Normal rat size imo.
If you get pest control round, they're usually pretty good at finding places to put traps/poison where pets can't get at it/them.
We've had rat problems twice. One very cold winter, Mrs Rat decided it was too cold to have her babies out of doors and set up a maternity unit under our kitchen floor. We'd have the dogs (a pair of terriers) trying to dig up the flooring for approx 10 days at a time, then it would stop, then start again about 10 days later. Thankfully, the rats couldn't get out from under the floor or behind the cupboards.
The rat man worked out where they were getting in (a tiny bit of mortar missing in the brickwork, where 3 bricks joined together) and advised us to block this as soon as the dogs' behaviour showed that Mrs Rat was no longer in residence and that sorted it. He also went all round the house and in the loft, and was most reassuring that there was no sign of them anywhere else. We blocked the hole and all was fine.
The dog used to leave a dead rat in the garden now and again (her record was 4 in 10 days), so we knew they were about. But that's not surprising where we live, on the edge of fields, with 2 houses out our 4 keeping chickens and 3 lots of stables within a mile.
Then she got too old (and deaf, and almost blind) to catch them, and I used to see one every few days, either crossing the garden or trying to get the lid off the dustbin. But last winter, we heard what I thought was scratching in the house, and she took to sniffing intently in a few places, mostly around the back wall of the house. There's no mistaking a terrier that's smelt a rat - they go almost rigid with excitement.
A few days later, we woke to a sound like Old Faithful, went downstairs and found kitchen ankle deep in water, which was still pissing out of the cupboard under the sink. The bastard rat had chewed through the dishwasher hose.
I rang the council and they put us down on the list for a rat man visit, but the wait was 13 weeks. We bought some traps and put them down, but no success. A few nights later, I woke to what sounded like scrabbling coming from above the bedroom ceiling and the thought that the fucker was in the loft above my head freaked me right out. I got no sleep, even though I went downstairs and tried to sleep on the sofa.
The following morning, I phoned the council again, and this time I burst into tears (I was shocked - I never cry!) and had the best service I've ever had from our normally shite council. She rang me back and said that they couldn't get anyone round that day, but could do the following day. He came, found the entry point (behind the drainpipe, another tiny gap in the mortar) dropped poisoned bait down it and laid a couple of traps, one in the loft, one on a shelf in the garage and one under the bath, where the dog couldn't get to it.
We checked the traps religiously and never heard the rat again. We stopped checking the traps (which turned out to be a big mistake as we found when we had a horrible smell in the bathroom, which turned out to be a rotting rat under the bath) and so far, so good.
The neighbours no longer have any chooks, and since the last hen disappeared at the start of the summer, I don't think I've seen a rat. They've now got a cat that's a real hunter, so maybe the cat presence has put them off. Or maybe they just go elsewhere in the summer.
However, a colleague who lives a few hundred yards away had them earlier this year. They were getting in through a broken drain and she had to have her whole garden dug up and the drains replaced, it cost them a few grand.