- Two ratios apply — front-end at 28% of gross income for housing, back-end at 36% for housing plus all other debt — and the tighter one sets your maximum.
- Every dollar of existing monthly debt payment comes straight off the back-end budget, so clearing a car loan can raise your ceiling more than a raise does.
- Property taxes and homeowners insurance belong inside the front-end ratio — left at zero, the price shown is optimistic by tens of thousands.
- 28/36 is a conservative guideline, not a legal cap: qualified-mortgage rules allow a back-end ratio up to 43%, and FHA underwriting often goes higher.
How much house you can afford
Enter your gross annual income, the minimum payments on debt you already carry, your down payment, a rate and a loan term. The calculator finds the largest monthly housing payment that stays inside both of the debt-to-income ratios a lender applies, converts that payment into a mortgage, and adds your down payment to get a purchase price.
Two ratios, not one. The front-end ratio caps housing costs on their own; the back-end ratio caps housing plus every other monthly payment you make. Whichever leaves less room is the one that decides your number — which is why paying off a car loan can raise your maximum price more than a raise would.
The result is a ceiling, not a target, and it is not a pre-approval. A lender also weighs your credit score, your employment history and the loan program you apply under, several of which allow ratios well above the standard pair. Treat the figure as the top of the range worth shopping in, then decide how far below it you actually want to live.
The math
Gross monthly income is your annual income divided by twelve. The front-end (housing) DTI ratio is capped at 28% of it and covers principal, interest, property taxes and homeowners insurance — the PITI payment. The back-end (total) DTI ratio is capped at 36% and adds every other monthly obligation: car loans, student loans, minimum credit-card payments, child support. The calculator takes the smaller of 28% of income and 36% of income minus your existing debt payments, subtracts the taxes and insurance you enter under Advanced options, and treats the remainder as the mortgage payment budget.
That payment becomes a loan by running the amortization formula backwards: L = P · (1 − (1 + r)⁻ⁿ) ÷ r, where P is the monthly payment, r is the annual rate divided by 12 and n is the number of months. Adding the down payment gives the purchase price.
28/36 is the conservative conventional guideline, not a legal limit. Qualified-mortgage rules run on a back-end ratio up to 43%, FHA loans routinely approve past that with compensating factors, and automated underwriting stretches further still. The number here is deliberately tighter than the largest loan you could probably get — which is a different question from the largest one you should take.
Worked example
Take the numbers the calculator opens with: $120,000 of gross income, $400 a month of existing debt payments, $60,000 down, 6.5% over 30 years. Gross monthly income is $10,000. The front-end cap allows $2,800 a month; the back-end cap allows $3,600 less the $400 already committed, so $3,200. Front-end is tighter, so $2,800 is the budget — a mortgage of about $442,990 and a purchase price of about $502,990.
Now put $500 a month of property taxes and homeowners insurance into Advanced options, which is what the front-end ratio is meant to include. The mortgage budget drops to $2,300, the loan to about $363,885 and the price to about $423,885 — roughly $79,000 less house for a cost most buyers forget to enter. Paying off the $400 debt instead changes nothing here, because the back-end ratio was never binding.
Key terms
- Front-end DTI
- Housing costs — principal, interest, property taxes and homeowners insurance — as a share of gross monthly income. Conventionally capped at 28%.
- Back-end DTI
- All monthly debt payments including housing, as a share of gross monthly income. Conventionally capped at 36%; qualified-mortgage rules allow up to 43%.
- PITI
- Principal, interest, taxes and insurance — the four parts of the payment a lender measures against the front-end ratio, not just the loan payment itself.
- Gross income
- Income before tax and deductions. Every ratio here is measured against it rather than take-home pay, which is why the maximum can look larger than your real budget.