The quality of being formidable; the state of inspiring fear or respect through being large, powerful, or threatening.
From Latin 'formidabilis' (fearful, dreadful) from 'formidare' (to fear), related to 'formido' (fear). The '-ability' suffix converts the adjective into a noun expressing the abstract quality or state.
The word 'formidable' comes from the Latin word for fear itself, so formidability is literally 'the quality of making people afraid'—it's why we use it for everything from powerful chess players to massive storms.
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