Is there some sort of formula for how much shade is cast?

Get a 3D program, build a rough stand in for the house, animate the sun and how it moves throughout the day, and render out a small raytraced animation.
Then you can also play around with other props, for example, if you think that at a certain time of day there is too much sun, place a tree somewhere and see how it goes. Play around with its shape and size.
Or strategically place a parasol.
Or shrubs of different sizes.
Or modify the shape of the pool depending on the shadow cast by the house.

Send this to @LuckyGuy.

This may be off topic and flag if you like but i remember the stress you went through last time you built a house. Wouldn’t it be better to just look for something already built that has what you want. I can’t imagine it being good for your health to go through that again.

I’m very surprised and concerned that you would be out by a pool at all considering the high rate of skin cancer in the US. I, myself have not been out in the sun for years, but I still have had several pre cancerous cells removed from all over my body, including my head.

How about building a Roman Domus?

Any licensed architect that you would trust with desining a house would know this.

Keep in mind that the sun travels farther North before summer and back South after the first day of summer. The distance the edge of the eaves are from the (Southern facing) walls of the house will determine if the sun shines on the wall during summer (increasing A/C costs) and in the winter (decreasing heating costs.
I live at about 43 degrees longitude. At midday, June 21, the sun isn’t quite directly overhead. The eaves on the South facing side of my house are about 30” from side of house, so sun doesn’t directly hit wall. With the eaves being 30”, also, during the hottest days of July, August, and September, the sun doesn’t hit either. But I get good sun through my South facing kitchen window during the coldest days of winter.
For a single story house in your area, I might suggest eaves that are at least 24” from wall. 2 story house, 48”
Maybe you could plant a perfectly vertical pole, 10” tall and observe the shadow at noon on certain days to make your decision.
But, since you live in Florida, and you want the house to shade the pool, you’ll either have to build the house directly next to the pool, or build a VERY tall house!!
And, it depends on if you plan to build the house with the pool directly North of the house, or directly West. Or East.
?

Might be cheaper to construct a frame and put up shade sail big enough to accomplish the job. They’re not that expensive.

I sent this to luckyguy as soon as I wrote it.

I was thinking/hoping the architect will have the ability to know this through his CAD design or whatever they use.

Whoever talked about skin cancer, you do understand that the question is about wanting shade over the pool right? Plus, sitting by the pool would be completely under a roof, it’s a new Florida home, so like most Florida homes it has a covered patio. It’s just the water that gets some sun, and since it’s south facing-ish that is sun almost all day, but I’m hoping the sides of the house and well placed trees will give shade for at least half the day over the water as well. I’m my “whitest” when I live in Florida, most Floridians are like me. Go to the pool to watch them play volleyball and many of the players are covered in sleeves and hats. Our damage was mostly done living up north when the sun finally would come out in June and we baked ourselves in the summer.

I have considered doing the pool at least partly under roofline. Not sure.

@jleslie Meh, so flag my answer. Obviously my concern was misplaced.

^^It provided me the chance to clarify in case someone thought I didn’t want the shade. It’s fine. People might be assuming the wrong thing if their idea of swimming pools is everyone is in the sun.

One reason I want to make sure there is shade is for my mom who swims every day, and when she’s here she doesn’t get to do it much. The developer didn’t create shade for the public pools over the water. I mention it every year on the developer questionnaire hoping they will build a shady lap lane/sports pool or indoor pool.

For a formula it is probably going to take some university level calculus to solve. Sorry that I only have grade 12 math. It would be a first time to use math out of class. Easier way is to use quadratics.