A home purchase is really three linked numbers, not one. What a lender is willing to approve, what your household can actually carry every month once taxes, insurance, HOA dues, and maintenance are added to principal and interest, and how much cash needs to be sitting in your account on closing day. Treating any one of those in isolation is how a technically-approved buyer ends up house-poor, or short of cash at the closing table.

Where an affordability estimate usually breaks

Using gross income for a debt-to-income ratio instead of checking what take-home pay can actually absorb.
Comparing only principal and interest across two homes, when HOA dues, insurance, or PMI make the true monthly cost very different.
Treating a pre-approval letter as a guarantee rather than a snapshot based on the income, debt, and rate at the time it was issued.
Forgetting that PMI usually drops off automatically once a loan reaches a specific loan-to-value threshold — not just "eventually."

The calculators above cover each of these pieces separately so they can be checked against each other rather than folded into one opaque number. For the fuller picture of what a mortgage payment leaves out, and how a purchase price becomes a closing-day cash requirement, see the true cost of a mortgage payment, the homebuyer cost checklist, and what closing costs mean for your cash.