our four year old went through a phase of this when he was three as well. It was beyond frustrating. There were days I wondered if it would ever stop and if our approach was at all effective as he just kept doing it when he would get frustrated. I will say that he has almost stopped doing this. He still has some days where we see this. But it helped me tremendously to know this is quite common in some kids at this age and I wasn't alone.
What I have put together from the last year is that for our son, the hitting was always present when he had some big feelings to deal with and he didn't know how, so this is how it would come out. When I started trying to help him with these feelings rather than just try to stop the behaviour, we got a lot farther. In the moment, I would tell him it's not ok to hit, get the situation under control. Then I would make the observation that something must be bothering him for him to act this way. He couldn't tell me for the longest time what was upsetting him, so I'd start guessing. I could tell when I'd hit the nail on the head as his whole body would change from wound up to relaxed. We would talk about what was bothering him, which usually involved me naming it for him and explaining the situation a bit more so he didn't have to be as anxious or angry about it. And usually that settled things for him for the rest of the day. Now we take things a bit further by expecting him to verbalize what's going on for him. He is starting to be able to do this often, but not always. We help when he needs the help with this. Sometimes I think he just tells us something but there's more going on, so again we start guessing what it could be.
I'm not sure our approach is ideal as my son went through a period where he would almost excuse his behaviour by saying something was upsetting him. But we continue with this train of conversation by explaining its ok to feel a certain way but the hitting isn't an ok way to deal with it. He's coming around.
I find I tend to do sort of a time out when he acts up these days - I pull him out of the situation and we sit for a minimum of four minutes. if he keeps hitting, I increase the time by a minute for every hit. We spend the time sitting, I don't interact much with him but encourage him to spend the time sitting with his feelings (We have a book Ahn's Anger where the child sits with his anger so we find ourselves using some of this same lingo. He likes this book). I do stay with him in the chair so it doesn't turn into a game of him trying to get out of the chair, and I think having a parent with him helps him. We do chat about the situation a bit once he's calm and we have begun strongly encouraging him to find ways of making the situation right again, by apologizing or showing some sort of affection toward the person he upset or hurt.
So for us, it's been a process. I can say we have seen an improvement.
married to DH, mother to two amazing little boys born May 18/2010 and May 20/2013!
Infertility has been part of this journey - no more littles for us, but so grateful we have two happy healthy boys and we can now begin to heal from that experience