Personally I don’t believe in magic numbers where one specific square footage per chick works for every brooder in the world with every brood of chicks ever hatched. In brooders, chicks, and our management methods there are enough differences that what works for one person does not work for another. I believe in letting your chicks tell you what they need.
I’m a proponent of providing more space than the absolute minimum, whether that is in a coop, run, brooder, in a nest, or on the roost. Chickens may be social animals but they also need their personal space to minimize behavioral problems. With more space you normally don’t have to work as hard either.
My concern with your brooder is that it might get too hot. Too hot is more dangerous that too cool. To me the ideal brooder is one that keeps one area warm enough but allows those that want to be cooler enough room to find that temperature. The ends away from the heat need to cool off so they can find their comfort level. If you put a bunch of humans in a room and set the thermostat on an “average” setting, some people are too warm, some too cool, and some just right. Why? People are different. Chicks are different too. There is no one perfect magic temperature that keeps all chicks happy.
My 3’ x 6’ brooder is in the coop. They go in there straight from the incubator or when they arrive from the post office. Outside my brooder the temperature was in the single digits Fahrenheit a couple of days after my current brood arrived in the mail. The chicks didn’t care, they were not outside the brooder. One end of my brooder was in the 90’s. The far end was below freezing at times. Some water down there froze so I know it was below freezing. The chicks did not go to that end but stayed in the warm end. On days it gets a lot warmer, they stay further away from the heat source. I allow them to self-regulate and they do. If you have your coop ready and you have electricity to it, you can brood directly in there as long as you can keep one area warm enough. The chicks don’t care how deep the snow is outside as long as they are not outside.
You asked “why do so many people show brooding chicks in smaller tubs than what I have”. Even if some people consider them wrong, they can and do work. If you have them in the house your temperatures are pretty stable. You don’t have to worry about a possible daily 30 degree temperature change outside the way I have to. You can fine tune yours and keep the temperature in a safe range. The chicks may not enjoy it as much, but they can survive as long as you don’t cook them. We have different conditions, different concerns, and different management techniques. There is not one magic number that covers us all.
I don’t provide nearly 2 square feet per chick at any time they are in the brooder. I’ve had some at five weeks that were in about ½ a square foot, but that was 28 chicks, mostly pullets, in a 3’ x 5’ brooder. Another time I had 23 chicks, almost all cockerels, in that same brooder. In both cases it was getting pretty crowded at five weeks. They were all full sized, by the way, no bantams. That can make a difference too. Because my brooder was fairly large the square footage was less important. I’m going to use whole numbers and inches to make the math easier. The numbers I’m going to use are not that realistic but I want to illustrate a point, not get into arguments about how much space a chick that grows pretty fast might actually take up at some age. Assume each chick occupies 10 square inches of brooder space and you give each chick 100 square inches total of brooder space. That leaves 90 square inches unoccupied for each chick.
Say you have 4 chicks. They occupy 40 square inches and have 360 square inches unoccupied to explore since you give each chick 100 square inches. You need to fit a feeder and waterer in that free space too. Now say you have 20 chicks. They occupy 200 square inches but have 1800 square inches to explore. Even with the feeder and waterer that’s quite a difference. The more chicks you have the less space you have to give each one to keep them from being crowded. I still recommend giving them plenty of space. I think they are better off.
You need room in the brooder for the feeder and waterer. In a smaller brooder they might take up a higher percentage of the available space. You need room for them to get away from the heat if it gets too hot. Then you need room for them to play. Chick TV is better than any cable channel but they need room to perform. They do grow really fast so that room to play requirement goes up pretty fast.
In your temperatures I can understand you not being comfortable brooding them outside. If you lose power they won’t last long out there. In the house you’d be surprised at how cool they can take it. I have a generator ready to go just in case. I think it helps to have some experience in how tough they really are also.
I don’t remember reading how many chicks you plan to get. You can try them in that brooder as is. It will probably work for a while. Watch them and adjust the temperature to suit. If they spend most of their time hiding behind that waterer or feeder, it is too warm. If they huddle under the heat, they are too cool. When they sleep they normally huddle together in a nice warm spot so don’t confuse that with them being too cool. You may find you need to put up a barrier they can hide behind to get away from the direct heat of that lamp. There is some trial and error involved in all of this.
I also recommend you have a contingency plan ready in case you need more room, which you probably will fairly soon. Some people brood their s in the bathtub in a spare bathroom. Another good one is to get one or two large appliance boxes and tape them together. If I had an attached garage that stayed somewhat warm I’d use that. There are a tremendous number of different things that can work.
As long as you provide the basics of food, clean water, a dry brooder, block a breeze from hitting them, and sufficient but not too much warmth they will do fine, regardless of all the things people tell you that you are doing wrong.
Good luck and welcome to the adventure. It’s a good ride.