
umsonst
free
Without having to pay for it; free of charge.
Der Eintritt ins Museum ist heute für alle Besucher umsonst.
Admission to the museum is free for all visitors today.
free / in vain
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free
Without having to pay for it; free of charge.
Der Eintritt ins Museum ist heute für alle Besucher umsonst.
Admission to the museum is free for all visitors today.

in vain
Without the desired success or hoped-for result; futile.
All unsere Mühe war umsonst, der Kunde hat den Auftrag trotzdem storniert.
All our effort was in vain; the customer canceled the order anyway.
'Umsonst' (free / in vain) has two main meanings. The context makes clear what is meant: Is it about money and payment (free of charge), or about a missing result (in vain)?
Der Kaffee im Büro ist umsonst.
The coffee at the office is free.
In the meaning of 'kostenlos' (free of charge), 'umsonst' (free) often appears with verbs like 'sein' (to be), 'bekommen' (to get), or 'mitnehmen' (to take along). It is usually about products or services.
Die Beratung beim Anwalt war zum Glück umsonst.
Luckily, the consultation with the lawyer was free.
In the meaning of 'vergeblich' (in vain), 'umsonst' (in vain) describes an action without success. It is often combined with verbs like 'arbeiten' (to work), 'lernen' (to study), 'warten' (to wait), or 'sich Sorgen machen' (to worry).
Sie hat für die Prüfung gelernt, aber die ganze Mühe war umsonst.
She studied for the exam, but all the effort was in vain.
free
Frei and umsonst can both mean that you do not have to pay anything. In this sense, frei is especially common in fixed expressions such as „Eintritt frei“. Umsonst is more colloquial and can also mean „vergeblich“ (in vain) in another context.

Kinder unter sechs Jahren kommen umsonst ins Museum.
Children under six can enter the museum for free.
Für Kinder unter sechs Jahren ist der Eintritt frei.
Admission is free for children under six.