When does the card clear?
The number that decides everything
Interest is charged on the balance every month. If what you pay is less than that month's interest, the balance grows no matter how long you keep paying, and the card never clears. The line above shows this month's interest so you can compare it against your payment directly.
Above that line, every extra dollar shortens the term sharply, because the balance the interest is charged on falls faster.
What this leaves out
It assumes a fixed APR and no new spending on the card. Adding purchases while paying it down changes the answer completely. Cards with a promotional rate revert to the standard APR on a date the statement gives; use the rate you will actually be charged.
Minimum payments are usually set as a small percentage of the balance, so they fall as the balance does. That is what makes minimum-only payoff take decades.