The formula
EMI = [P × r × (1 + r)^n] ÷ [(1 + r)^n − 1], where P is the principal, r is the monthly interest rate (annual rate ÷ 12 ÷ 100) and n is the number of months. Nothing else is involved, which is why two calculators that use the same inputs give the same answer.
A worked example
Take ₹10 lakh at 9% for 15 years. The monthly rate is 0.0075 and n is 180. (1.0075)^180 is about 3.838. The EMI works out to roughly ₹10,143. Over 180 months you pay about ₹18.26 lakh, so the interest is about ₹8.26 lakh — close to the amount you borrowed.
Why the split changes every month
In month one, interest is 0.75% of ₹10 lakh, or ₹7,500. The remaining ₹2,643 reduces the principal. In month two, interest is charged on ₹9,97,357 instead, so slightly less goes to interest and slightly more to principal. By the final year almost the entire EMI is principal.
What this means in practice
Because interest is front-loaded, prepaying in the first years saves far more than prepaying at the end. That is the single most useful fact about loan repayment, and it is why a small extra payment early is worth more than a large one later.