In the dictionary form 피곤하다(to be tired), 피곤하 is a verb/adjective stem and 다 is infinitive ending suffix. 다 is replaced with each ending suffix. There are seven speech levels in Korean, and each level has it's ending suffix. -다 is the ending suffix of Haera-che -(어/아/여)요 and -에요 are the ending suffix Haeyo-che -어요 is used after a verb or adjective of which final vowel is ㅓ, ㅕ, ㅜ, ㅡ, ㅣ, ㅐ, ㅔ, ㅖ, ㅞ, ㅚ, ㅟ, ㅢ -아요 is used after a verb or adjective of which final vowel is ㅏ, ㅑ, ㅗ, ㅘ -여요 is used after 하다 verb -에요 is used after 이다 or 아니다 Haeyo-che(Formality: low, Politeness :high) is remarkable in that it is used both with higher level pronouns (namely, titles) as well as the middle level second person pronoun dangsin. It is used mainly: In Korean phrasebooks for foreigners. Between strangers, especially those older or of equal age. Between female co-workers or friends. Haera-che(Formality: high, Politeness :low) is generally called the "plain" style. It is used: To close friends or relatives of similar age, and by adults to children. In impersonal writing (books, newspapers, and magazines) and indirect quotations ("She said that..."). In grammar books, to give examples. For example with 피곤하다 나는 피곤하다 is Haera-che 저는 피곤해요(<=조용하여요:하여 is contracted to 해) is Haeyo-che with 크다 집이 크다 is Haera-che 집이 커요 is Haeyo-che with 작다 집이 작다 is Haera-che 집이 작아요 is Haeyo-che with 먹다 사과를 먹는다 is Haera-che 사과를 먹어요 is Haeyo-che Refer to https://en.wikipedia.org/wiki/Korean_speech_levels

They have the same meaning but a different register because of the different ending forms. There are several ending forms in Korean depending on the exact meaning the speaker wants to express. Learners first need to know the four standard ones of these with no special connotation other than formality and politeness. Formality is about how official(stiff) or familiar(soft) it sounds, and politeness how respectful one is to the listener. Here are the four common declarative endings in the present tense, with the 피곤하다 example. 1. -ㅂ니다 (피곤합니다) - [formal, polite] For someone older than you or a group of people in a formal setting. 2. -다 (피곤하다) - [formal, plain] For addressing the public through a media, or when speaking to friends. 3. -아요/어요 (피곤해요) - [informal, polite] For adults outside of your close circle. 4. -아/어 (피곤해) - [informal, plain] For friends and siblings, or children. * These four styles are not strictly only for the occasions listed above - we often mix them in ordinary speech. So both 피곤해요 and 피곤하다 are natural and in common use, but usually to different types of people.

There are a lot of ways to say "I'm tired" in 한글 - 피곤하다 - 지친다 - 졸린다 - 잠온다 - 힘들다 - 쉬고싶다 etc. etc. --- If you have any question, feel free to ask me ;D

피곤해요. = I'm tired. (present tense. Also he's tired, she's tired; they're tired, etc) 피곤하다 = to be tired (unconjugated verb)