You may be able to squish a shower in, but you'll have a tiny, cramped bathroom that will surely turn into a design dilemma down the road. How about making a nice half bath/powder room? Are there windows in this room? A floor plan would be helpful.

Thank you for your comment. I have an exterior wall that we can put a window on. and I can take more space from my laundry mudroom if we need to. I was hoping to get a shower in there so we can have a downstairs shower to help care for my mom after a knee surgery since we only have showers upstairs currently. What do you think is the minimum space I should allocate so it is not weird and cramped?

Knowing that you will need it or a person who will have issues with mobility, I'd want a larger shower/bathroom space if possible. Can you post an image of the space, with dimensions? There might be a way to make it work. Would you consider combining the bath/laundry functions into one space?

A shower that is 32 X 48 is plenty of size and could even accommodate a small stool if your mum needs it and I'd recommend a hand held shower so she can easily handle it or have help if needed.

I found some examples of small bathroom layouts. Some have metric measurements but you can convert that to inches by dividing by 2.54.

small bathroom layout - Google Search · More Info

Common Bathroom Floor Plans: Rules of Thumb for Layout – Board & Vellum · More Info

small bathroom layout - Google Search · More Info

Bathroom layout planner - this may also help you plan and get ideas for the best layout for your area.

I'd use a glass enclosure shower rather than one with doors that close around it. You don't want your small space to feel even smaller with a cramped looking closed off shower area.

I think that @Sammie J has the best idea for your needs. But, as you can see from @mvcanada's post, just adding a couple of feet to your length will give you a tolerable sized bath.

I think the 24" x 18" sink is the factor that is going to be too big, possibly. You could do a 6'6" x 36 shower and have the toilet on 15" centers on one wall and a shallow sink on the opposite wall. You would have even more floor space if you could do a wall hung toilet with the tank in the wall studs. The standard family bath template is 5x7 and older houses sometimes had smaller so this is workable even though many modern bathrooms are much bigger.

There's nothing wrong with having a combo bath/laundry like Sammy suggests (you can still put the potty in its own room if you like). That would probably be the best way to get closer to an ADA bathroom in your space. It might not BE completely ADA but you can incorporate enough features to make it good for first-floor bound guests.

Here are various layouts with dimensions.

I think your best bet with a square room is to have a corner shower as shown in one the the layout mvcanada posted.

Nancy in Mich is right on target here. She speaks from experience. Buy a walker (your mom will need one following knee surgery.). USE IT to figure out patterns of movement in the bathroom. And to figure out space for turning. (My husband could not fit his walker past the sink in our powder room after his knee surgery.) Nancy’s recommendation to provide grab bars is also smart. At the very least…install blocking for FUTURE installation of grab bars. A 4” threshold for a shower can be a MOUNTAIN to someone who can’t bend her or his knee. And a small shower…try fitting two people into a 36” square shower! Think this through.

If you post the full plan including the proposed laundry room and existing space, someone in here might come up with a better idea on how to share the spaces.