The minimum space you'll need for a home gym is roughly somewhere between 9ft x 12ft and 9ft x 15ft depending on how it's configured. You can get away with less space if you can perform non-rack exercises inside your rack. To be truly comfortable you probably want to add 2ft to each dimension.
You may be asking yourself how much space you need for a home gym and you may be looking at the dimensions of various bits of kit to see if they'll fit in the space you have. Hopefully this article will help because I've been through this a few times myself and currently train (effectively) in quite a limited space. I therefore feel qualified to give you the minimum dimensions.
It's probably worth stating what sort of training I'm talking about because that could make a difference. I'm talking about strength training or bodybuilding where the need is for a rack of some sort and free-weight exercises.
The depth of the area you need is partly determined by the depth of the rack or machine you're going to be using. I have an Ironmaster IM2000 and that's 48 inches (4ft, 121cm) deep.
The thing is, the footprint of a piece of equipment is not always the same as the space you actually need because levers (like on a cable system) need to move. You also need some room to manoeuvre and I'm suggesting 60 inches (5ft, 152.5cm) is a good minimum.
However, you're going to need a bench with your rack too and when a bench is added to my rack — in roughly the bench press position — it extends the depth to 96 inches (8ft, 244cm).
So, as a rough guide, if we added 4 inches of space to the depth for comfort you're going to need the depth of the rack plus 52 inches.
The width of the area you need is likely to be determined by the width of the barbell you're using rather than the width of the rack. Most barbells are wider than the racks they sit on. My Olympic barbell is 87 inches (7ft3, 221cm) long but I also need room to load plates on either side and I reckon 8 inches per side is the minimum. In my case, that comes to 103 inches (8ft7, 262cm).
So, the width you're going to need is the length of your barbell plus 16 inches.
Working outside the rack or on non-rack exercises
You're may want to come outside the rack for some exercises and you'll need additional space to accommodate that. That space will need to fit your barbell in one direction (with room to add plates to it) and you in the other direction.
I would therefore suggest you're going to need some free space of about 103 inches by 60 inches.
You might be able to double up your space use to accommodate this. If the space between the front and back uprights of your rack is deep enough (and you have the width), you may be able to do non-rack exercises within the rack (if you see what I mean). In my case that's not really possible so I have to work outside the rack.
See the diagram below for possible configurations of the space you'll need.
If you can work within your rack for non-rack exercises, you can probably get away with 103 x 100 inches (8ft7 x 8ft4, 262 x 254cm).
Otherwise you'll probably need an area between 103 x 140 inches (8ft7 x 11ft8, 262 x 356cm) and 103 by 180 inches (8ft7 x 15ft, 262 x 458cm).
Those are absolute minimums and such a space would be quite tight, so I'd suggest an extra couple of feet on both dimensions would make things more comfortable.
Note I haven't accounted for things like weight plate storage trees and other bits of kit, which might require additional space. Also be careful about doors and where they open if you're training in a very small room; I've found that doors take no notice no matter how much you shout at them.