House Affordability Calculator

How lenders decide what you can afford

Affordability is driven by ratios, not just income. The front-end (28%) rule limits housing costs to 28% of gross monthly income; the back-end (36%) rule limits all debt to 36%. Whichever gives the smaller housing budget wins. In the worked example — $120,000 a year, $500 of monthly debts, $40,000 down at 6.5% — the budget supports about $2,800 a month, a $442,990 loan, and roughly a $482,990 home. The front-end ratio is the binding limit here. These figures come from the same tested engine as the calculator above.

Guide: How affordability is estimated follows the 28/36 guideline, the payment factor and the closed-form property-tax rearrangement step by step. Every guide on this site is listed at /guides/.

The six steps the engine runs

The methodology page states the rule in one sentence: "Affordability uses the 28/36 debt-to-income guidelines, and property tax that scales with the home price is solved with a closed-form rearrangement rather than an approximation." This section follows that sentence through the engine on the fictional inputs behind the hint above — $120,000 of gross annual income, $500 of existing monthly debt payments, $40,000 down, a 6.5% rate and a 30-year term. None of these is a rate or price to expect; they are labels for the arithmetic.

1. Gross monthly income. The annual figure is divided by twelve: $10,000. The engine works in months because the payment it will eventually size is monthly.
2. Front-end ceiling. Gross monthly income multiplied by the housing share. With no other debts the budget is this ceiling alone, and on these inputs it is $2,800.00 — 28% of $10,000.
3. Back-end ceiling. Gross monthly income multiplied by the total-debt share, $3,600.00 (36%), minus the $500 already committed to other payments: $3,100.00.
4. The housing budget. The smaller of the two ceilings. Here the front-end figure is lower, so the budget is $2,800.00 and the result is labelled front-end. If the smaller ceiling is zero or negative the engine stops and returns an error rather than a price.
5. From budget to loan. The engine computes the payment factor — the monthly payment per dollar borrowed under the standard amortized-loan (PMT) formula with monthly compounding — for the rate and term, and divides the budget by it: a loan of $442,990. Running that loan back through the payment formula gives $2,800.00 a month, the budget to the cent. The same formula prices the methodology's reference loan, $200,000 at 6% over 30 years, at $1,199.10.
6. From loan to price. The down payment is added to the loan: $482,990. With no property tax entered that is the whole calculation, and the "principal and interest at that price" line, $2,800.00, equals the budget because nothing else is reserved from it.

Which ceiling binds, and why the label matters

The "Limited by" line in the result box names the ceiling that produced the budget, and so the input that moves the result. While the front-end ceiling binds, existing debts have no effect on the price at all: on the fictional inputs, debts of $500 give a budget of $2,800.00 and debts of $700 give $2,800.00, the same figure and the same front-end label, because the back-end ceiling — $2,900.00 at $700 of debts — is still above the front-end one. Push the debts to $1,200 a month and the back-end ceiling drops to $2,400.00, below the front-end figure; the label flips to back-end, the loan falls to $379,706 and the price to $419,706. From that point every dollar of monthly debt removes a dollar from the budget, and the price falls by that dollar divided by the payment factor.

Two reading notes. First, the ceilings are compared at full precision, not as displayed cents: the engine labels a result front-end when the front-end ceiling is less than or equal to the back-end ceiling, and back-end otherwise. At $800 of debts on these inputs both ceilings display as $2,800.00, yet the comparison resolves on a difference far smaller than a cent and the result is labelled back-end — equal-looking ceilings can carry either label. Second, the label describes the arithmetic, not a verdict on your finances: a back-end label means only that the debts field, rather than the income field alone, set the budget.

What a property tax rate does to the price

Adding a property tax rate turns the division into a small equation. Tax is charged on the home price, but the price is the unknown being solved, so the engine cannot compute the tax first and subtract it. Instead it writes the budget as two terms — the loan times the payment factor, plus the price times the monthly tax rate — substitutes price minus down payment for the loan, and rearranges to isolate the price. That is the closed-form rearrangement the methodology page refers to: exact, with no iteration and no rounding between steps.

On the fictional base inputs with a 1.2% annual tax rate added, the budget is unchanged at $2,800.00 — tax does not alter the income-and-debts ceiling — but the price falls from $482,990 to $417,014 and the loan from $442,990 to $377,014. Principal and interest at the new price are $2,382.99; the remaining $417.01 of the budget is the monthly tax reserve, 1.2% of $417,014 spread over twelve months. The two parts add back to the budget to the cent, which is the check that the rearrangement is right.

The same rearrangement explains a result that surprises people. Without a tax rate the down payment is added after the loan is sized, so each extra dollar down lifts the price by one dollar: raising the fictional down payment from $40,000 to $80,000 lifts the price from $482,990 to $522,990, a difference of $40,000. With the 1.2% tax rate in place the same change lifts the price only from $417,014 to $451,550, a difference of $34,536. The larger price carries a larger tax reserve, that reserve has to fit inside the same budget, and so part of the extra down payment goes to covering tax on the higher price rather than to the price itself.

