Hallo 
The other day I came across the word umsonst . Can it be used as a synonym for kostenlos or does it have another meaning?
Thanks
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I’m not German, but I believe umsonst has more of a negative connotation… I think kostenlos is more like “for free” and umsonst is “for nothing”
I’ll defer to the actual Germans though
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Perfekt erklärt!
Es gibt auch den Satz:
Schulbildung ist kostenlos, in manchen Fällen aber auch umsonst!
Oder Meine Schulbildung war kostenlos, deine war umsonst! 
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I love that one jajajajaja
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Like @Mona_O said perfekt erklärt 
To make her examples even more clear, a synonym for umsonst is vergebens ( in vain )
Kostenlos just means kostenlos = es kostet nichts
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That´s true, but you can use umsonst also for “for free”, whereas kostenlos can´t be used for “for nothing”.
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The explanation is great and makes lots of sense, but I use it in both ways I would say 
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In the informal speech those words are often used as synonyms.
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