kostenfrei
free of charge
Without having to pay for it; free.
Der Versand ist bei Bestellungen über 50 Euro kostenfrei.
Shipping is free of charge for orders over 50 euros.

free of charge
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free of charge
Without having to pay for it; free.
Der Versand ist bei Bestellungen über 50 Euro kostenfrei.
Shipping is free of charge for orders over 50 euros.

The word is a clear compound of 'Kosten' (costs) and 'frei' (free). It literally means 'free of costs' and is therefore easy to understand.
Die Teilnahme am Webinar ist für alle Mitglieder kostenfrei.
Participation in the webinar is free of charge for all members.
'Kostenfrei' (free of charge) is very often used as an adverb to describe a verb. In this case, it remains unchanged in the sentence.
Sie können die Software kostenfrei herunterladen und testen.
You can download and test the software free of charge.
This word tends to belong in a formal or commercial context. It is often found in offers, on websites, or in official notices.
Wir bieten Ihnen eine kostenfreie Beratung an.
We offer you a free consultation.
free
'kostenlos' and 'kostenfrei' both mean that you do not have to pay anything. They can be used the same way in many sentences. 'kostenlos' is very common in everyday language and sounds neutral. 'kostenfrei' often sounds a bit more factual, for example in information from companies, public authorities, or on websites. In terms of meaning, the difference is small: both words say that there are no costs.

Die Beratung in der Arztpraxis ist für Versicherte kostenfrei.
The consultation at the doctor's office is free of charge for insured patients.
Meine Nachbarin hat beim Einkaufen eine kostenlose Stofftasche bekommen.
My neighbor got a free cloth bag while shopping.