Rate and term: the payment factor

Income and debts fix the budget; the rate and term fix how much loan the budget buys. The link is the payment factor from the amortized-loan formula, under this engine's convention of monthly compounding at the annual rate divided by twelve with a payment at the end of each month — the standard amortized-loan (PMT) convention the methodology page describes as the one behind US mortgages and most consumer loans. A higher rate or a shorter term raises the factor, so the same budget divides into a smaller loan. The tables hold the fictional income, debts and down payment constant and vary one input at a time; the rates are illustrative, not quotes.

Varying the rate — fictional 30-year term, $2,800 budget, $40,000 down:

Varying the term — fictional 6.5% rate, same budget and down payment:

Read the tables as a statement about the factor, not about markets: the budget would be identical in every row, which is why it is not a column. The formula also covers the limiting case. At a 0% rate there is no interest term, the factor is one divided by the number of monthly payments, and the loan is the budget multiplied by that number — $1,008,000 on the base inputs, handled by the same formula with no special case.

What the price does not reserve for

The affordability function accepts three optional cost inputs: an annual property tax rate, an annual insurance amount and a monthly HOA figure. Tax enters the closed-form equation because it scales with the price. Insurance and HOA do not, so the engine subtracts them from the budget before the loan is sized. The form on this page exposes the tax rate only, so the estimate here treats insurance and HOA as zero. For scale, a fictional $1,800 a year of insurance passed to the engine leaves the budget at $2,800.00 but reduces the principal-and-interest line to $2,650.00 — a difference of $150.00 a month, one twelfth of the annual amount — and lowers the price to $459,259.

There is no mortgage-insurance input to this function at all, so nothing in the price allows for PMI; the Mortgage Calculator is where a PMI rate is entered against a chosen price. Likewise the engine knows nothing about utilities, maintenance, savings or any other outgoing, because none of them is part of the guideline arithmetic. The methodology page's limitations apply in full: the calculators model fixed-rate, fully amortizing loans and "do not model adjustable-rate mortgages, interest-only periods, balloon payments, or negative amortization"; "property tax, insurance, PMI, and HOA are estimates from the rates and amounts you enter"; and "affordability reflects general lender guidelines, not an underwriting decision. Actual approval depends on credit, employment history, the loan program, and lender-specific overlays."

A ceiling, not a target

The number the engine returns is the top of the guideline on the inputs you gave it — computed deliberately as a maximum, so that you know where the line is. Nothing in the calculation says that spending up to it is appropriate, and the engine has no information with which to say so. The result answers one precise question — what price fits inside these ratios at this rate and term — not the different question of what to spend.

Reading the result box

The result box shows five lines, all taken directly from the engine's output: the maximum home price; the maximum loan amount, which is the price minus the down payment; the maximum monthly housing budget, which is the binding ceiling; the principal and interest at that price, which is the loan times the payment factor; and the ceiling that limited it. The price and loan are rounded to the whole dollar and the monthly figures to the cent; internally nothing is rounded, so recombining the on-screen figures by hand can disagree with the engine by a few cents. As the methodology page puts it, "the difference is presentational, not an error."

Blank optional fields are read as zero: no debts, no down payment, no property tax. Income and rate are required, and the box returns to its placeholder while either is empty. An entry that is not a number is rejected at the field with a message; a negative amount or a value beyond the supported range is refused by the engine's own validation, and its message is shown in the result box — in every case before any arithmetic runs. Two input combinations pass validation but still cannot produce a price, and the engine says so in words rather than returning a number: a fictional $60,000 income with $2,000 of monthly debts produces "Existing debts leave no room in the budget for a housing payment.", and insurance or HOA figures larger than the budget produce "Insurance and HOA costs exceed the affordable housing budget."

Common misreadings

• Entering take-home pay. The field asks for gross annual income because the guideline ratios are shares of gross income. A net figure shrinks both ceilings and understates the price relative to the guideline.
• Entering annual debts, or balances. The debts field is the sum of monthly payments. An annual total is subtracted from the monthly back-end ceiling twelve times over; a balance is not a payment at all.
• Reading the tax effect as a payment line. A tax rate does not add a line to the result; it lowers the price. The budget stays the same, and the tax reserve is the gap between the budget and the principal-and-interest line.
• Expecting the down payment to add dollar-for-dollar. It does only when no tax rate is entered; with tax the lift is smaller, as the worked figures above show.
• Treating the maximum as a recommendation. It is the guideline ceiling on your inputs and nothing more.
• Assuming PMI is inside the number. It is not; the affordability function has no PMI input.

Once you have a candidate price, the Mortgage Calculator prices the full monthly payment at that figure with tax, insurance, PMI and HOA, and the Debt-to-Income Calculator reports the front-end and back-end ratios from a housing payment you specify. For the derivation in full, read the guide How affordability is estimated.

Frequently asked questions

Not financial advice: a general educational estimate only. Real approval depends on credit, employment, the specific loan program, and lender overlays — get a pre-approval from a licensed lender before house-hunting. Values are processed locally in your browser and never transmitted. See the methodology page.