5x5 is a decent half bath ... 5x6 allows for more leg room in front of the toilet and is more comfortable (and if a person my small size thinks so, big people will really appreciate that extra space). I suggest you drop a tape measure into your purse and measure all the bathrooms you come in contact with: at work, at the dentist's office, in friends' houses. Verify for yourself what you find comfortable.

As for where to place it ... I'd scoot the mudroom's from-the-yard door down a bit, and I'd place the powder room at the far right /just by the from-the-yard entrance. This would create a small hallway, and the powder room door'd be in that hallway. This will allow a window in your powder room, which is always a positive.

The negative is that 1st floor traffic must walk through your kitchen to reach the powder room, and a person at the sink will block that pathway -- but I don't see a way around that.

You need a minimum of 15" from the center of the toilet to whatever is on either side of it, so 30" minimum. But you also have to check your local codes. I'd tuck behind the back door and run the plumbing on an interior wall if you live somewhere cold where pipes can freeze.

Here's a recent tiny favorite of mine.

There are 3 doorways into a room that measures 18'x10'.

I don't see how you can carve out space for even a small powder room without changing the doorways. The doorway to the kitchen looks like it can't be moved, but if you eliminate the doorway to the outside, you could fit the powder room there. Then replace the window closest to the kitchen with a door. Then you would need to reconfigure the mudroom--not sure what that rectangle at the top of the room is--hooks? benches? lockers?

It seems like you are asking too much of the existing space. You might consider making it larger. Can you borrow some space from the garage?

Has construction started on the house?

I was assuming that this house is already built and the owners are living in it. If not, then all bets are off, and you can do much better.

It’s not a new house

Then my original comment stands.

You don’t think there is any room in the current mudroom to build a powder room, even if we move the side door?

If you moved the outside door to that short wall of the garage that's adjacent, you could enter the garage from the outside, then the mudroom/powder room from the garage. That would allow you to put a good size powder room (or even with a shower) on the back part of the room and still have mudroom space on the kitchen side. And the bathroom would be farther from the kitchen, which is desirable.

Every inch will be needed and accurate measuring/placement, so maybe start there.

Powder room: I think removing the outside door is key (is it an option?). A pocket door between the two areas is also recommended.

Mudroom: Sink/storage on left (vs appliances) given the door’s swing. Measure how much space this would take up, then plan powder room’s size.

Figure out the depth of appliances + a walk through + a drop zone (if possible) situated opposite appliances.

Decide on what you are willing to give up and/or if taking space from the garage is possible, in order to define possibilities.

Thank you! Where would you then put the side door to get into the house?

move the side drive door to replace back window..add a 3x6 powderroom with pocket door…you have a nice size space to work with.

Home Interiors and I were thinking the same thing ... 'cept I would've put the Powder Room at the top /outside corner (so it could have that window), and I'd move the from-the-yard door to where Home Interiors placed the toilet.

That would mean the Powder Room could be 6', and the hallway from outside could be 4'.

Quick google search for "small powder rooms" ...