The same loan, asked from either end
Most loan calculators run one way: here is the term, here is the payment. The more useful question is often the other one. You know what you can afford each month; what you want to know is how long it takes to be rid of the balance.
This page answers both, and it answers them with one definition. Solving for a term runs the same monthly schedule with the payment you gave and counts the instalments until the balance reaches nothing. There is no second formula and no approximation anywhere in it.
What that buys is a schedule that closes on itself: take the payment this page works out for a term, hand it back as a payment, and the same term and the same rows come out to the minor unit. Note the direction of that sentence. Paying more than the contractual instalment finishes sooner, so a term read off a larger payment is a shorter term, and typing it back gives the smaller payment that also clears the balance in it.
What the two directions tell you
Running it from a term prices a decision already taken: this is the agreement, this is what it costs each month, this is the interest over its life. Running it from a payment prices the decision itself, and it shows something the first direction hides. Once interest is involved, raising the payment shortens the loan by more than simple proportion would suggest, because every unit above the interest goes straight against the balance and the interest on it then disappears for every month that remains.
The effect is largest on expensive debt. Half again on the payment does considerably better than the third off the term that proportion alone would give, and the higher the rate the wider that gap. It is worth trying a few figures in the payment direction rather than accepting the one on the statement.
Two ways a payment fails
Below a certain payment a loan never ends, and the page says which of the two reasons applies.
The first is a payment that does not cover the first month's interest. Then the balance grows every month and no schedule exists at all. This is the arithmetic behind a minimum payment that never seems to move a balance, and it is worth seeing stated plainly.
The second is a payment that does clear the balance, but takes longer than fifty years, which is as far as this page goes. Nudging it up moves the term sharply, which is the whole lesson of the section above.
The conventions behind the schedule
Payments are monthly. Interest for a month is the balance times the annual rate divided by twelve, rounded to the nearest minor unit in a single step, so a monthly rate is never formed as a number of its own and never drifts over hundreds of instalments. The last payment is whatever is left, which is usually a little smaller than the rest and is only equal to them when the balance happens to divide exactly.
The rate is the nominal annual rate on the agreement. It is not an annual percentage rate, because this page asks about no fees. Where a fee is involved, the personal loan page takes one and prints the rate it works out to.
There is no variable rate here, no payment holiday, no fee, no insurance and no penalty for early repayment. Anything the contract adds on top has to be added by hand.