Why do people in spoken conversation sometimes say 간다 instead of 가요 when they are leaving? I thought 간다 was a written form.
1Short answers: No rules say -ㄴ다 should be used only in written language. 간다 belongs to 해라체; 가요 to 해요체.– KlmoJul 13, 2019 at 5:56
In spoken conversation, "간다" has the meaning of leave or join the get-together. It is only used when communicating your action to other or others. Usually, it is a stronger tone than "가요" to make person or people aware of your action. So it is mainly used by a friend, or by a boss.
In written expression, "간다" has a much more general meaning.
First of all, note that ~ㄴ(는)다 is 반말. Also note that it is technically narrative form, which is commonly used in writing but also sometimes used in spoken Korean. I learned that this form, when spoken, is "announcing" (narrating) something to everyone/no one in particular.