Something that one cannot or does not want to imagine because it is extremely unlikely, shocking, or unacceptable.
example
Vor 50 Jahren wäre ein Computer in jeder Hosentasche undenkbar gewesen.
Fifty years ago, a computer in every pocket would have been unthinkable.
Usage tips
Word structure
The word is built logically: the prefix 'un-' negates, the stem 'denk-' comes from 'denken' (to think), and the ending '-bar' means '-able' or 'capable of'. So 'undenkbar' literally means 'not think-able'.
EXAMPLE
Eine Welt ohne Internet ist für junge Leute heute undenkbar.
A world without the internet is unthinkable for young people today.
Sentence structure
'Undenkbar' is very often used in the fixed structure 'Es ist/wäre undenkbar, ...' (It is/would be unthinkable ...), followed by a 'dass' clause or an infinitive with 'zu'.
EXAMPLE
Es ist undenkbar, dass er den Termin vergessen hat.
It is unthinkable that he forgot the appointment.
Typical intensifiers
To strengthen the meaning, 'undenkbar' is often combined with adverbs like 'völlig' (completely), 'absolut' (absolutely), or 'einfach' (simply).
EXAMPLE
Ein Umzug in eine andere Stadt ist für sie zurzeit absolut undenkbar.
Moving to another city is absolutely unthinkable for her at the moment.
Compare with
antonym
undenkbar vs möglich
possible
'möglich' and 'undenkbar' are opposites here. 'möglich' says that something is conceivable or can happen, even if it is not certain. 'undenkbar' says much more strongly that one can hardly imagine something, or cannot imagine it at all, often because it would be extremely unlikely, shocking, or unacceptable. So 'möglich' leaves a door open. 'undenkbar' almost completely rules out the idea.
undenkbar
Für die Ärztin ist es undenkbar, einen Patienten ohne Hilfe nach Hause zu schicken.
For the doctor, it is unthinkable to send a patient home without help.
möglich
Nach dem Gespräch ist eine Lösung wieder möglich.
After the conversation, a solution is possible again.