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Eucatastrophe is a neologism coined by Tolkien from Greek ευ- "good" and καταστροφή "sudden turn".
In essence, a eucatastrohpe is a massive turn in fortune from a seemingly unconquerable situation to an unforseen victory, usually brought by grace rather than heroic effort. Such a turn is catastrophic in the sense of its breadth and surprise and positive in that a great evil or misfortune is averted.
 Coining of the term
In his On Fairy-Stories Tolkien described the concept:
- "But the 'consolation' of fairy-tales has another aspect than the imaginative satisfaction of ancient desires. Far more important is the Consolation of the Happy Ending. Almost I would venture to assert that all complete fairy-stories must have it. At least I would say that Tragedy is the true form of Drama, its highest function; but the opposite is true of Fairy-story. Since we do not appear to possess a word that expresses this opposite — I will call it Eucatastrophe. The eucatastrophic tale is the true form of fairy-tale, and its highest function.
The consolation of fairy-stories, the joy of the happy ending: or more correctly of the good catastrophe, the sudden joyous “turn” (for there is no true end to any fairy-tale): this joy, which is one of the things which fairy-stories can produce supremely well, is not essentially 'escapist', nor 'fugitive'. In its fairy-tale—or otherworld—setting, it is a sudden and miraculous grace: never to be counted on to recur. It does not deny the existence of dyscatastrophe, of sorrow and failure: the possibility of these is necessary to the joy of deliverance; it denies (in the face of much evidence, if you will) universal final defeat and in so far is evangelium, giving a fleeting glimpse of Joy, Joy beyond the walls of the world, poignant as grief.
It is the mark of a good fairy-story, of the higher or more complete kind, that however wild its events, however fantastic or terrible the adventures, it can give to child or man that hears it, when the “turn” comes, a catch of the breath, a beat and lifting of the heart, near to (or indeed accompanied by) tears, as keen as that given by any form of literary art, and having a peculiar quality."
- ― On Fairy-Stories
Tolkien would further elaborate on eucatastrophes in one of his letters:
- "I coined the word 'eucatastrophe': the sudden happy turn in a story which pierces you with a joy that brings tears (which I argued it is the highest function of fairy-stories to produce). And I was there led to the view that it produces its peculiar effect because it is a sudden glimpse of Truth, your whole nature chained in material cause and effect, the chain of death, feels a sudden relief as if a major limb out of joint had suddenly snapped back. It perceives – if the story has literary 'truth' on the second plane (....) – that this is indeed how things really do work in the Great World for which our nature is made. And I concluded by saying that the Resurrection was the greatest 'eucatastrophe' possible in the greatest Fairy Story – and produces that essential emotion: Christian joy which produces tears because it is qualitatively so like sorrow, because it comes from those places where Joy and Sorrow are at one, reconciled, as selfishness and altruism are lost in Love."
- ― Letter 89
 Within the legendarium
Tolkien himself made use of the trope of eucatastrophe several times in his own writings. The most famous usage is the final destruction of the One Ring within Mount Doom. Frodo was unable to destroy the Ring by his own strength. The Ring is destroyed by the intervention of Ilúvatar after it is taken from Frodo by Gollum, who Frodo himself spared earlier in the story. Had Gollum not been there, the Ring may only have been destroyed by Frodo casting himself into the fire, if it was destroyed at all.
The other famous example of a eucatastrophe is the War of Wrath fought on behalf of the Eldar at the end of the First Age. Eärendil was able to reach Valinor and persuade the Valar to go to war against Morgoth for the sake of Elves and Men. Without the intervention of the Valar, Morgoth would never have been defeated by any mortal strength.