なきゃ ＆ なくちゃ

These mean 'to have to do something' or 'must do something'.

When you want to say, 'I have to go now', you could translate it as
もう （私は）行かなくてはいけない。Or
もう （私は）行かなければならない。
These are rather formal, and in day to day conversations, these sentences would become:
もう行かなくちゃ。Or
もう行かなきゃ。

More examples
食べなきゃ（いけない）。I have to eat.
食べなくちゃ（いけない）。I have to eat.


When we use them:
With possible consequences:
勉強し「なくちゃ／なきゃ」試験に受からない。If I don't study, I will fail the exam.

Showing your determination:
ぜったいに勝たなくちゃ（いけない）or （だめだ）。I really have to win.

When you tell other people what to do:
もっと日本語の勉強しなくちゃ。You have to study Japanese more.

For the most part, なきゃ and なくちゃ, are interchangeable, but there is a slight difference. なきゃ is a bit stronger than なくちゃ. It we feel something has to be done urgently or we really feel obliged to do something  we tend to use なきゃ.


Similarly, てはいけないー＞ちゃいけない
ではいけないー＞じゃいけない


Source: http://www.maggiesensei.com/2010/11/20/%E3%80%9C%E3%81%AA%E3%81%8D%E3%82%83%EF%BC%86%E3%80%9C%E3%81%AA%E3%81%8F%E3%81%A1%E3%82%83-nakya-nakucha-suffixes/