Unreasonable; unjustifiable; also used to mean impossible or impractical depending on context.
そんな条件は無理だよ、交渉のしようがない。
Those conditions are unreasonable; there's no way to negotiate.
彼の提案は無理があると思う。
I think his proposal has unreasonable aspects.
無理な要求を断るのは大事だ。
It's important to refuse unreasonable demands.
Impossible; cannot be done in practice or reality.
明日までにこれを全部終わらせるのは無理だ。
It's impossible to finish all this by tomorrow.
一人で40箱を運ぶのは無理だ。
It's impossible for one person to carry 40 boxes.
彼を説得して来させるのは無理だろう。
It will probably be impossible to persuade him to come.
Forcible; forced; done by compulsion (often used adverbially as 〜に).
荷物を無理に押し込んだら壊れてしまった。
When I forced the luggage in, it got damaged.
彼は無理に会話を続けようとした。
He tried to force the conversation to continue.
Excessive; immoderate — describes overwork or unreasonable burden.
毎日の無理な残業で体を壊した。
I ruined my health with daily excessive overtime.
無理なダイエットは健康に悪い。
An excessive diet is bad for your health.
To overdo; to push oneself too hard; to try too hard (usually expressed as 無理をする).
体調が悪いのに無理をして出社した。
Even though I felt unwell, I forced myself to go to work.
無理をすると後で後悔するよ。
If you overdo it, you'll regret it later.
Interjection meaning 'no way', 'not a chance' — colloquial, used to strongly refuse or deny.
『手伝ってくれる？』『無理！今日は忙しいし』
'Can you help me?' 'No way! I'm busy today.'
そんな高額な買い物は無理だよ。
Buying something that expensive — no way.
Mathematics: indicating 'irrational' (not rational) in specialist contexts.
この数は有理数ではなく無理だと示された（文脈により無理数の意味）。
In context it was shown that this number is not rational but irrational.