Should you refinance?
The part other calculators hide
A lower monthly payment is not the same as paying less. Refinancing eight years into a thirty-year loan back into a fresh thirty-year loan stretches the remaining balance over a longer period, so the monthly figure falls even when the rate barely moves. You can end up paying more in total interest and feel like you saved.
So this one always shows the lifetime number next to the monthly one, and says plainly when the payment falls but the total rises. The same-term comparison tells you how much of the saving came from the rate rather than from the extra years.
Break-even is the closing costs divided by the monthly saving: the month you start being ahead. Refinance and move before then and the refinance cost you money.
What this leaves out
The arithmetic here assumes you pay closing costs upfront rather than rolling them into the balance, and it compares principal and interest only, so escrow, PMI and points are not in it. It is a comparison of two loans, not tax advice, and mortgage interest deductibility can change the answer if you itemise.
It also cannot tell you whether waiting for a better rate beats refinancing today. That is a genuine option, and holding it has value.