Potty training a 3 year old can take as long as a few days to a few months or even longer.
The average time it takes to potty train a 3 year old is between 3 months to 6 months, although some 3 year olds may potty train easier and faster than others.
It also depends on the readiness of the 3 year old.
I've worked with kids and I've had one 3 year old boy potty train and use the toilet successfully within a few days of starting the potty training.
Then again, I've also had another boy that was 3 years old when we started potty training him and he took around 6 months to fully potty train and sometimes he would regress and start peeing and pooping his pants again and demand a diaper.
If the child is not ready, yet then it's okay to go back to diapers, especially if he's having a lot of accidents and then try again a few months later.
It's usually nothing to worry about if the child is not potty trained, unless they are 4 years old and still not using the toilet.
I've also known some kids that didn't potty train until they were 5 and eventually they got it.
Success in potty training also hinges on readiness of the child, which includes the child being able to stay dry for a couple of hours, having a predictable bowel movement pattern and being able to communicate, follow directions and also pull up their pants and pull down their pants.
Every child is different and some children will master the toilet use sooner than others and others can take longer.
Also daytime dryness is also often achieved within a few months or so, but nighttime dryness can take years to develop.
Even if the child is potty trained in the day, it's still okay and normal for the child to wear diapers at night for bed wetting, even when they are 5, 6, 7, 8, 9, 10, 11, 12 etc.
Starting potty training too early can also make the potty training process take longer.
Give your child plenty of fluids to increase their need to urinate and potty, and talk to your child about using the potty and make sure they understand the process.
But if they truly aren't ready, you should wait awhile and try again.