I gotta go = informal I gotta run = informal I have to go = informal/formal I need to go. = formal That's how I would put it. I hope it helps.

If you end a conversation with "I'm leaving", it sounds a bit brutal, it means like: "I am going and I don't care if you like it or not", it shows a determination in what you are doing. I would suggest you to say " I am (really) sorry but I have to go now" If you say, sorry i got to go that's probably a phrase you would use with your friends. I hope this helps :)!

Francesco has made a really good point. Sometimes, a factual and truthful statement can sound rude in English-speaking culture. "I have to go" or even the informal "I('ve) gotta go" suggest that you don't want to go, but something else is causing you to go. You have an obligation somewhere else. These are perfectly fine. You can also give your reason for leaving, instead of telling the other person that you are going. For example, "I have a class now", "Dinner's on the table", or "Someone's just arrived" are polite ways of excusing yourself and leaving. If you can learn to speak indirectly in English (but still make your message clear), then you have a very useful skill. :)

I am inclined to find a good excuse to leave such as "I am sorry to leave now since I have an appointment with a friend of mine at home." or any excuse that may comfort you and the correspondent.

Those were all great answers. Another polite way to end the conversation is to say "It was great talking to you. Hope to see you next time." This way you send the message that you really enjoyed talking to the person while at the same time you are letting them know in a subtle, indirect way that you have to go without actually bluntly saying you have to go. That response is if you are leaving the event altogether. If you are staying at the gathering, but want to talk to other people, then you could say "Great meeting you." then go off to the rest room or to get a drink and when you are done with your break you just inconspicuously mingle with other people. Another way is before you introduce a 3rd person into your conversation and then while the other two are talking, you motion to your glass and slip away to get a refill then meet another group of people.