In short

Both particles can sit on the subject, so the choice is about information, not grammar: 이/가 presents something new or picks out who/what, while 은/는 flags the already-known topic or draws a contrast. Inside a modifier clause, on the complement of 되다/아니다, and on the subject of 있다/없다/필요하다, 이/가 is the particle you need.

The rule

Lesson Marking the subject and the topic: 이/가 and 은/는 gave you the shapes (이/은 after a 받침, 가/는 after a vowel). This lesson is about which to reach for when both would be grammatical.

Step 1 - New information takes 이/가, old information takes 은/는

When a referent enters the discourse for the first time, it is new, so it takes 이/가. Once it is on the table and you say more about it, it is the topic, so it switches to 은/는. This is why stories begin one way and continue another:

옛날에 한 사람이 살았어요. 그 사람은… (Yennare han sarami sarasseoyo. Geu sarameun…) - Long ago there lived a person. That person… First mention 사람이, next mention 사람은.

Step 2 - Question words and their answers take 이/가

An unknown thing can never be your topic, so a question word in subject position uses 이/가 - and the answer that fills the same slot is new information, so it does too:

누가 왔어요? 제가 왔어요. (Nuga wasseoyo? Jega wasseoyo.) - Who came? I came. Answering 저는 왔어요 would be wrong here.

Step 3 - Contrast takes 은/는

은/는 carries a built-in “as for X (as opposed to something else)”. Put it on two nouns to set them against each other:

커피는 좋아하는데 차는 싫어해요. (Keopineun joahaneunde chaneun sireohaeyo.) - I like coffee, but tea I dislike.

The same contrastive 은/는 shows up in negation and comparison: 고기는 안 먹어요 (Gogineun an meogeoyo) - meat I don’t eat (but other things I do). Note what happened to 을/를 there: 은/는 pushes out 이/가 and 을/를 exactly as 도 and 만 do (lesson 15), but it stacks after 에, 에서, 한테, 부터 and 보다 - 이달부터는 값이 올라요 (idalbuteoneun gapsi ollayo), 거기에서는 안 팔아요 (geogieseoneun an parayo).

Step 4 - Inside a clause, only 이/가 survives

은/는 marks a whole-sentence topic, so it cannot live inside a modifier (relative) clause. The subject there must be 이/가:

Modifier clause: [ …이/가 + Verb-(으)ㄴ/는 ] + Noun.

제가 산 책 (jega san chaek) - the book I bought. 저는 산 책 is blocked.

Step 5 - Double marking: topic 은/는 + inner subject 이/가

Many “have / hurt / need / be long” sentences carry both particles - a topic, then a grammatical subject inside the comment. This is normal, not a mistake:

Noun-은/는 + Noun-이/가 + Predicate. 저는 머리가 아파요 (Jeoneun meoriga apayo) - I have a headache (as for me, the head hurts).

Step 6 - Verbs that force 이/가 on their complement

The complement of 되다 (become), 아니다 (not be), and the subject of 있다/없다 (exist/have) and 필요하다 (be needed) take 이/가, never 을/를 and never a bare 은/는:

의사가 됐어요 (uisaga dwaesseoyo) - became a doctor; 시간이 없어요 (sigani eopseoyo) - have no time; 돈이 필요해요 (doni piryohaeyo) - need money.

Step 7 - In casual speech the particle is often dropped

Spoken Korean freely drops both particles: 밥 먹었어요? (Bap meogeosseoyo?) - Did you eat? Dropping neutralizes the topic/subject/contrast distinction, and intonation and context carry it instead - so in writing, put the particle back.

Forms & patterns

The shapes (revision):

Which one, by situation:

The double-subject frame (topic + inner subject):

Examples

Common mistakes

• 옛날에 한 사람은 살았어요. (Yennare han sarameun sarasseoyo.) -> 옛날에 한 사람이 살았어요. (Yennare han sarami sarasseoyo.) - A referent appearing for the first time is new information; new = 이/가, not topic 은/는.
• 누가 했어요? 저는 했어요. (Nuga haesseoyo? Jeoneun haesseoyo.) -> 누가 했어요? 제가 했어요. (Nuga haesseoyo? Jega haesseoyo.) - The answer fills the “who” slot with new information, so it takes 이/가 (fused 제가), never 은/는.
• 저는 산 책이에요. (Jeoneun san chaegieyo.) -> 제가 산 책이에요. (Jega san chaegieyo.) - 은/는 is blocked inside a modifier clause; the embedded subject must be 이/가.
• 책는 재미있어요. (Chaekneun jaemiisseoyo.) -> 책은 재미있어요. (Chaegeun jaemiisseoyo.) - 책 ends in the 받침 ㄱ, so the topic particle is 은. Check the actual last syllable every time.
• 저는 돈을 필요해요. (Jeoneun doneul piryohaeyo.) -> 저는 돈이 필요해요. (Jeoneun doni piryohaeyo.) - 필요하다 means is needed, so what you need is its subject: 이/가, not object 을/를.

Tips

• New vs known is the master key. 이/가 puts something on the table or points at it (who did it?); 은/는 comments on what is already there (as for it…). If you could answer “who?” or “what?” with the noun, use 이/가.
• Read 은/는 as “as for”, and hear the contrast in it. Even a lone 커피는 quietly implies “coffee, as opposed to other drinks” - which is exactly why negation and comparison love 은/는.
• A subject inside brackets is always 이/가. The moment a subject sits inside a [ …(으)ㄴ/는 ] 것/책/사람 modifier, 은/는 cannot reach it.
• 저는 X가 sentences are everywhere. Feelings, body, needs and skills use double marking: 저는 머리가 아파요, 저는 시간이 없어요, 저는 한국어가 좋아요. Learn the pattern, not each verb.