light set up with 12 x 2gal pots I just rotate them everyday from the outsides to under the light...but my autos only get 25" max so I get good light all the way to the bottoms..