Learn Hardcore Portuguese (Portugal): Eu acho que ele está cansado hoje.

Achar literally means “to find”, but in everyday speech it very often means “to think” / “to feel (that)” in the sense of giving an opinion or impression:

Eu acho que ele está cansado hoje.
→ I think / I feel that he is tired today.

Pensar is also “to think”, but:

penso is a bit more formal or careful, like a considered thought.
acho is more common in conversation, often more subjective, like “I have the impression that…”.

You can say:

Eu penso que ele está cansado hoje.
This is correct, just slightly more formal / neutral than acho in everyday European Portuguese.

Why do we need que after acho? Is it the same as English “that”?

Yes. Que here is a complementizer: it introduces the clause “ele está cansado hoje”.

Eu acho que ele está cansado hoje.
Literally: “I think that he is tired today.”

In English, “that” is often dropped:

I think (that) he is tired today.

In Portuguese, you normally must keep que:

✅ Eu acho que ele está cansado hoje.
❌ Eu acho ele está cansado hoje. (incorrect in standard Portuguese)

In very informal spoken language, some people may drop que, but that’s not standard and can sound broken to a teacher’s ear.

Can I drop eu and just say Acho que ele está cansado hoje?

Yes.

Portuguese is a pro-drop language: you can usually omit the subject pronoun because the verb ending tells you who the subject is.

Eu acho que ele está cansado hoje.
Acho que ele está cansado hoje.

Both mean “I think he is tired today.”
Omitting eu is very common in speech and writing, and sounds natural.

Why is it está cansado and not é cansado?

This is the classic ser vs. estar difference.

ser = more permanent / essential characteristics
estar = temporary state / condition or location

Cansado (tired) is a temporary state, so we use estar:

Ele está cansado hoje.
→ He is tired today (just now, temporarily).

If you said:

Ele é cansado.

it would sound like “He is (by nature) a tired person”, as if it’s a permanent trait, which is unusual and a bit odd.

Where can I put hoje in this sentence? Are other positions also correct?

Several positions are correct; the nuance is small:

Eu acho que ele está cansado hoje.
→ Most neutral, very common.
Eu acho que hoje ele está cansado.
→ Slightly emphasizes “today” (as opposed to other days).
Hoje, eu acho que ele está cansado.
→ Emphasizes “today” even more, and sounds a bit more structured or written-like.

All three are grammatically correct in European Portuguese. The default everyday choice is probably (1).

Could I say Eu acho-o cansado hoje? Is that correct?

Grammatically, yes, but it’s unusual in everyday speech and the meaning shifts a bit.

Eu acho-o cansado hoje.
Literally: “I find him tired today.”

Nuance:

Sounds more formal or literary.
Feels more like a judgement/assessment of him at this moment, often based on immediate perception.

For the normal “I think he is tired today” in everyday European Portuguese, you should prefer:

Eu acho que ele está cansado hoje.

Can I omit ele and just say Eu acho que está cansado hoje?

Yes, if the context already makes it clear who you’re talking about.

Eu acho que ele está cansado hoje.
→ Explicit “he”
Eu acho que está cansado hoje.
→ Literally “I think (he/she/you) is tired today”, so the subject is understood from context.

In a conversation where it’s obvious that you’re talking about some specific he, Eu acho que está cansado hoje is natural in European Portuguese.

How would I say this with the informal “tu” form instead of “ele”?

If you want to say “I think you (informal, singular) are tired today”, you’d use tu:

Eu acho que tu estás cansado hoje. (to a man)
Eu acho que tu estás cansada hoje. (to a woman)

As usual, you can drop eu:

Acho que tu estás cansado/cansada hoje.

In many regions of Portugal, tu is the normal informal “you”; você is rarer or more formal/distant than in Brazil.

How do you pronounce acho and está in European Portuguese?

Approximate pronunciation (European):

acho → [ˈa-ʃu]
- a like “a” in “father” (but shorter)
- ch = sh sound (like “shoe”)
- final o is close to English “oo” but shorter
está → often [ʃˈta] in fast EP speech
- the written e often disappears, leaving something like “shta”
- á has a stressed “ah” sound

So a natural EP pronunciation of the whole sentence might sound like:

[ew ˈaʃu kɨ ʃˈta kɐ̃ˈsaðu ˈoʒɨ]
(very roughly: “ehw ASH-oo kɨ SHTA kun-SAH-do OH-zh(uh)”)

Is there a difference between “Eu acho que ele está cansado hoje” and “Na minha opinião, ele está cansado hoje”?

They’re close in meaning, but the tone is different.

Eu acho que ele está cansado hoje.
→ Most natural, everyday way to say “I think he’s tired today.”
Na minha opinião, ele está cansado hoje.
→ Literally “In my opinion, he is tired today.”
→ Sounds more formal, more like you’re explicitly giving an opinion, e.g. in a discussion or argument.

In casual conversation, Eu acho que… is far more common.

How do I say “I don’t think he is tired today”?

You normally negate the main verb “achar”, not the verb in the subordinate clause:

Eu não acho que ele esteja cansado hoje.
(subjunctive esteja is common here in more careful speech)

In everyday European Portuguese, many people will also say:

Eu não acho que ele está cansado hoje.

Both are heard; the version with esteja is more grammatically conservative.

More informal still:

Não acho que ele esteja/está cansado hoje.
(dropping eu)

Can achar be used without que, like “Eu acho isto difícil”? How is that different from “achar que”?

Yes, achar has two common patterns:

achar + que + clause
- Eu acho que ele está cansado hoje.
  → I think (that) he is tired today.
achar + direct object + adjective / noun
- Eu acho isto difícil.
  → I find this difficult.
- Ela acha o filme interessante.
  → She finds the film interesting.

Difference:

achar que + clause = “think that …”
achar + object + adjective = “find/consider [something] [adjective]”

Your original sentence uses pattern 1, which is the standard way to say “I think (that) …” in Portuguese.