It is also Dante. It isn't doctrine. And the true answer to "where is it?" is simpler and a little stranger.
What the Church has and hasn't said
The Church has defined that Purgatory exists, that the souls there are purified, and that the living can help them (Lyons II, Florence, Trent, and CCC 1030-1032). That is the whole of it. She has never defined where it is, how long a soul stays, whether the fire is literal, or what a soul feels from one moment to the next.
The Council of Trent was almost fussy on the point. It told bishops to keep the "difficult and subtle questions" out of ordinary preaching, along with whatever feeds curiosity, superstition or the hunt for money. The bishops of the sixteenth century had seen what happens when a doctrine gets a map. It gets a price list.
A condition, not an address
Some medieval writers placed Purgatory under the earth, close to Hell. Aquinas, thinking within the science of his day, wondered whether its fire might lie near the fire of the damned. These were serious men making serious attempts, with the only tools they had.
The clearest modern guidance came from Pope John Paul II, in a general audience on August 4, 1999. He said that the word Purgatory doesn't point to a place. It points to a condition of existence, the state of someone being purified before entering the fullness of communion with God.
When you think about it, that's what we'd expect. After death the soul is no longer a body in a physical world, so it isn't sitting at a set of coordinates. The Catechism says the same about the other two destinations: Heaven is a state of communion with God (CCC 1024), and Hell a state of definitive self-exclusion from it (CCC 1033). If someone insists on an answer to "where," the most faithful one may be: wherever souls are being drawn toward God.
How long?
You've heard it said, and probably said it yourself: "She'll probably be in Purgatory for years." It's a kind thing to say, and as a way of speaking it's fine. As a statement of fact it doesn't hold.
Earthly time is measured by the sun and the clock, and the soul after death is outside of both. We have no way to say a soul has spent ten years in purification, because years belong to this world. Pope Benedict XVI touched on this in Spe Salvi. The moment of meeting Christ, he wrote, can't be measured by earthly chronology. It's what he called the heart's time, the time of passing over into communion with God. What counts isn't how much but how deeply.
Two old customs have fed the confusion, so they're worth explaining. Older indulgences were once labeled with numbers like "300 days" or "seven years," and many people took that to mean time taken off Purgatory. It never did. The numbers referred to the length of public penance the ancient Church used to impose, and Pope Paul VI dropped them entirely in 1967 so nobody would be misled.
Then there are the Gregorian Masses, thirty Masses on thirty consecutive days for one soul, a devotion going back to Pope Gregory the Great around the year 600. It's an ancient and beautiful custom, and the Church allows it. But it's an act of trust, not a timer. Nobody can say that a soul is released on the thirty-first day.
A word about visions
Saints and mystics have described Purgatory in vivid language, among them Catherine of Genoa, Gertrude, Faustina Kowalska and Padre Pio. Many of these accounts are moving, and they've led people to pray more faithfully for the dead. But the Church classes them as private revelation. Nobody is bound to believe them, even when the Church has judged them safe. The shape of the torments, the number of years, the layers: these are the mystic's experience put into the images of the age.
Will it ever end?
Yes. Purgatory is temporary for every soul that enters it. And the Church teaches that after the Last Judgment, when Christ returns and the dead are raised, there will be no Purgatory at all, only the fullness of Heaven for the saved and the finality of Hell for those who refused Him (CCC 1038-1041). Its work will be finished, and it will have emptied itself into Heaven.
A better question
Often "where?" and "how long?" are really cover for something else: is my mother all right? The Church can't answer that with a map or a date. What she can say is that those who die in God's friendship are in His hands, and that our prayers reach them. So rather than trying to calculate, do something. Have a Mass offered. Say the Rosary. Give to someone in need, in her name. In God's economy, love spent on the dead is never wasted.
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