I own a gym. It’s not so much based on the square footage of your space as it is on how many members you have and what type of a gym it is. My gym is strictly private. I only have three cardio pieces. Other gyms I’ve been involved with had 3500 members and we had roughly 22 pieces of cardio.
Knowing peak time member usage is helpful to determine needed equipment, but there is no formula that I know of. Typically bikes and stair machines take up 24 sq. ft; rowers 40 sq ft; and treadmills 45 sq ft. These numbers included the space needed between pieces.
I did a quick search online and came up with many options that can help answering your question. Even my just copy and paste your question on my search engine I was able to find some good options and tips. Give it a try and see if that helps. It all depends on your budget and the type of members/clients you are looking to attract. Good luck.