Something that cannot be imagined or thought possible.
Examples:
The complexity of space travel is inconceivable to most.Her skills in chess are inconceivable to her peers.An inconceivable chain of events led to his unexpected win.
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Unthinkable
/ʌnˈθɪŋkəbəl/
Something so unlikely or impossible that it cannot be considered.
Examples:
To climb that summit alone was once unthinkable.The idea of peace seemed unthinkable in those times.Building a city underwater remains largely unthinkable.
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Ways to tell them apart:
Inconceivable often conveys a stronger sense of disbelief than unthinkable.
Unthinkable can imply something is not likely to happen, but not impossible, whereas inconceivable suggests it can't even be imagined.
Think of inconceivable as beyond imagination because its not possible, and unthinkable as beyond consideration because its highly undesirable.
Inconceivable can be used in more abstract contexts where something defies logic or understanding.
Unthinkable is often used in moral or ethical contexts, where a situation or action is shocking or unreasonable.